Spherical_Neutron_Transport_Report.ipynb

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    "**Engy-5050** Reactor Physics, UMass Lowell, Chem. Eng. Nuclear Program Spring 2022; Prof. V. F. de Almeida\n",
    "\n",
    "# 1-D Point Source Neutron Transport\n",
    "$  \n",
    "  \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
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    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
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    "  \\newcommand{\\uvar}{\\boldsymbol{u}}\n",
    "  \\newcommand{\\fvar}{\\boldsymbol{f}}\n",
    "  \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "  \\newcommand{\\Power}{\\mathcal{P}}\n",
    "$"
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   "source": [
    "**Student(s):** Anthony Bowers, Andrew Hamel <br>\n",
    "**Course:** Engy-5050 Reactor Physics  <br>\n",
    "\n",
    "\n",
    "UMass Lowell, Dept. of Chemical Engineering, Nuclear Energy Program \n",
    "<br>\n",
    "**7March2022**"
   ]
  },
  {
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   "source": [
    "---\n",
    "## Table of Contents<a id=\"toc\"></a>\n",
    "* [Introduction](#intro)\n",
    "* [Problem Statement](#problem)\n",
    "* [Objectives](#obj)\n",
    "* [FEM Approach](#app)\n",
    " + [Analytical Solution](#analyticalsol)\n",
    " + [Weak Form of Problem Statement](#weakform)\n",
    " + [MOOSE Kernels](#kernels)\n",
    " + [Setup](#setup)\n",
    "    - [One-Group Energy](#onegroupenergy)\n",
    "    - [Two-Group Energy](#twogroupenergy)\n",
    "* [FDM Approach](#appFDM)\n",
    " + [Discretization](#setupFDM)\n",
    "    - [One-Group Energy](#onegroupenergyFDM)\n",
    "    - [Two-Group Energy](#twogroupenergyFDM)\n",
    "    - [Issue occurs when coupling flux at boundary to albedo condition](#issue)\n",
    "* [Results and Analysis](#ranalysis)\n",
    "* [Conclusions](#conclusions)\n",
    "* [References](#refs)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Introduction](#toc)<a id=\"intro\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Problem Statement](#toc)<a id=\"problem\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This investigation looks to determine how Finite Element Method (FEM) computation of the neutron diffusion equation compare to that of the Finite Difference Method (FDM) computation given standard assumptions about the definition of the diffusion coefficient in homogenous mediums far from and close to voids. Defining diffusion coefficients for neutron transport is an active field of research and includes approximations such as isotropic scattering, linear in angle, nonlocal weighting of nearby average transport properties, Monte Carlo study and experiment.\n",
    "\n",
    "\n",
    "\n",
    "### [Strong Form of Problem Statement BARE REACTOR](#toc)<a id=\"dbcstrong\"></a>\n",
    "\n",
    " Find $\\Phi_1:[a,b]\\subset \\mathbb{R} \\rightarrow\\mathbb{R}$ and $\\Phi_2:[a,b]\\subset\\mathbb{R}\\rightarrow\\mathbb{R}$ for $D_1 > 0$ and $D_2 > 0$ such that:\n",
    "\n",
    "\\begin{align*}\n",
    " 0= -div_{x}(-D_1\\, \\nabla_{x}\\Phi_1)- \\Sigma_{1,a} \\Phi_1(x)+ S(\\Phi_1, \\Phi_2) + \\chi(E_{1}) \\frac{v}{k}\\Sigma_{1,f}\\Phi_1(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    "-D_1 \\nabla \\Phi_1(a) &= 0, \\\\\n",
    " -D_1 \\nabla \\Phi_1(b) &= ( \\frac{1}{2} \\Phi_1).\n",
    "\\end{align*}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{align*}\n",
    "  0= -div_{x}(-D_2\\,\\nabla_{x}\\Phi_2) -\\Sigma_{2,a} \\Phi_2(x) - S(\\Phi_1, \\Phi_2) + \\chi(E_{2}) \\frac{v}{k}\\Sigma_{2,f}\\Phi_2(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    " -D_2 \\nabla \\Phi_2(a) &= 0, \\\\\n",
    " -D_2 \\nabla \\Phi_2(b) &= ( \\frac{1}{2} \\Phi_2).\n",
    "\\end{align*}\n",
    "\n",
    "The *diffusion flux* associated to the quantity $\\Phi_i, \\, \\ i=1,2$ is denoted $q_i := -D_i\\,\\Phi_i'$, and it is often of interest as a derived quantity of the neutron spatial transport theory."
   ]
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    "\n",
    "### [Strong Form of Problem Statement PARTIALLY REFLECTIVE REACTOR](#toc)<a id=\"dbcstrong\"></a>\n",
    "\n",
    " Find $\\Phi_1:[a,b]\\subset \\mathbb{R} \\rightarrow\\mathbb{R}$ and $\\Phi_2:[a,b]\\subset\\mathbb{R}\\rightarrow\\mathbb{R}$ for $D_1 > 0$ and $D_2 > 0$ such that:\n",
    "\n",
    "\\begin{align*}\n",
    " 0= -div_{x}(-D_1\\, \\nabla_{x}\\Phi_1)- \\Sigma_{1,a} \\Phi_1(x)+ S(\\Phi_1, \\Phi_2) + \\chi(E_{1}) \\frac{v}{k}\\Sigma_{1,f}\\Phi_1(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    "-D_1 \\nabla \\Phi_1(a) &= 0, \\\\\n",
    " -D_1 \\nabla \\Phi_1(b) &= \\frac{1}{2} (\\frac{1-\\alpha}{1+\\alpha}) \\Phi_1.\n",
    "\\end{align*}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{align*}\n",
    "  0= -div_{x}(-D_2\\,\\nabla_{x}\\Phi_2) -\\Sigma_{2,a} \\Phi_2(x) - S(\\Phi_1, \\Phi_2) + \\chi(E_{2}) \\frac{v}{k}\\Sigma_{2,f}\\Phi_2(x)  \\quad \\forall \\quad x\\in [a,b], \\\\\n",
    " -D_2 \\nabla \\Phi_2(a) &= 0, \\\\\n",
    " -D_2 \\nabla \\Phi_2(b) &= \\frac{1}{2} (\\frac{1-\\alpha}{1+\\alpha}) \\Phi_2.\n",
    "\\end{align*}\n",
    "\n",
    "The *diffusion flux* associated to the quantity $\\Phi_i, \\, \\ i=1,2$ is denoted $q_i := -D_i\\,\\Phi_i'$, and it is often of interest as a derived quantity of the neutron spatial transport theory."
   ]
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   "source": [
    "## [Source Coupling](#toc)<a id=\"sourcecoupling\"></a>\n",
    "\n",
    "Consider the following source coupling:\n",
    "\n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = S_1 - h_1\\,\\bigl(\\Phi_1-\\Phi_1^*\\bigr) - \\Bigl( S_2 - h_2\\, \\bigl(\\Phi_2 - \\Phi_2^*\\bigr) \\Bigr)\n",
    "\\end{align*}\n",
    "\n",
    "where $S_i$ is a fixed source (sink) for each Neutron group, $h_i$ is a transfer coefficient, and $\\Phi_i^*$ is a saturation value.\n",
    "\n",
    "Moreover, for this particular problem:\n",
    "\n",
    "\\begin{align*}\n",
    " S_1=0 \\\\\n",
    " S_2=0 \\\\\n",
    " \\Phi_2=0 \\\\\n",
    " \\Phi_1^*=0 \\\\\n",
    " \\Phi_2^*=0 \\\\\n",
    " h_1=\\Sigma_{s,1 \\rightarrow 2} \\\\\n",
    " h_2=0\n",
    "\\end{align*}\n",
    "\n",
    "Enstating these values reduces the source coupling to \n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1 \n",
    "\\end{align*}\n",
    "\n",
    "Where the conceptual reads this means that group one neutrons looses neutrons due to the downscattering into group two. Conversely this means group two has a source term. Moreover, if upscattering was to be taken into account $h_2 = \\Sigma_{s,2 \\rightarrow 1}$ and $\\Phi_2$ would exist for a combined source term of, \n",
    "\n",
    "\\begin{align*}\n",
    " S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1 + \\Sigma_{s,2 \\rightarrow 1} \\Phi_2\n",
    "\\end{align*}"
   ]
  },
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   "source": [
    "## [FEM Approach](#toc)<a id=\"app\"></a>"
   ]
  },
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    "### [Weak Form of Problem Statement](#toc)<a id=\"weakform\"></a> \n",
    "\n",
    "The Galerkin weak formulation of the strong form is as follows. Find $\\Phi_1 \\in H^1\\!\\bigl([a,b]\\bigr)$ and $\\Phi_2 \\in H^1\\!\\bigl([a,b]\\bigr)$\n",
    "so that \n",
    "\n",
    "\\begin{align*}\n",
    " \\int\\limits_a^b \\Sigma_{1,a}  \\Phi_1(x)\\, w(x)\\,dx + \\int\\limits_a^b D\\, \\Phi_1'(x)\\,w'(x)\\,dx - \\int\\limits_a^b S(\\Phi_1, \\Phi_2)\\,w(x)\\,dx &= 0 \\quad \\forall \\quad w \\in H^1_0\\!\\bigl([a,b]\\bigr), \\text{and}\n",
    " \\\\\n",
    "  \\int\\limits_a^b \\Sigma_{2,a}  \\Phi_2(x)\\, w(x)\\,dx + \\int\\limits_a^b D\\, \\Phi_2'(x)\\,w'(x)\\,dx + \\int\\limits_a^b S(\\Phi_1, \\Phi_2)\\,w(x)\\,dx &= 0 \\quad \\forall \\quad w \\in H^1_0\\!\\bigl([a,b]\\bigr),\n",
    "\\end{align*}\n",
    "\n",
    "where $H^1\\!\\bigl([a,b]\\bigr) := \\bigl\\{ \\Phi:[a,b]\\subset\\mathbb{R}\\rightarrow\\mathbb{R} \\mid \\int_a^b \\Phi'^2\\,dx < \\infty\\bigr\\}$ and $H^1_0\\!\\bigl([a,b]\\bigr) := \\bigl\\{ w \\mid w \\in H^1(a,b), w(a) = 0, w(b) =0 \\bigr\\}$. Both function sets as just defined are Hilbert spaces. The function $w$ is called a test function. Because $w$, $\\Phi_1$, $\\Phi_2$ are sought in very similar sets of functions, this weak form is called Galerkin's weak form.\n",
    "\n",
    "The new form of the source term is the key term to be computed here. Since the MOOSE framework performs the integration, and provides the implementation of the test function, we need to provide the integrand of the integral, that is, the kernel. Therefore the kernel needed is an expansion of what has been covered so far in the course:\n",
    "\n",
    " 1. $\\pm S(\\Phi_1, \\Phi_2)\\,w(x)$.\n",
    " \n",
    "The kernels are to be evaluated at quadrature points provided by the MOOSE framework.\n",
    "1. Multiply NDE by a test function $\\phi$.\n",
    "2. Integrate over spatial and angular domain.\n",
    "3. Use divergence theorem to set the boundary condition across the domain surface.\n",
    "\n",
    "The weak form becomes:\n",
    "\n",
    "\\begin{align*}\n",
    "    ( \\nabla \\phi, D_1 \\nabla \\Phi_1  )\\ - < \\phi, D_1 \\nabla \\Phi_1 \\cdot \\bar{n_b} > +\\ (\\phi , \\lambda \\Phi_1) = 0 \\ \\ \\ (G1)\\\\\\\\\n",
    " \\lambda = \\chi(E_{1}) \\frac{v}{k}\\Sigma_{1,f} - S(\\Phi_1, \\Phi_2) -\\Sigma_{a,1} ;\\\\ S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1  \\\\ \\\\\n",
    "      ( \\nabla \\phi, D_2 \\nabla \\Phi_2  )\\ - < \\phi, D_2 \\nabla \\Phi_2 \\cdot \\bar{n_b} > +\\ (\\phi , \\lambda \\Phi_2)  (\\phi,S(\\Phi_1, \\Phi_2)) = 0 \\ \\ \\ (G2)\\\\\\\\\n",
    "      \\lambda =\\chi(E_{2}) \\frac{v}{k}\\Sigma_{2,f} -\\Sigma_{a,2}\\\\\n",
    "      S(\\Phi_1, \\Phi_2) = -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1 \\\\\n",
    "\\end{align*}\n",
    "\n",
    "#### Neumann B.C Weak Form:\n",
    "This weak form contains the volume and surface integral as written with parenthesis and brackets respectively. \n",
    "\n",
    "Then boundary conition at the center, $a$, is implemented and descritized as such: \n",
    "\\begin{align*}\n",
    "\\\\\n",
    " -D_1\\nabla \\Phi_1(a) &= 0 \\\\\n",
    "  -D_2 \\nabla \\Phi_2(a) &= 0 \\\\\\\\\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "     <\\phi ,-D_1 \\nabla \\Phi_1(b) \\cdot \\bar{n_b}> =0 \\\\\n",
    "     <\\phi,-D_2 \\nabla \\Phi_2(b) \\cdot \\bar{n_b}> = 0\n",
    "\\end{align*}\n",
    "#### Vacuum B.C  Weak Form:\n",
    "Then the boundary conditions for the partial currents at the surface, $b$, given as $\\Gamma^{\\pm}$ must be solved for:\n",
    "\n",
    "\\begin{align*}\n",
    "    J_n^{+} = J^{out}({R_S}) =  J^{out}({b}) = J^{+}\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "    J_n^{-} = J^{in}({R_S}) = 0\n",
    "\\end{align*}\n",
    "\n",
    "Here we will use the Robin Vacuum boundary condition, at position $b$, such that the reflectivity at the boundary is 0 as:\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    "    J^{\\pm}_{E,n} = \\frac{1}{4} \\Phi \\pm \\frac{1}{2} D \\nabla \\Phi \\cdot \\bar{n_b} \\\\\n",
    "   J^{-}_{E,n} = 0 = \\frac{\\Phi}{4} - \\frac{J_{E,n}}{2}  = \\frac{\\Phi}{4} - \\frac{-D \\nabla \\Phi}{2}\\\\\n",
    "    \\frac{\\Phi}{4} = \\frac{-D \\nabla \\Phi}{2}\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "Solving for the weak form boundary condition and multiplying our test function $\\phi$:\n",
    "\n",
    "\\begin{align*}\n",
    "     - <\\phi,D_1 \\nabla \\Phi_1(b) \\cdot \\bar{n_b}> = \\phi( \\frac{1}{2}  \\Phi_1) \\\\\n",
    "    - <\\phi,D_2 \\nabla \\Phi_2(b) \\cdot \\bar{n_b}> = \\phi( \\frac{1}{2}  \\Phi_2)\n",
    "\\end{align*}\n",
    "#### Albedo B.C (Partially Reflective)  Weak Form:\n",
    "\n",
    "Then the boundary conditions for the partial currents at the surface, $b$, given as $\\Gamma^{\\pm}$ must be solved for:\n",
    "\n",
    "\\begin{align*}\n",
    "  \\frac{ J^{+}_{E,n}}{J^{-}_{E,n}} = \\alpha = \\frac{ J^{+}_{E,n}}{J^{-}_{E,n}-J_{E,n}}\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "  \\frac{ J^{+}_{E,n}}{J^{-}_{E,n}-J_{E,n}} = \\frac{ 1}{1-\\frac{ J_{E,n}}{J^{+}_{E,n}}} = \\alpha\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    " 1-\\alpha^{-1}= \\frac{ J_{E,n}}{J^{+}_{E,n}}\n",
    "\\end{align*}\n",
    "\n",
    "Here we will use the Albedo  boundary condition, at position $b$ as:\n",
    "\n",
    "\\begin{align*}\n",
    "   J^{\\pm}_{E,n}= \\frac{1}{4} \\Phi + \\frac{1}{2} D \\nabla \\Phi \\cdot \\bar{n_b} \\\\\n",
    "     J^{+}_{E,n}= \\frac{\\Phi}{4} + \\frac{J_{E,n}}{2} = \\frac{\\Phi}{4} + \\frac{D \\nabla \\Phi}{2}\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "J_{E,n}= ( 1-\\alpha^{-1})(\\frac{\\Phi}{4} + \\frac{J_{E,n}}{2})\\\\\n",
    "\\frac{J_{E,n}}{2}= (\\frac{1-\\alpha}{1+\\alpha})(\\frac{\\Phi}{4})\\\\\n",
    "(\\frac{-D \\nabla \\Phi}{2})= (\\frac{1-\\alpha}{1+\\alpha})(\\frac{\\Phi}{4})\n",
    "\\end{align*}\n",
    "\n",
    "Solving for the weak form boundary condition and multiplying our test function $\\phi$:\n",
    "\n",
    "\\begin{align*}\n",
    "    - <\\phi,D_1 \\nabla \\Phi_1(b) \\cdot \\bar{n_b}> = \\phi( \\frac{1}{2} (\\frac{1-\\alpha}{1+\\alpha}) \\Phi_1) \\\\\n",
    "    -<\\phi,D_2 \\nabla \\Phi_2(b) \\cdot \\bar{n_b})>= \\phi( \\frac{1}{2} (\\frac{1-\\alpha}{1+\\alpha}) \\Phi_2)\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "#### 2 Group NDE  Weak Form:\n",
    "\n",
    "Assuming no upscattering from group 2 to group 1:\n",
    "\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_1 \\nabla \\Phi_1(r)  + \\Sigma_{a,1} \\Phi_1(r) + \\chi(E_{1}) \\frac{v}{k}\\Sigma_{1,f}\\Phi_1(x)=  -\\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\ \n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "    -\\nabla \\cdot D_2 \\nabla \\Phi_2(r)  + \\Sigma_{a,2} \\Phi_2(r) + \\chi(E_{2}) \\frac{v}{k}\\Sigma_{2,f}\\Phi_2(x)=  \\Sigma_{s,1 \\rightarrow 2} \\Phi_1(r) \\ \\ \\  \n",
    "\\end{align*}\n"
   ]
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   "source": [
    "![Image](Pic.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "from numpy import linalg as LA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diffusion Coefficent for group-1 [cm] =  1.83180150273944\n",
      "Diffusion Coefficent for group-2 [cm]= 1.2037552732287748\n",
      "Downscattering Macroscopic cross section [cm^-1]= 0.03560287029288703\n",
      "Macroscopic cross section for Fission (group-1) [cm^-1]= 0.07713955230125523\n",
      "Macroscopic cross section for Fission (group-2) [cm^-1]= 0.07041456569037657\n",
      "Macroscopic cross section for Absorption (group-1) [cm^-1]= 0.003955874476987448\n",
      "Macroscopic cross section for Absorption (group-2) [cm^-1]= 0.011867623430962343\n"
     ]
    }
   ],
   "source": [
    "# Parameters of fissioning Pu-239\n",
    "#Mircoscopic cross section for transport, fission, and absorption\n",
    "eta_tr=[4.6e-24, 7.0e-24]\n",
    "eta_f=[1.95e-24, 1.78e-24]\n",
    "eta_a=[.1e-24, .3e-24]\n",
    "eta_12=0.9e-24\n",
    "\n",
    "#Parameters for atomic density\n",
    "Na=6.022e23\n",
    "molar_mass=239\n",
    "rho=15.7\n",
    "N_density= Na*rho/molar_mass\n",
    "\n",
    "#Macroscopic cross section for transport, fission, and absorption\n",
    "sigma_tr=[N_density*eta_tr[0], N_density*eta_tr[1]] \n",
    "sigma_f=[N_density*eta_f[0], N_density*eta_f[1]]\n",
    "sigma_a=[N_density*eta_a[0], N_density*eta_a[1]]\n",
    "#Macroscopic cross section for group-1 downscattering into group-2\n",
    "sigma_12=N_density*eta_12\n",
    "\n",
    "#Fission emission\n",
    "v=[3.1 ,2.93]\n",
    "\n",
    "#Fission Spectrum\n",
    "chi=[.575, .425]\n",
    "\n",
    "#Diffusion Coefficent\n",
    "D1=1/(3*sigma_tr[0])\n",
    "D2=1/(3*sigma_tr[1])\n",
    "\n",
    "\n",
    "print('Diffusion Coefficent for group-1 [cm] = ',D1)\n",
    "print('Diffusion Coefficent for group-2 [cm]=',D2)\n",
    "print('Downscattering Macroscopic cross section [cm^-1]=',sigma_12)\n",
    "print('Macroscopic cross section for Fission (group-1) [cm^-1]=',sigma_f [0])\n",
    "print('Macroscopic cross section for Fission (group-2) [cm^-1]=',sigma_f [1])\n",
    "\n",
    "print('Macroscopic cross section for Absorption (group-1) [cm^-1]=',sigma_a[0])\n",
    "print('Macroscopic cross section for Absorption (group-2) [cm^-1]=',sigma_a[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [One-Group Energy](#toc)<a id=\"onegroupenergy\"></a>"
   ]
  },
  {
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   "execution_count": 3,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Framework Information:\n",
      "MOOSE Version:           git commit b98ea2c450 on 2021-09-23\n",
      "LibMesh Version:         \n",
      "PETSc Version:           3.15.1\n",
      "SLEPc Version:           3.15.1\n",
      "Current Time:            Mon May  9 11:31:37 2022\n",
      "Executable Timestamp:    Mon May  9 11:31:32 2022\n",
      "\n",
      "Parallelism:\n",
      "  Num Processors:          1\n",
      "  Num Threads:             1\n",
      "\n",
      "Mesh: \n",
      "  Parallel Type:           replicated\n",
      "  Mesh Dimension:          1\n",
      "  Spatial Dimension:       1\n",
      "  Nodes:                   61\n",
      "  Elems:                   30\n",
      "  Num Subdomains:          1\n",
      "\n",
      "Nonlinear System:\n",
      "  Num DOFs:                61\n",
      "  Num Local DOFs:          61\n",
      "  Variables:               \"u_v\" \n",
      "  Finite Element Types:    \"LAGRANGE\" \n",
      "  Approximation Orders:    \"SECOND\" \n",
      "\n",
      "Execution Information:\n",
      "  Executioner:             Eigenvalue\n",
      "  Solver Mode:             Preconditioned JFNK\n",
      "\n",
      "\n",
      "Postprocessor Values:\n",
      "+----------------+----------------+\n",
      "| time           | u-normalized   |\n",
      "+----------------+----------------+\n",
      "|   0.000000e+00 |   1.000000e+00 |\n",
      "+----------------+----------------+\n",
      "\n",
      "\n",
      " -------------------------------\n",
      " Free power iteration starts ...\n",
      " -------------------------------\n",
      "\n",
      " 0 Nonlinear |R| = \u001b[32m2.682076e+00\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m2.682076e+00\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m2.323133e+00\u001b[39m\n",
      "      2 Linear |R| = \u001b[32m2.077664e+00\u001b[39m\n",
      "      3 Linear |R| = \u001b[33m2.041642e+00\u001b[39m\n",
      "      4 Linear |R| = \u001b[33m2.021866e+00\u001b[39m\n",
      "      5 Linear |R| = \u001b[33m1.985666e+00\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m1.916475e+00\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m1.885892e+00\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m1.852115e+00\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m1.816808e+00\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m1.751441e+00\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m1.708470e+00\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m1.657649e+00\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m1.608147e+00\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m1.536374e+00\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m1.472922e+00\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m1.405155e+00\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m1.336485e+00\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m1.258121e+00\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m1.177441e+00\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m1.096566e+00\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m1.014574e+00\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m9.307801e-01\u001b[39m\n",
      "     23 Linear |R| = \u001b[32m8.431418e-01\u001b[39m\n",
      "     24 Linear |R| = \u001b[32m7.560336e-01\u001b[39m\n",
      "     25 Linear |R| = \u001b[32m6.701774e-01\u001b[39m\n",
      "     26 Linear |R| = \u001b[32m5.833340e-01\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m4.929672e-01\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m3.980289e-01\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m2.992292e-01\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m1.924134e-01\u001b[39m\n",
      "     31 Linear |R| = \u001b[32m1.761641e-01\u001b[39m\n",
      "     32 Linear |R| = \u001b[33m1.715703e-01\u001b[39m\n",
      "     33 Linear |R| = \u001b[33m1.682094e-01\u001b[39m\n",
      "     34 Linear |R| = \u001b[33m1.646552e-01\u001b[39m\n",
      "     35 Linear |R| = \u001b[33m1.590895e-01\u001b[39m\n",
      "     36 Linear |R| = \u001b[33m1.538285e-01\u001b[39m\n",
      "     37 Linear |R| = \u001b[33m1.499572e-01\u001b[39m\n",
      "     38 Linear |R| = \u001b[33m1.470795e-01\u001b[39m\n",
      "     39 Linear |R| = \u001b[33m1.440679e-01\u001b[39m\n",
      "     40 Linear |R| = \u001b[33m1.408821e-01\u001b[39m\n",
      "     41 Linear |R| = \u001b[33m1.373613e-01\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m1.349167e-01\u001b[39m\n",
      "     43 Linear |R| = \u001b[33m1.324672e-01\u001b[39m\n",
      "     44 Linear |R| = \u001b[33m1.304745e-01\u001b[39m\n",
      "     45 Linear |R| = \u001b[33m1.280663e-01\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m1.258849e-01\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m1.239631e-01\u001b[39m\n",
      "     48 Linear |R| = \u001b[33m1.222586e-01\u001b[39m\n",
      "     49 Linear |R| = \u001b[33m1.207850e-01\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m1.191367e-01\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m1.174878e-01\u001b[39m\n",
      "     52 Linear |R| = \u001b[33m1.162108e-01\u001b[39m\n",
      "     53 Linear |R| = \u001b[33m1.150738e-01\u001b[39m\n",
      "     54 Linear |R| = \u001b[33m1.139875e-01\u001b[39m\n",
      "     55 Linear |R| = \u001b[33m1.129754e-01\u001b[39m\n",
      "     56 Linear |R| = \u001b[33m1.116672e-01\u001b[39m\n",
      "     57 Linear |R| = \u001b[33m1.111136e-01\u001b[39m\n",
      "     58 Linear |R| = \u001b[33m1.101920e-01\u001b[39m\n",
      "     59 Linear |R| = \u001b[33m1.085980e-01\u001b[39m\n",
      "     60 Linear |R| = \u001b[33m1.083254e-01\u001b[39m\n",
      "     61 Linear |R| = \u001b[33m1.063674e-01\u001b[39m\n",
      "     62 Linear |R| = \u001b[33m1.061063e-01\u001b[39m\n",
      "     63 Linear |R| = \u001b[33m1.059616e-01\u001b[39m\n",
      "     64 Linear |R| = \u001b[33m1.059562e-01\u001b[39m\n",
      "     65 Linear |R| = \u001b[33m1.058187e-01\u001b[39m\n",
      "     66 Linear |R| = \u001b[33m1.056689e-01\u001b[39m\n",
      "     67 Linear |R| = \u001b[33m1.056660e-01\u001b[39m\n",
      "     68 Linear |R| = \u001b[33m1.056652e-01\u001b[39m\n",
      "     69 Linear |R| = \u001b[33m1.056355e-01\u001b[39m\n",
      "     70 Linear |R| = \u001b[33m1.055239e-01\u001b[39m\n",
      "     71 Linear |R| = \u001b[33m1.054539e-01\u001b[39m\n",
      "     72 Linear |R| = \u001b[33m1.054317e-01\u001b[39m\n",
      "     73 Linear |R| = \u001b[33m1.054031e-01\u001b[39m\n",
      "     74 Linear |R| = \u001b[33m1.053387e-01\u001b[39m\n",
      "     75 Linear |R| = \u001b[33m1.052579e-01\u001b[39m\n",
      "     76 Linear |R| = \u001b[33m1.051718e-01\u001b[39m\n",
      "     77 Linear |R| = \u001b[33m1.050602e-01\u001b[39m\n",
      "     78 Linear |R| = \u001b[33m1.049929e-01\u001b[39m\n",
      "     79 Linear |R| = \u001b[33m1.049334e-01\u001b[39m\n",
      "     80 Linear |R| = \u001b[33m1.048390e-01\u001b[39m\n",
      "     81 Linear |R| = \u001b[33m1.046149e-01\u001b[39m\n",
      "     82 Linear |R| = \u001b[33m1.043692e-01\u001b[39m\n",
      "     83 Linear |R| = \u001b[33m1.042972e-01\u001b[39m\n",
      "     84 Linear |R| = \u001b[33m1.042677e-01\u001b[39m\n",
      "     85 Linear |R| = \u001b[33m1.041807e-01\u001b[39m\n",
      "     86 Linear |R| = \u001b[33m1.025175e-01\u001b[39m\n",
      "     87 Linear |R| = \u001b[33m1.023826e-01\u001b[39m\n",
      "     88 Linear |R| = \u001b[33m1.023768e-01\u001b[39m\n",
      "     89 Linear |R| = \u001b[33m9.988319e-02\u001b[39m\n",
      "     90 Linear |R| = \u001b[32m8.199130e-02\u001b[39m\n",
      "     91 Linear |R| = \u001b[33m8.019087e-02\u001b[39m\n",
      "     92 Linear |R| = \u001b[33m7.838530e-02\u001b[39m\n",
      "     93 Linear |R| = \u001b[33m7.624661e-02\u001b[39m\n",
      "     94 Linear |R| = \u001b[33m7.617033e-02\u001b[39m\n",
      "     95 Linear |R| = \u001b[33m7.609606e-02\u001b[39m\n",
      "     96 Linear |R| = \u001b[33m7.592700e-02\u001b[39m\n",
      "     97 Linear |R| = \u001b[33m7.535516e-02\u001b[39m\n",
      "     98 Linear |R| = \u001b[33m7.507983e-02\u001b[39m\n",
      "     99 Linear |R| = \u001b[33m7.507593e-02\u001b[39m\n",
      "    100 Linear |R| = \u001b[33m7.507592e-02\u001b[39m\n",
      "    101 Linear |R| = \u001b[33m7.491150e-02\u001b[39m\n",
      "    102 Linear |R| = \u001b[33m7.447842e-02\u001b[39m\n",
      "    103 Linear |R| = \u001b[33m7.435903e-02\u001b[39m\n",
      "    104 Linear |R| = \u001b[33m7.435520e-02\u001b[39m\n",
      "    105 Linear |R| = \u001b[33m7.433400e-02\u001b[39m\n",
      "    106 Linear |R| = \u001b[33m7.413429e-02\u001b[39m\n",
      "    107 Linear |R| = \u001b[33m7.385163e-02\u001b[39m\n",
      "    108 Linear |R| = \u001b[33m7.383290e-02\u001b[39m\n",
      "    109 Linear |R| = \u001b[33m7.383229e-02\u001b[39m\n",
      "    110 Linear |R| = \u001b[33m7.375939e-02\u001b[39m\n",
      "    111 Linear |R| = \u001b[33m7.348728e-02\u001b[39m\n",
      "    112 Linear |R| = \u001b[33m7.333281e-02\u001b[39m\n",
      "    113 Linear |R| = \u001b[33m7.331749e-02\u001b[39m\n",
      "    114 Linear |R| = \u001b[33m7.317261e-02\u001b[39m\n",
      "    115 Linear |R| = \u001b[33m7.300841e-02\u001b[39m\n",
      "    116 Linear |R| = \u001b[33m7.294191e-02\u001b[39m\n",
      "    117 Linear |R| = \u001b[33m7.251755e-02\u001b[39m\n",
      "    118 Linear |R| = \u001b[33m7.248314e-02\u001b[39m\n",
      "    119 Linear |R| = \u001b[33m7.132206e-02\u001b[39m\n",
      "    120 Linear |R| = \u001b[33m7.099889e-02\u001b[39m\n",
      "    121 Linear |R| = \u001b[33m7.099198e-02\u001b[39m\n",
      "    122 Linear |R| = \u001b[33m7.097749e-02\u001b[39m\n",
      "    123 Linear |R| = \u001b[33m7.092326e-02\u001b[39m\n",
      "    124 Linear |R| = \u001b[33m7.072199e-02\u001b[39m\n",
      "    125 Linear |R| = \u001b[33m7.031088e-02\u001b[39m\n",
      "    126 Linear |R| = \u001b[33m6.998167e-02\u001b[39m\n",
      "    127 Linear |R| = \u001b[33m6.950958e-02\u001b[39m\n",
      "    128 Linear |R| = \u001b[33m6.901243e-02\u001b[39m\n",
      "    129 Linear |R| = \u001b[33m6.848347e-02\u001b[39m\n",
      "    130 Linear |R| = \u001b[33m6.795657e-02\u001b[39m\n",
      "    131 Linear |R| = \u001b[33m6.739678e-02\u001b[39m\n",
      "    132 Linear |R| = \u001b[33m6.678768e-02\u001b[39m\n",
      "    133 Linear |R| = \u001b[33m6.605995e-02\u001b[39m\n",
      "    134 Linear |R| = \u001b[33m6.532115e-02\u001b[39m\n",
      "    135 Linear |R| = \u001b[33m6.433452e-02\u001b[39m\n",
      "    136 Linear |R| = \u001b[33m6.327136e-02\u001b[39m\n",
      "    137 Linear |R| = \u001b[33m6.220685e-02\u001b[39m\n",
      "    138 Linear |R| = \u001b[33m6.077593e-02\u001b[39m\n",
      "    139 Linear |R| = \u001b[33m5.852766e-02\u001b[39m\n",
      "    140 Linear |R| = \u001b[32m5.414278e-02\u001b[39m\n",
      "    141 Linear |R| = \u001b[32m4.882676e-02\u001b[39m\n",
      "    142 Linear |R| = \u001b[32m4.412953e-02\u001b[39m\n",
      "    143 Linear |R| = \u001b[32m4.083809e-02\u001b[39m\n",
      "    144 Linear |R| = \u001b[32m3.873830e-02\u001b[39m\n",
      "    145 Linear |R| = \u001b[33m3.696365e-02\u001b[39m\n",
      "    146 Linear |R| = \u001b[33m3.519820e-02\u001b[39m\n",
      "    147 Linear |R| = \u001b[33m3.350728e-02\u001b[39m\n",
      "    148 Linear |R| = \u001b[32m2.907774e-02\u001b[39m\n",
      "    149 Linear |R| = \u001b[32m2.207812e-02\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m2.207778e-02\u001b[39m\n",
      " Iteration 1 eigenvalue = 0.3823135635\n",
      " 0 Nonlinear |R| = \u001b[32m8.620462e-02\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m8.620462e-02\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m8.523972e-02\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m8.518660e-02\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m7.644517e-02\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m6.892760e-02\u001b[39m\n",
      "      5 Linear |R| = \u001b[33m6.572355e-02\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m6.381741e-02\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m5.869039e-02\u001b[39m\n",
      "      8 Linear |R| = \u001b[32m5.451748e-02\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m5.282033e-02\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m5.173891e-02\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m5.030029e-02\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m4.952667e-02\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m4.942620e-02\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m4.939806e-02\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m4.928952e-02\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m4.923822e-02\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m4.923622e-02\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m4.922232e-02\u001b[39m\n",
      "     19 Linear |R| = \u001b[33m4.921313e-02\u001b[39m\n",
      "     20 Linear |R| = \u001b[33m4.919947e-02\u001b[39m\n",
      "     21 Linear |R| = \u001b[33m4.919892e-02\u001b[39m\n",
      "     22 Linear |R| = \u001b[33m4.911766e-02\u001b[39m\n",
      "     23 Linear |R| = \u001b[33m4.908627e-02\u001b[39m\n",
      "     24 Linear |R| = \u001b[33m4.907023e-02\u001b[39m\n",
      "     25 Linear |R| = \u001b[33m4.881965e-02\u001b[39m\n",
      "     26 Linear |R| = \u001b[33m4.727219e-02\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m4.202120e-02\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m2.945536e-02\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m1.979723e-02\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m1.543465e-02\u001b[39m\n",
      "     31 Linear |R| = \u001b[33m1.493020e-02\u001b[39m\n",
      "     32 Linear |R| = \u001b[33m1.442077e-02\u001b[39m\n",
      "     33 Linear |R| = \u001b[32m1.368978e-02\u001b[39m\n",
      "     34 Linear |R| = \u001b[32m1.286131e-02\u001b[39m\n",
      "     35 Linear |R| = \u001b[32m1.194804e-02\u001b[39m\n",
      "     36 Linear |R| = \u001b[32m1.110343e-02\u001b[39m\n",
      "     37 Linear |R| = \u001b[32m1.028623e-02\u001b[39m\n",
      "     38 Linear |R| = \u001b[32m9.595798e-03\u001b[39m\n",
      "     39 Linear |R| = \u001b[32m8.930909e-03\u001b[39m\n",
      "     40 Linear |R| = \u001b[32m8.368630e-03\u001b[39m\n",
      "     41 Linear |R| = \u001b[32m7.865960e-03\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m7.507383e-03\u001b[39m\n",
      "     43 Linear |R| = \u001b[32m7.123016e-03\u001b[39m\n",
      "     44 Linear |R| = \u001b[32m6.761235e-03\u001b[39m\n",
      "     45 Linear |R| = \u001b[32m6.392984e-03\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m6.145928e-03\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m5.859999e-03\u001b[39m\n",
      "     48 Linear |R| = \u001b[32m5.539182e-03\u001b[39m\n",
      "     49 Linear |R| = \u001b[32m5.182256e-03\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m4.946353e-03\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m4.717024e-03\u001b[39m\n",
      "     52 Linear |R| = \u001b[32m4.423897e-03\u001b[39m\n",
      "     53 Linear |R| = \u001b[32m4.040132e-03\u001b[39m\n",
      "     54 Linear |R| = \u001b[32m3.804333e-03\u001b[39m\n",
      "     55 Linear |R| = \u001b[32m3.463976e-03\u001b[39m\n",
      "     56 Linear |R| = \u001b[32m3.189459e-03\u001b[39m\n",
      "     57 Linear |R| = \u001b[32m2.118859e-03\u001b[39m\n",
      "     58 Linear |R| = \u001b[32m1.418307e-03\u001b[39m\n",
      "     59 Linear |R| = \u001b[32m1.060096e-03\u001b[39m\n",
      "     60 Linear |R| = \u001b[32m9.057339e-04\u001b[39m\n",
      "     61 Linear |R| = \u001b[33m9.057299e-04\u001b[39m\n",
      "     62 Linear |R| = \u001b[33m9.053791e-04\u001b[39m\n",
      "     63 Linear |R| = \u001b[33m9.047217e-04\u001b[39m\n",
      "     64 Linear |R| = \u001b[33m9.046991e-04\u001b[39m\n",
      "     65 Linear |R| = \u001b[33m9.046904e-04\u001b[39m\n",
      "     66 Linear |R| = \u001b[33m9.039030e-04\u001b[39m\n",
      "     67 Linear |R| = \u001b[33m9.034596e-04\u001b[39m\n",
      "     68 Linear |R| = \u001b[33m9.033593e-04\u001b[39m\n",
      "     69 Linear |R| = \u001b[33m9.031400e-04\u001b[39m\n",
      "     70 Linear |R| = \u001b[33m9.024766e-04\u001b[39m\n",
      "     71 Linear |R| = \u001b[33m9.016781e-04\u001b[39m\n",
      "     72 Linear |R| = \u001b[33m9.011412e-04\u001b[39m\n",
      "     73 Linear |R| = \u001b[33m9.006773e-04\u001b[39m\n",
      "     74 Linear |R| = \u001b[33m8.997286e-04\u001b[39m\n",
      "     75 Linear |R| = \u001b[33m8.986885e-04\u001b[39m\n",
      "     76 Linear |R| = \u001b[33m8.978260e-04\u001b[39m\n",
      "     77 Linear |R| = \u001b[33m8.973017e-04\u001b[39m\n",
      "     78 Linear |R| = \u001b[33m8.966756e-04\u001b[39m\n",
      "     79 Linear |R| = \u001b[33m8.955790e-04\u001b[39m\n",
      "     80 Linear |R| = \u001b[33m8.945694e-04\u001b[39m\n",
      "     81 Linear |R| = \u001b[33m8.937623e-04\u001b[39m\n",
      "     82 Linear |R| = \u001b[33m8.927515e-04\u001b[39m\n",
      "     83 Linear |R| = \u001b[33m8.910639e-04\u001b[39m\n",
      "     84 Linear |R| = \u001b[33m8.891142e-04\u001b[39m\n",
      "     85 Linear |R| = \u001b[33m8.864920e-04\u001b[39m\n",
      "     86 Linear |R| = \u001b[33m8.834854e-04\u001b[39m\n",
      "     87 Linear |R| = \u001b[33m8.781387e-04\u001b[39m\n",
      "     88 Linear |R| = \u001b[33m8.681543e-04\u001b[39m\n",
      "     89 Linear |R| = \u001b[33m8.536290e-04\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m8.536805e-04\u001b[39m\n",
      " Iteration 2 eigenvalue = 0.3639193661\n",
      " 0 Nonlinear |R| = \u001b[32m6.124398e-03\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m6.124398e-03\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m5.884399e-03\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m5.863123e-03\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m5.462091e-03\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m4.687672e-03\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m4.168751e-03\u001b[39m\n",
      "      6 Linear |R| = \u001b[32m3.809212e-03\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m3.421009e-03\u001b[39m\n",
      "      8 Linear |R| = \u001b[32m3.085952e-03\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m2.976591e-03\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m2.918361e-03\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m2.865386e-03\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m2.821428e-03\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m2.812379e-03\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m2.811685e-03\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m2.805203e-03\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m2.804246e-03\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m2.804033e-03\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m2.803543e-03\u001b[39m\n",
      "     19 Linear |R| = \u001b[33m2.801919e-03\u001b[39m\n",
      "     20 Linear |R| = \u001b[33m2.801524e-03\u001b[39m\n",
      "     21 Linear |R| = \u001b[33m2.799852e-03\u001b[39m\n",
      "     22 Linear |R| = \u001b[33m2.791477e-03\u001b[39m\n",
      "     23 Linear |R| = \u001b[33m2.748114e-03\u001b[39m\n",
      "     24 Linear |R| = \u001b[33m2.708669e-03\u001b[39m\n",
      "     25 Linear |R| = \u001b[33m2.658127e-03\u001b[39m\n",
      "     26 Linear |R| = \u001b[32m2.442593e-03\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m2.042473e-03\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m1.753682e-03\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m1.338020e-03\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m7.563896e-04\u001b[39m\n",
      "     31 Linear |R| = \u001b[32m7.030367e-04\u001b[39m\n",
      "     32 Linear |R| = \u001b[32m6.577595e-04\u001b[39m\n",
      "     33 Linear |R| = \u001b[32m6.052714e-04\u001b[39m\n",
      "     34 Linear |R| = \u001b[33m5.787849e-04\u001b[39m\n",
      "     35 Linear |R| = \u001b[33m5.602514e-04\u001b[39m\n",
      "     36 Linear |R| = \u001b[33m5.349034e-04\u001b[39m\n",
      "     37 Linear |R| = \u001b[32m5.017134e-04\u001b[39m\n",
      "     38 Linear |R| = \u001b[33m4.853478e-04\u001b[39m\n",
      "     39 Linear |R| = \u001b[33m4.783726e-04\u001b[39m\n",
      "     40 Linear |R| = \u001b[33m4.687933e-04\u001b[39m\n",
      "     41 Linear |R| = \u001b[33m4.506262e-04\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m4.392356e-04\u001b[39m\n",
      "     43 Linear |R| = \u001b[33m4.367587e-04\u001b[39m\n",
      "     44 Linear |R| = \u001b[33m4.343890e-04\u001b[39m\n",
      "     45 Linear |R| = \u001b[33m4.248115e-04\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m4.149587e-04\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m4.131562e-04\u001b[39m\n",
      "     48 Linear |R| = \u001b[33m4.128518e-04\u001b[39m\n",
      "     49 Linear |R| = \u001b[33m4.093287e-04\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m4.018725e-04\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m4.001141e-04\u001b[39m\n",
      "     52 Linear |R| = \u001b[33m4.000600e-04\u001b[39m\n",
      "     53 Linear |R| = \u001b[33m3.999472e-04\u001b[39m\n",
      "     54 Linear |R| = \u001b[33m3.966039e-04\u001b[39m\n",
      "     55 Linear |R| = \u001b[33m3.955511e-04\u001b[39m\n",
      "     56 Linear |R| = \u001b[33m3.955370e-04\u001b[39m\n",
      "     57 Linear |R| = \u001b[33m3.938102e-04\u001b[39m\n",
      "     58 Linear |R| = \u001b[33m3.878440e-04\u001b[39m\n",
      "     59 Linear |R| = \u001b[33m3.878438e-04\u001b[39m\n",
      "     60 Linear |R| = \u001b[33m3.860606e-04\u001b[39m\n",
      "     61 Linear |R| = \u001b[33m3.860378e-04\u001b[39m\n",
      "     62 Linear |R| = \u001b[33m3.860374e-04\u001b[39m\n",
      "     63 Linear |R| = \u001b[33m3.860354e-04\u001b[39m\n",
      "     64 Linear |R| = \u001b[33m3.860309e-04\u001b[39m\n",
      "     65 Linear |R| = \u001b[33m3.860302e-04\u001b[39m\n",
      "     66 Linear |R| = \u001b[33m3.860292e-04\u001b[39m\n",
      "     67 Linear |R| = \u001b[33m3.860292e-04\u001b[39m\n",
      "     68 Linear |R| = \u001b[33m3.860242e-04\u001b[39m\n",
      "     69 Linear |R| = \u001b[33m3.860154e-04\u001b[39m\n",
      "     70 Linear |R| = \u001b[33m3.860149e-04\u001b[39m\n",
      "     71 Linear |R| = \u001b[33m3.860149e-04\u001b[39m\n",
      "     72 Linear |R| = \u001b[33m3.860069e-04\u001b[39m\n",
      "     73 Linear |R| = \u001b[33m3.859772e-04\u001b[39m\n",
      "     74 Linear |R| = \u001b[33m3.859494e-04\u001b[39m\n",
      "     75 Linear |R| = \u001b[33m3.859447e-04\u001b[39m\n",
      "     76 Linear |R| = \u001b[33m3.859322e-04\u001b[39m\n",
      "     77 Linear |R| = \u001b[33m3.858617e-04\u001b[39m\n",
      "     78 Linear |R| = \u001b[33m3.857524e-04\u001b[39m\n",
      "     79 Linear |R| = \u001b[33m3.856672e-04\u001b[39m\n",
      "     80 Linear |R| = \u001b[33m3.856228e-04\u001b[39m\n",
      "     81 Linear |R| = \u001b[33m3.854715e-04\u001b[39m\n",
      "     82 Linear |R| = \u001b[33m3.851382e-04\u001b[39m\n",
      "     83 Linear |R| = \u001b[33m3.846816e-04\u001b[39m\n",
      "     84 Linear |R| = \u001b[33m3.842704e-04\u001b[39m\n",
      "     85 Linear |R| = \u001b[33m3.838211e-04\u001b[39m\n",
      "     86 Linear |R| = \u001b[33m3.820806e-04\u001b[39m\n",
      "     87 Linear |R| = \u001b[33m3.803708e-04\u001b[39m\n",
      "     88 Linear |R| = \u001b[33m3.766763e-04\u001b[39m\n",
      "     89 Linear |R| = \u001b[33m3.724194e-04\u001b[39m\n",
      "     90 Linear |R| = \u001b[33m3.595696e-04\u001b[39m\n",
      "     91 Linear |R| = \u001b[33m3.572175e-04\u001b[39m\n",
      "     92 Linear |R| = \u001b[33m3.550682e-04\u001b[39m\n",
      "     93 Linear |R| = \u001b[33m3.503871e-04\u001b[39m\n",
      "     94 Linear |R| = \u001b[33m3.501283e-04\u001b[39m\n",
      "     95 Linear |R| = \u001b[33m3.500550e-04\u001b[39m\n",
      "     96 Linear |R| = \u001b[33m3.493563e-04\u001b[39m\n",
      "     97 Linear |R| = \u001b[33m3.472072e-04\u001b[39m\n",
      "     98 Linear |R| = \u001b[33m3.463905e-04\u001b[39m\n",
      "     99 Linear |R| = \u001b[33m3.463403e-04\u001b[39m\n",
      "    100 Linear |R| = \u001b[33m3.463175e-04\u001b[39m\n",
      "    101 Linear |R| = \u001b[33m3.458358e-04\u001b[39m\n",
      "    102 Linear |R| = \u001b[33m3.449137e-04\u001b[39m\n",
      "    103 Linear |R| = \u001b[33m3.445033e-04\u001b[39m\n",
      "    104 Linear |R| = \u001b[33m3.445027e-04\u001b[39m\n",
      "    105 Linear |R| = \u001b[33m3.444540e-04\u001b[39m\n",
      "    106 Linear |R| = \u001b[33m3.444037e-04\u001b[39m\n",
      "    107 Linear |R| = \u001b[33m3.442182e-04\u001b[39m\n",
      "    108 Linear |R| = \u001b[33m3.441874e-04\u001b[39m\n",
      "    109 Linear |R| = \u001b[33m3.441659e-04\u001b[39m\n",
      "    110 Linear |R| = \u001b[33m3.441280e-04\u001b[39m\n",
      "    111 Linear |R| = \u001b[33m3.441261e-04\u001b[39m\n",
      "    112 Linear |R| = \u001b[33m3.441190e-04\u001b[39m\n",
      "    113 Linear |R| = \u001b[33m3.440983e-04\u001b[39m\n",
      "    114 Linear |R| = \u001b[33m3.440673e-04\u001b[39m\n",
      "    115 Linear |R| = \u001b[33m3.439088e-04\u001b[39m\n",
      "    116 Linear |R| = \u001b[33m3.438410e-04\u001b[39m\n",
      "    117 Linear |R| = \u001b[33m3.431862e-04\u001b[39m\n",
      "    118 Linear |R| = \u001b[33m3.413115e-04\u001b[39m\n",
      "    119 Linear |R| = \u001b[32m2.848603e-04\u001b[39m\n",
      "    120 Linear |R| = \u001b[32m9.899108e-05\u001b[39m\n",
      "    121 Linear |R| = \u001b[32m4.185359e-05\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m4.185132e-05\u001b[39m\n",
      " Iteration 3 eigenvalue = 0.3629458528\n",
      " 0 Nonlinear |R| = \u001b[32m5.190880e-04\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m5.190880e-04\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m5.005805e-04\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m4.981849e-04\u001b[39m\n",
      "      3 Linear |R| = \u001b[33m4.758812e-04\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m4.194764e-04\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m3.895997e-04\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m3.715502e-04\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m3.570630e-04\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m3.436405e-04\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m3.407986e-04\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m3.398736e-04\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m3.389109e-04\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m3.373938e-04\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m3.366183e-04\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m3.365662e-04\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m3.364932e-04\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m3.356022e-04\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m3.354120e-04\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m3.354119e-04\u001b[39m\n",
      "     19 Linear |R| = \u001b[33m3.342571e-04\u001b[39m\n",
      "     20 Linear |R| = \u001b[33m3.311194e-04\u001b[39m\n",
      "     21 Linear |R| = \u001b[33m3.256249e-04\u001b[39m\n",
      "     22 Linear |R| = \u001b[33m3.121627e-04\u001b[39m\n",
      "     23 Linear |R| = \u001b[32m2.854682e-04\u001b[39m\n",
      "     24 Linear |R| = \u001b[32m2.587372e-04\u001b[39m\n",
      "     25 Linear |R| = \u001b[32m2.088206e-04\u001b[39m\n",
      "     26 Linear |R| = \u001b[32m1.131158e-04\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m8.928901e-05\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m6.707974e-05\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m1.975748e-05\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m1.582096e-05\u001b[39m\n",
      "     31 Linear |R| = \u001b[32m1.475742e-05\u001b[39m\n",
      "     32 Linear |R| = \u001b[32m1.378478e-05\u001b[39m\n",
      "     33 Linear |R| = \u001b[32m1.263402e-05\u001b[39m\n",
      "     34 Linear |R| = \u001b[32m1.146172e-05\u001b[39m\n",
      "     35 Linear |R| = \u001b[32m1.049470e-05\u001b[39m\n",
      "     36 Linear |R| = \u001b[32m9.865286e-06\u001b[39m\n",
      "     37 Linear |R| = \u001b[32m9.350500e-06\u001b[39m\n",
      "     38 Linear |R| = \u001b[32m8.854387e-06\u001b[39m\n",
      "     39 Linear |R| = \u001b[32m8.271131e-06\u001b[39m\n",
      "     40 Linear |R| = \u001b[32m7.728310e-06\u001b[39m\n",
      "     41 Linear |R| = \u001b[32m7.321180e-06\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m7.044646e-06\u001b[39m\n",
      "     43 Linear |R| = \u001b[33m6.737612e-06\u001b[39m\n",
      "     44 Linear |R| = \u001b[33m6.432470e-06\u001b[39m\n",
      "     45 Linear |R| = \u001b[33m6.148110e-06\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m5.971599e-06\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m5.781687e-06\u001b[39m\n",
      "     48 Linear |R| = \u001b[33m5.549424e-06\u001b[39m\n",
      "     49 Linear |R| = \u001b[33m5.345274e-06\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m5.217218e-06\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m5.113887e-06\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m5.114085e-06\u001b[39m\n",
      " Iteration 4 eigenvalue = 0.3628256586\n",
      "\n",
      " -------------------------------------\n",
      " Nonlinear Newton iteration starts ...\n",
      " -------------------------------------\n",
      "\n",
      " 0 Nonlinear |R| = \u001b[32m4.891557e-05\u001b[39m\n",
      " Iteration 0 eigenvalue = 0.3628256586\n",
      "      0 Linear |R| = \u001b[32m4.891557e-05\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m4.735513e-05\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m4.727988e-05\u001b[39m\n",
      "      3 Linear |R| = \u001b[33m4.517236e-05\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m4.052097e-05\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m3.750857e-05\u001b[39m\n",
      "      6 Linear |R| = \u001b[32m3.544978e-05\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m3.338940e-05\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m3.183681e-05\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m3.149254e-05\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m3.136458e-05\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m3.124507e-05\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m3.110310e-05\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m3.109448e-05\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m3.109362e-05\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m3.109217e-05\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m3.106719e-05\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m3.106707e-05\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m3.104510e-05\u001b[39m\n",
      "     19 Linear |R| = \u001b[33m3.103621e-05\u001b[39m\n",
      "     20 Linear |R| = \u001b[33m3.090568e-05\u001b[39m\n",
      "     21 Linear |R| = \u001b[33m3.084367e-05\u001b[39m\n",
      "     22 Linear |R| = \u001b[33m3.077734e-05\u001b[39m\n",
      "     23 Linear |R| = \u001b[33m3.017517e-05\u001b[39m\n",
      "     24 Linear |R| = \u001b[33m2.907019e-05\u001b[39m\n",
      "     25 Linear |R| = \u001b[33m2.811132e-05\u001b[39m\n",
      "     26 Linear |R| = \u001b[32m2.505704e-05\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m2.076417e-05\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m1.675914e-05\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m7.407268e-06\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m5.743481e-06\u001b[39m\n",
      "     31 Linear |R| = \u001b[32m5.181386e-06\u001b[39m\n",
      "     32 Linear |R| = \u001b[32m4.493733e-06\u001b[39m\n",
      "     33 Linear |R| = \u001b[32m3.938840e-06\u001b[39m\n",
      "     34 Linear |R| = \u001b[32m3.658567e-06\u001b[39m\n",
      "     35 Linear |R| = \u001b[33m3.567565e-06\u001b[39m\n",
      "     36 Linear |R| = \u001b[32m3.353667e-06\u001b[39m\n",
      "     37 Linear |R| = \u001b[32m3.123937e-06\u001b[39m\n",
      "     38 Linear |R| = \u001b[32m2.944791e-06\u001b[39m\n",
      "     39 Linear |R| = \u001b[33m2.854426e-06\u001b[39m\n",
      "     40 Linear |R| = \u001b[33m2.775560e-06\u001b[39m\n",
      "     41 Linear |R| = \u001b[33m2.679813e-06\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m2.614925e-06\u001b[39m\n",
      "     43 Linear |R| = \u001b[33m2.579122e-06\u001b[39m\n",
      "     44 Linear |R| = \u001b[33m2.533378e-06\u001b[39m\n",
      "     45 Linear |R| = \u001b[33m2.468645e-06\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m2.430282e-06\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m2.417791e-06\u001b[39m\n",
      "     48 Linear |R| = \u001b[33m2.405981e-06\u001b[39m\n",
      "     49 Linear |R| = \u001b[33m2.383886e-06\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m2.368915e-06\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m2.364958e-06\u001b[39m\n",
      "     52 Linear |R| = \u001b[33m2.362789e-06\u001b[39m\n",
      "     53 Linear |R| = \u001b[33m2.360629e-06\u001b[39m\n",
      "     54 Linear |R| = \u001b[33m2.360267e-06\u001b[39m\n",
      "     55 Linear |R| = \u001b[33m2.360251e-06\u001b[39m\n",
      "     56 Linear |R| = \u001b[33m2.359706e-06\u001b[39m\n",
      "     57 Linear |R| = \u001b[33m2.353695e-06\u001b[39m\n",
      "     58 Linear |R| = \u001b[33m2.353599e-06\u001b[39m\n",
      "     59 Linear |R| = \u001b[33m2.334307e-06\u001b[39m\n",
      "     60 Linear |R| = \u001b[33m2.293826e-06\u001b[39m\n",
      "     61 Linear |R| = \u001b[33m2.291972e-06\u001b[39m\n",
      "     62 Linear |R| = \u001b[33m2.291551e-06\u001b[39m\n",
      "     63 Linear |R| = \u001b[33m2.291025e-06\u001b[39m\n",
      "     64 Linear |R| = \u001b[33m2.290490e-06\u001b[39m\n",
      "     65 Linear |R| = \u001b[33m2.289690e-06\u001b[39m\n",
      "     66 Linear |R| = \u001b[33m2.289265e-06\u001b[39m\n",
      "     67 Linear |R| = \u001b[33m2.288521e-06\u001b[39m\n",
      "     68 Linear |R| = \u001b[33m2.287907e-06\u001b[39m\n",
      "     69 Linear |R| = \u001b[33m2.286713e-06\u001b[39m\n",
      "     70 Linear |R| = \u001b[33m2.286444e-06\u001b[39m\n",
      "     71 Linear |R| = \u001b[33m2.285715e-06\u001b[39m\n",
      "     72 Linear |R| = \u001b[33m2.285071e-06\u001b[39m\n",
      "     73 Linear |R| = \u001b[33m2.283520e-06\u001b[39m\n",
      "     74 Linear |R| = \u001b[33m2.283463e-06\u001b[39m\n",
      "     75 Linear |R| = \u001b[33m2.283019e-06\u001b[39m\n",
      "     76 Linear |R| = \u001b[33m2.282303e-06\u001b[39m\n",
      "     77 Linear |R| = \u001b[33m2.280097e-06\u001b[39m\n",
      "     78 Linear |R| = \u001b[33m2.280078e-06\u001b[39m\n",
      "     79 Linear |R| = \u001b[33m2.279773e-06\u001b[39m\n",
      "     80 Linear |R| = \u001b[33m2.279032e-06\u001b[39m\n",
      "     81 Linear |R| = \u001b[33m2.275303e-06\u001b[39m\n",
      "     82 Linear |R| = \u001b[33m2.274293e-06\u001b[39m\n",
      "     83 Linear |R| = \u001b[33m2.274258e-06\u001b[39m\n",
      "     84 Linear |R| = \u001b[33m2.273376e-06\u001b[39m\n",
      "     85 Linear |R| = \u001b[33m2.268334e-06\u001b[39m\n",
      "     86 Linear |R| = \u001b[33m2.260759e-06\u001b[39m\n",
      "     87 Linear |R| = \u001b[33m2.260727e-06\u001b[39m\n",
      "     88 Linear |R| = \u001b[33m2.242904e-06\u001b[39m\n",
      "     89 Linear |R| = \u001b[33m2.236905e-06\u001b[39m\n",
      "     90 Linear |R| = \u001b[33m2.200369e-06\u001b[39m\n",
      "     91 Linear |R| = \u001b[33m2.199148e-06\u001b[39m\n",
      "     92 Linear |R| = \u001b[33m2.198221e-06\u001b[39m\n",
      "     93 Linear |R| = \u001b[33m2.195117e-06\u001b[39m\n",
      "     94 Linear |R| = \u001b[33m2.194594e-06\u001b[39m\n",
      "     95 Linear |R| = \u001b[33m2.194402e-06\u001b[39m\n",
      "     96 Linear |R| = \u001b[33m2.193269e-06\u001b[39m\n",
      "     97 Linear |R| = \u001b[33m2.192313e-06\u001b[39m\n",
      "     98 Linear |R| = \u001b[33m2.191922e-06\u001b[39m\n",
      "     99 Linear |R| = \u001b[33m2.191728e-06\u001b[39m\n",
      "    100 Linear |R| = \u001b[33m2.191168e-06\u001b[39m\n",
      "    101 Linear |R| = \u001b[33m2.190619e-06\u001b[39m\n",
      "    102 Linear |R| = \u001b[33m2.190427e-06\u001b[39m\n",
      "    103 Linear |R| = \u001b[33m2.190409e-06\u001b[39m\n",
      "    104 Linear |R| = \u001b[33m2.190273e-06\u001b[39m\n",
      "    105 Linear |R| = \u001b[33m2.189910e-06\u001b[39m\n",
      "    106 Linear |R| = \u001b[33m2.189774e-06\u001b[39m\n",
      "    107 Linear |R| = \u001b[33m2.189555e-06\u001b[39m\n",
      "    108 Linear |R| = \u001b[33m2.189552e-06\u001b[39m\n",
      "    109 Linear |R| = \u001b[33m2.189236e-06\u001b[39m\n",
      "    110 Linear |R| = \u001b[33m2.188864e-06\u001b[39m\n",
      "    111 Linear |R| = \u001b[33m2.187716e-06\u001b[39m\n",
      "    112 Linear |R| = \u001b[33m2.186874e-06\u001b[39m\n",
      "    113 Linear |R| = \u001b[33m2.186014e-06\u001b[39m\n",
      "    114 Linear |R| = \u001b[33m2.185700e-06\u001b[39m\n",
      "    115 Linear |R| = \u001b[33m2.185518e-06\u001b[39m\n",
      "    116 Linear |R| = \u001b[33m2.184982e-06\u001b[39m\n",
      "    117 Linear |R| = \u001b[33m2.184927e-06\u001b[39m\n",
      "    118 Linear |R| = \u001b[33m2.180975e-06\u001b[39m\n",
      "    119 Linear |R| = \u001b[33m2.177672e-06\u001b[39m\n",
      "    120 Linear |R| = \u001b[32m1.981030e-06\u001b[39m\n",
      "    121 Linear |R| = \u001b[32m1.870484e-06\u001b[39m\n",
      "    122 Linear |R| = \u001b[33m1.869356e-06\u001b[39m\n",
      "    123 Linear |R| = \u001b[33m1.869340e-06\u001b[39m\n",
      "    124 Linear |R| = \u001b[33m1.866741e-06\u001b[39m\n",
      "    125 Linear |R| = \u001b[33m1.864983e-06\u001b[39m\n",
      "    126 Linear |R| = \u001b[33m1.864953e-06\u001b[39m\n",
      "    127 Linear |R| = \u001b[33m1.864302e-06\u001b[39m\n",
      "    128 Linear |R| = \u001b[33m1.864085e-06\u001b[39m\n",
      "    129 Linear |R| = \u001b[33m1.862306e-06\u001b[39m\n",
      "    130 Linear |R| = \u001b[33m1.862266e-06\u001b[39m\n",
      "    131 Linear |R| = \u001b[33m1.861917e-06\u001b[39m\n",
      "    132 Linear |R| = \u001b[33m1.861276e-06\u001b[39m\n",
      "    133 Linear |R| = \u001b[33m1.857775e-06\u001b[39m\n",
      "    134 Linear |R| = \u001b[33m1.857640e-06\u001b[39m\n",
      "    135 Linear |R| = \u001b[33m1.857117e-06\u001b[39m\n",
      "    136 Linear |R| = \u001b[33m1.855948e-06\u001b[39m\n",
      "    137 Linear |R| = \u001b[33m1.845986e-06\u001b[39m\n",
      "    138 Linear |R| = \u001b[33m1.844592e-06\u001b[39m\n",
      "    139 Linear |R| = \u001b[33m1.839702e-06\u001b[39m\n",
      "    140 Linear |R| = \u001b[33m1.838969e-06\u001b[39m\n",
      "    141 Linear |R| = \u001b[33m1.825936e-06\u001b[39m\n",
      "    142 Linear |R| = \u001b[33m1.815917e-06\u001b[39m\n",
      "    143 Linear |R| = \u001b[33m1.813081e-06\u001b[39m\n",
      "    144 Linear |R| = \u001b[33m1.811759e-06\u001b[39m\n",
      "    145 Linear |R| = \u001b[33m1.811673e-06\u001b[39m\n",
      "    146 Linear |R| = \u001b[33m1.793086e-06\u001b[39m\n",
      "    147 Linear |R| = \u001b[33m1.763476e-06\u001b[39m\n",
      "    148 Linear |R| = \u001b[33m1.760061e-06\u001b[39m\n",
      "    149 Linear |R| = \u001b[32m1.651484e-06\u001b[39m\n",
      "    150 Linear |R| = \u001b[32m9.892867e-07\u001b[39m\n",
      "    151 Linear |R| = \u001b[32m7.347761e-07\u001b[39m\n",
      "    152 Linear |R| = \u001b[32m6.510794e-07\u001b[39m\n",
      "    153 Linear |R| = \u001b[32m6.076347e-07\u001b[39m\n",
      "    154 Linear |R| = \u001b[33m5.867122e-07\u001b[39m\n",
      "    155 Linear |R| = \u001b[33m5.734373e-07\u001b[39m\n",
      "    156 Linear |R| = \u001b[33m5.655054e-07\u001b[39m\n",
      "    157 Linear |R| = \u001b[33m5.571142e-07\u001b[39m\n",
      "    158 Linear |R| = \u001b[33m5.492258e-07\u001b[39m\n",
      "    159 Linear |R| = \u001b[33m5.429760e-07\u001b[39m\n",
      "    160 Linear |R| = \u001b[33m5.394464e-07\u001b[39m\n",
      "    161 Linear |R| = \u001b[33m5.367090e-07\u001b[39m\n",
      "    162 Linear |R| = \u001b[33m5.336990e-07\u001b[39m\n",
      "    163 Linear |R| = \u001b[33m5.308484e-07\u001b[39m\n",
      "    164 Linear |R| = \u001b[33m5.290701e-07\u001b[39m\n",
      "    165 Linear |R| = \u001b[33m5.281600e-07\u001b[39m\n",
      "    166 Linear |R| = \u001b[33m5.272338e-07\u001b[39m\n",
      "    167 Linear |R| = \u001b[33m5.263691e-07\u001b[39m\n",
      "    168 Linear |R| = \u001b[33m5.256799e-07\u001b[39m\n",
      "    169 Linear |R| = \u001b[33m5.253106e-07\u001b[39m\n",
      "    170 Linear |R| = \u001b[33m5.249613e-07\u001b[39m\n",
      "    171 Linear |R| = \u001b[33m5.246029e-07\u001b[39m\n",
      "    172 Linear |R| = \u001b[33m5.242924e-07\u001b[39m\n",
      "    173 Linear |R| = \u001b[33m5.238788e-07\u001b[39m\n",
      "    174 Linear |R| = \u001b[33m5.236085e-07\u001b[39m\n",
      "    175 Linear |R| = \u001b[33m5.221267e-07\u001b[39m\n",
      "    176 Linear |R| = \u001b[33m5.221175e-07\u001b[39m\n",
      "    177 Linear |R| = \u001b[33m5.184921e-07\u001b[39m\n",
      "    178 Linear |R| = \u001b[33m5.057204e-07\u001b[39m\n",
      "    179 Linear |R| = \u001b[32m3.983416e-07\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m3.981011e-07\u001b[39m\n",
      " Iteration 1 eigenvalue = 0.3628141175\n",
      "      0 Linear |R| = \u001b[32m3.981011e-07\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m3.630455e-07\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m3.587527e-07\u001b[39m\n",
      "      3 Linear |R| = \u001b[33m3.523750e-07\u001b[39m\n",
      "      4 Linear |R| = \u001b[33m3.477798e-07\u001b[39m\n",
      "      5 Linear |R| = \u001b[33m3.431690e-07\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m3.365361e-07\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m3.323794e-07\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m3.283255e-07\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m3.252130e-07\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m3.219011e-07\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m3.191110e-07\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m3.172117e-07\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m3.154156e-07\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m3.125900e-07\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m3.110349e-07\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m3.099729e-07\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m3.080332e-07\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m3.053842e-07\u001b[39m\n",
      "     19 Linear |R| = \u001b[33m3.028888e-07\u001b[39m\n",
      "     20 Linear |R| = \u001b[33m2.996922e-07\u001b[39m\n",
      "     21 Linear |R| = \u001b[33m2.948252e-07\u001b[39m\n",
      "     22 Linear |R| = \u001b[33m2.853298e-07\u001b[39m\n",
      "     23 Linear |R| = \u001b[33m2.761844e-07\u001b[39m\n",
      "     24 Linear |R| = \u001b[32m2.562131e-07\u001b[39m\n",
      "     25 Linear |R| = \u001b[32m2.038876e-07\u001b[39m\n",
      "     26 Linear |R| = \u001b[32m1.580689e-07\u001b[39m\n",
      "     27 Linear |R| = \u001b[32m9.280760e-08\u001b[39m\n",
      "     28 Linear |R| = \u001b[32m3.544104e-08\u001b[39m\n",
      "     29 Linear |R| = \u001b[32m2.334572e-08\u001b[39m\n",
      "     30 Linear |R| = \u001b[32m2.098302e-08\u001b[39m\n",
      "     31 Linear |R| = \u001b[33m2.091846e-08\u001b[39m\n",
      "     32 Linear |R| = \u001b[33m2.076552e-08\u001b[39m\n",
      "     33 Linear |R| = \u001b[33m2.058123e-08\u001b[39m\n",
      "     34 Linear |R| = \u001b[33m2.038915e-08\u001b[39m\n",
      "     35 Linear |R| = \u001b[33m1.999890e-08\u001b[39m\n",
      "     36 Linear |R| = \u001b[33m1.951589e-08\u001b[39m\n",
      "     37 Linear |R| = \u001b[33m1.909346e-08\u001b[39m\n",
      "     38 Linear |R| = \u001b[33m1.875677e-08\u001b[39m\n",
      "     39 Linear |R| = \u001b[33m1.836039e-08\u001b[39m\n",
      "     40 Linear |R| = \u001b[33m1.787462e-08\u001b[39m\n",
      "     41 Linear |R| = \u001b[33m1.735448e-08\u001b[39m\n",
      "     42 Linear |R| = \u001b[33m1.681863e-08\u001b[39m\n",
      "     43 Linear |R| = \u001b[33m1.632264e-08\u001b[39m\n",
      "     44 Linear |R| = \u001b[33m1.577008e-08\u001b[39m\n",
      "     45 Linear |R| = \u001b[33m1.538578e-08\u001b[39m\n",
      "     46 Linear |R| = \u001b[33m1.510558e-08\u001b[39m\n",
      "     47 Linear |R| = \u001b[33m1.481895e-08\u001b[39m\n",
      "     48 Linear |R| = \u001b[33m1.446186e-08\u001b[39m\n",
      "     49 Linear |R| = \u001b[33m1.421274e-08\u001b[39m\n",
      "     50 Linear |R| = \u001b[33m1.397762e-08\u001b[39m\n",
      "     51 Linear |R| = \u001b[33m1.362247e-08\u001b[39m\n",
      "     52 Linear |R| = \u001b[33m1.345997e-08\u001b[39m\n",
      "     53 Linear |R| = \u001b[33m1.342150e-08\u001b[39m\n",
      "     54 Linear |R| = \u001b[33m1.333619e-08\u001b[39m\n",
      "     55 Linear |R| = \u001b[33m1.324501e-08\u001b[39m\n",
      "     56 Linear |R| = \u001b[33m1.311087e-08\u001b[39m\n",
      "     57 Linear |R| = \u001b[33m1.292324e-08\u001b[39m\n",
      "     58 Linear |R| = \u001b[33m1.278792e-08\u001b[39m\n",
      "     59 Linear |R| = \u001b[33m1.277392e-08\u001b[39m\n",
      "     60 Linear |R| = \u001b[33m1.241461e-08\u001b[39m\n",
      "     61 Linear |R| = \u001b[33m1.232763e-08\u001b[39m\n",
      "     62 Linear |R| = \u001b[33m1.225816e-08\u001b[39m\n",
      "     63 Linear |R| = \u001b[33m1.211663e-08\u001b[39m\n",
      "     64 Linear |R| = \u001b[33m1.208077e-08\u001b[39m\n",
      "     65 Linear |R| = \u001b[33m1.208056e-08\u001b[39m\n",
      "     66 Linear |R| = \u001b[33m1.206043e-08\u001b[39m\n",
      "     67 Linear |R| = \u001b[33m1.205755e-08\u001b[39m\n",
      "     68 Linear |R| = \u001b[33m1.203924e-08\u001b[39m\n",
      "     69 Linear |R| = \u001b[33m1.199899e-08\u001b[39m\n",
      "     70 Linear |R| = \u001b[33m1.198487e-08\u001b[39m\n",
      "     71 Linear |R| = \u001b[33m1.198330e-08\u001b[39m\n",
      "     72 Linear |R| = \u001b[33m1.198285e-08\u001b[39m\n",
      "     73 Linear |R| = \u001b[33m1.198160e-08\u001b[39m\n",
      "     74 Linear |R| = \u001b[33m1.197850e-08\u001b[39m\n",
      "     75 Linear |R| = \u001b[33m1.196756e-08\u001b[39m\n",
      "     76 Linear |R| = \u001b[33m1.194269e-08\u001b[39m\n",
      "     77 Linear |R| = \u001b[33m1.192141e-08\u001b[39m\n",
      "     78 Linear |R| = \u001b[33m1.191968e-08\u001b[39m\n",
      "     79 Linear |R| = \u001b[33m1.191939e-08\u001b[39m\n",
      "     80 Linear |R| = \u001b[33m1.191319e-08\u001b[39m\n",
      "     81 Linear |R| = \u001b[33m1.190041e-08\u001b[39m\n",
      "     82 Linear |R| = \u001b[33m1.188447e-08\u001b[39m\n",
      "     83 Linear |R| = \u001b[33m1.185083e-08\u001b[39m\n",
      "     84 Linear |R| = \u001b[33m1.182746e-08\u001b[39m\n",
      "     85 Linear |R| = \u001b[33m1.182697e-08\u001b[39m\n",
      "     86 Linear |R| = \u001b[33m1.181788e-08\u001b[39m\n",
      "     87 Linear |R| = \u001b[33m1.180398e-08\u001b[39m\n",
      "     88 Linear |R| = \u001b[33m1.177086e-08\u001b[39m\n",
      "     89 Linear |R| = \u001b[33m1.148868e-08\u001b[39m\n",
      "     90 Linear |R| = \u001b[32m9.572764e-09\u001b[39m\n",
      "     91 Linear |R| = \u001b[32m8.675184e-09\u001b[39m\n",
      "     92 Linear |R| = \u001b[33m8.410757e-09\u001b[39m\n",
      "     93 Linear |R| = \u001b[33m8.321967e-09\u001b[39m\n",
      "     94 Linear |R| = \u001b[33m8.271689e-09\u001b[39m\n",
      "     95 Linear |R| = \u001b[33m8.218129e-09\u001b[39m\n",
      "     96 Linear |R| = \u001b[33m8.183894e-09\u001b[39m\n",
      "     97 Linear |R| = \u001b[33m8.169454e-09\u001b[39m\n",
      "     98 Linear |R| = \u001b[33m8.155978e-09\u001b[39m\n",
      "     99 Linear |R| = \u001b[33m8.129658e-09\u001b[39m\n",
      "    100 Linear |R| = \u001b[33m8.098789e-09\u001b[39m\n",
      "    101 Linear |R| = \u001b[33m8.077737e-09\u001b[39m\n",
      "    102 Linear |R| = \u001b[33m8.065941e-09\u001b[39m\n",
      "    103 Linear |R| = \u001b[33m8.052767e-09\u001b[39m\n",
      "    104 Linear |R| = \u001b[33m8.039070e-09\u001b[39m\n",
      "    105 Linear |R| = \u001b[33m8.029581e-09\u001b[39m\n",
      "    106 Linear |R| = \u001b[33m8.024029e-09\u001b[39m\n",
      "    107 Linear |R| = \u001b[33m8.016580e-09\u001b[39m\n",
      "    108 Linear |R| = \u001b[33m8.008546e-09\u001b[39m\n",
      "    109 Linear |R| = \u001b[33m8.003139e-09\u001b[39m\n",
      "    110 Linear |R| = \u001b[33m8.000983e-09\u001b[39m\n",
      "    111 Linear |R| = \u001b[33m7.999258e-09\u001b[39m\n",
      "    112 Linear |R| = \u001b[33m7.997763e-09\u001b[39m\n",
      "    113 Linear |R| = \u001b[33m7.997337e-09\u001b[39m\n",
      "    114 Linear |R| = \u001b[33m7.996503e-09\u001b[39m\n",
      "    115 Linear |R| = \u001b[33m7.996402e-09\u001b[39m\n",
      "    116 Linear |R| = \u001b[33m7.980099e-09\u001b[39m\n",
      "    117 Linear |R| = \u001b[33m7.973334e-09\u001b[39m\n",
      "    118 Linear |R| = \u001b[33m7.963005e-09\u001b[39m\n",
      "    119 Linear |R| = \u001b[33m7.956194e-09\u001b[39m\n",
      "    120 Linear |R| = \u001b[32m7.489503e-09\u001b[39m\n",
      "    121 Linear |R| = \u001b[33m7.416067e-09\u001b[39m\n",
      "    122 Linear |R| = \u001b[33m7.409025e-09\u001b[39m\n",
      "    123 Linear |R| = \u001b[33m7.409025e-09\u001b[39m\n",
      "    124 Linear |R| = \u001b[33m7.399818e-09\u001b[39m\n",
      "    125 Linear |R| = \u001b[33m7.385778e-09\u001b[39m\n",
      "    126 Linear |R| = \u001b[33m7.379231e-09\u001b[39m\n",
      "    127 Linear |R| = \u001b[33m7.378775e-09\u001b[39m\n",
      "    128 Linear |R| = \u001b[33m7.378501e-09\u001b[39m\n",
      "    129 Linear |R| = \u001b[33m7.374512e-09\u001b[39m\n",
      "    130 Linear |R| = \u001b[33m7.368991e-09\u001b[39m\n",
      "    131 Linear |R| = \u001b[33m7.367348e-09\u001b[39m\n",
      "    132 Linear |R| = \u001b[33m7.367171e-09\u001b[39m\n",
      "    133 Linear |R| = \u001b[33m7.366965e-09\u001b[39m\n",
      "    134 Linear |R| = \u001b[33m7.366858e-09\u001b[39m\n",
      "    135 Linear |R| = \u001b[33m7.366528e-09\u001b[39m\n",
      "    136 Linear |R| = \u001b[33m7.364951e-09\u001b[39m\n",
      "    137 Linear |R| = \u001b[33m7.364122e-09\u001b[39m\n",
      "    138 Linear |R| = \u001b[33m7.363768e-09\u001b[39m\n",
      "    139 Linear |R| = \u001b[33m7.361116e-09\u001b[39m\n",
      "    140 Linear |R| = \u001b[33m7.351118e-09\u001b[39m\n",
      "    141 Linear |R| = \u001b[33m7.341577e-09\u001b[39m\n",
      "    142 Linear |R| = \u001b[33m7.333893e-09\u001b[39m\n",
      "    143 Linear |R| = \u001b[33m7.327165e-09\u001b[39m\n",
      "    144 Linear |R| = \u001b[33m7.316464e-09\u001b[39m\n",
      "    145 Linear |R| = \u001b[33m7.277028e-09\u001b[39m\n",
      "    146 Linear |R| = \u001b[33m7.266077e-09\u001b[39m\n",
      "    147 Linear |R| = \u001b[33m7.257834e-09\u001b[39m\n",
      "    148 Linear |R| = \u001b[33m7.211286e-09\u001b[39m\n",
      "    149 Linear |R| = \u001b[33m7.075862e-09\u001b[39m\n",
      "    150 Linear |R| = \u001b[32m5.124207e-09\u001b[39m\n",
      "    151 Linear |R| = \u001b[32m3.908374e-09\u001b[39m\n",
      " 2 Nonlinear |R| = \u001b[32m3.907467e-09\u001b[39m\n",
      " Iteration 2 eigenvalue = 0.3628140301\n",
      "\u001b[32m Solve Converged!\u001b[39m\n",
      "\n",
      "Postprocessor Values:\n",
      "+----------------+----------------+\n",
      "| time           | u-normalized   |\n",
      "+----------------+----------------+\n",
      "|   0.000000e+00 |   1.000000e+00 |\n",
      "|   1.000000e+00 |   2.756233e+00 |\n",
      "+----------------+----------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!rm inputEigenProblem_out_eigenvalue-data_0001*.csv\n",
    "!./neutron__transport-opt -i inputEigenProblem.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicity factor for group-1 =  0    0.722091\n",
      "Name: eigen_values_real, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "df = pd.read_csv('inputEigenProblem_out_eigenvalue-data_0001.csv')\n",
    "lam =df[\"eigen_values_real\"]\n",
    "\n",
    "k=v[0]*sigma_f[0]/(lam+sigma_a[0]-sigma_12)\n",
    "\n",
    "\n",
    "print('Multiplicity factor for group-1 = ',k)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('inputEigenProblem_out_x-data_0001.csv')\n",
    "df2 = pd.read_csv('inputEigenProblem_out.csv')\n",
    "unormal=df2[\"u-normalized\"]\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(df[\"x\"],df[\"u_v\"]/unormal[1],\"r-\")\n",
    "\n",
    "u_values=df[\"u_v\"]/unormal[1]\n",
    "plt.grid()\n",
    "\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Normalized Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "\n",
    "plt.title(\"Bare Sphere Criticality\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicity factor for FDM =  \n",
      " 0.41520314252470497\n",
      "Multiplicity factor for FEM =  \n",
      " 0    0.415202\n",
      "Name: eigen_values_real, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nr= 75\n",
    "\n",
    "rn=3.44\n",
    "r0=0\n",
    "\n",
    "h=(rn-r0)/(Nr-1)\n",
    "r = np.arange(r0,rn + h,h)\n",
    "\n",
    "A=np.zeros((Nr,Nr))\n",
    "B=np.zeros(Nr)\n",
    "\n",
    "\n",
    "A[0,0]=-2*D1/h**2\n",
    "A[0,1]=2*D1/h**2\n",
    "\n",
    "\n",
    "for i in range(1,Nr-1):\n",
    "    A[i,i-1]=(1-(h/r[i]))*D1/h**2  \n",
    "    A[i,i]=-2*D1/h**2\n",
    "    A[i,i+1]=(1+(h/r[i]))*D1/h**2\n",
    "\n",
    "\n",
    "A[-1,-1]=-(2*D1/h**2+1/h+1/(rn))\n",
    "A[-1,-2]=(2)*D1/h**2\n",
    "\n",
    "D, V = LA.eig(A)\n",
    "\n",
    "\n",
    "eigen_value=D\n",
    "eigen_vec=V[:,1]\n",
    "c_star_vec=eigen_vec/LA.norm(eigen_vec[:][0])\n",
    "\n",
    "\n",
    "eigen_values = np.flip(np.sort(abs(D)))\n",
    "\n",
    "k_FDM=(v[0]*chi[0]*sigma_f[0])/(min(abs(D))+sigma_a[0]-sigma_12)\n",
    "\n",
    "\n",
    "k_FEM=(v[0]*chi[0]*sigma_f[0])/(lam+sigma_a[0]-sigma_12)\n",
    "\n",
    "print('Multiplicity factor for FDM =  \\n',k_FDM)\n",
    "print('Multiplicity factor for FEM =  \\n',k_FEM)\n",
    "\n",
    "DD = abs(c_star_vec)\n",
    "DD /= DD.max()\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(r,DD,label=\"FDM\")\n",
    "plt.plot(df[\"x\"],df[\"u_v\"]/unormal[1],\"r*\",label=\"FEM\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Normalized Neutron Flux\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### [One-Group Energy Reflector Sphere](#toc)<a id=\"onegroupenergy\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Framework Information:\n",
      "MOOSE Version:           git commit b98ea2c450 on 2021-09-23\n",
      "LibMesh Version:         \n",
      "PETSc Version:           3.15.1\n",
      "SLEPc Version:           3.15.1\n",
      "Current Time:            Mon May  9 11:31:39 2022\n",
      "Executable Timestamp:    Mon May  9 11:31:32 2022\n",
      "\n",
      "Parallelism:\n",
      "  Num Processors:          1\n",
      "  Num Threads:             1\n",
      "\n",
      "Mesh: \n",
      "  Parallel Type:           replicated\n",
      "  Mesh Dimension:          1\n",
      "  Spatial Dimension:       1\n",
      "  Nodes:                   41\n",
      "  Elems:                   20\n",
      "  Num Subdomains:          1\n",
      "\n",
      "Nonlinear System:\n",
      "  Num DOFs:                41\n",
      "  Num Local DOFs:          41\n",
      "  Variables:               \"u_r\" \n",
      "  Finite Element Types:    \"LAGRANGE\" \n",
      "  Approximation Orders:    \"SECOND\" \n",
      "\n",
      "Execution Information:\n",
      "  Executioner:             Eigenvalue\n",
      "  Solver Mode:             Preconditioned JFNK\n",
      "\n",
      "\n",
      "Postprocessor Values:\n",
      "+----------------+----------------+\n",
      "| time           | u-normalized   |\n",
      "+----------------+----------------+\n",
      "|   0.000000e+00 |   1.000000e+00 |\n",
      "+----------------+----------------+\n",
      "\n",
      "\n",
      " -------------------------------\n",
      " Free power iteration starts ...\n",
      " -------------------------------\n",
      "\n",
      " 0 Nonlinear |R| = \u001b[32m1.985198e+00\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m1.985198e+00\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m1.835879e+00\u001b[39m\n",
      "      2 Linear |R| = \u001b[32m1.733541e+00\u001b[39m\n",
      "      3 Linear |R| = \u001b[33m1.713832e+00\u001b[39m\n",
      "      4 Linear |R| = \u001b[33m1.698644e+00\u001b[39m\n",
      "      5 Linear |R| = \u001b[33m1.666028e+00\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m1.603206e+00\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m1.567207e+00\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m1.511997e+00\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m1.458150e+00\u001b[39m\n",
      "     10 Linear |R| = \u001b[32m1.359673e+00\u001b[39m\n",
      "     11 Linear |R| = \u001b[32m1.289462e+00\u001b[39m\n",
      "     12 Linear |R| = \u001b[32m1.186485e+00\u001b[39m\n",
      "     13 Linear |R| = \u001b[32m1.097573e+00\u001b[39m\n",
      "     14 Linear |R| = \u001b[32m9.720813e-01\u001b[39m\n",
      "     15 Linear |R| = \u001b[32m8.642224e-01\u001b[39m\n",
      "     16 Linear |R| = \u001b[32m7.356934e-01\u001b[39m\n",
      "     17 Linear |R| = \u001b[32m6.191984e-01\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m4.862906e-01\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m3.529893e-01\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m2.083942e-01\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m6.687966e-02\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m2.051715e-03\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m2.051343e-03\u001b[39m\n",
      " Iteration 1 eigenvalue = 0.3203467609\n",
      " 0 Nonlinear |R| = \u001b[32m7.316959e-02\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m7.316959e-02\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m7.278223e-02\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m7.267093e-02\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m6.268076e-02\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m5.293839e-02\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m4.900346e-02\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m4.721546e-02\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m4.405752e-02\u001b[39m\n",
      "      8 Linear |R| = \u001b[32m4.151965e-02\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m4.128291e-02\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m4.124506e-02\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m4.100390e-02\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m4.076669e-02\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m4.074338e-02\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m4.068057e-02\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m4.049150e-02\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m3.977017e-02\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m3.919840e-02\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m3.666085e-02\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m2.632894e-02\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m1.196550e-02\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m1.751738e-03\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m5.173525e-05\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m5.176802e-05\u001b[39m\n",
      " Iteration 2 eigenvalue = 0.3077704401\n",
      " 0 Nonlinear |R| = \u001b[32m5.288710e-03\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m5.288710e-03\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m5.132839e-03\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m5.127663e-03\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m4.406789e-03\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m3.766166e-03\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m3.526990e-03\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m3.432622e-03\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m3.307686e-03\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m3.228547e-03\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m3.226275e-03\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m3.226070e-03\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m3.214793e-03\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m3.206239e-03\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m3.206224e-03\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m3.204866e-03\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m3.155247e-03\u001b[39m\n",
      "     16 Linear |R| = \u001b[32m2.971912e-03\u001b[39m\n",
      "     17 Linear |R| = \u001b[32m2.621411e-03\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m2.006990e-03\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m1.042988e-03\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m4.002255e-04\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m6.736219e-05\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m2.348275e-06\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m2.357208e-06\u001b[39m\n",
      " Iteration 3 eigenvalue = 0.3068050164\n",
      " 0 Nonlinear |R| = \u001b[32m4.483627e-04\u001b[39m\n",
      "      0 Linear |R| = \u001b[32m4.483627e-04\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m4.333022e-04\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m4.329463e-04\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m3.734066e-04\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m3.172821e-04\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m3.000474e-04\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m2.942960e-04\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m2.876067e-04\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m2.830335e-04\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m2.829614e-04\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m2.829614e-04\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m2.820250e-04\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m2.805114e-04\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m2.802866e-04\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m2.791186e-04\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m2.688328e-04\u001b[39m\n",
      "     16 Linear |R| = \u001b[32m2.401376e-04\u001b[39m\n",
      "     17 Linear |R| = \u001b[32m1.933822e-04\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m1.308087e-04\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m6.638948e-05\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m2.527068e-05\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m4.845171e-06\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m1.806261e-07\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m1.813037e-07\u001b[39m\n",
      " Iteration 4 eigenvalue = 0.3067202058\n",
      "\n",
      " -------------------------------------\n",
      " Nonlinear Newton iteration starts ...\n",
      " -------------------------------------\n",
      "\n",
      " 0 Nonlinear |R| = \u001b[32m3.987183e-05\u001b[39m\n",
      " Iteration 0 eigenvalue = 0.3067202058\n",
      "      0 Linear |R| = \u001b[32m3.987183e-05\u001b[39m\n",
      "      1 Linear |R| = \u001b[33m3.846485e-05\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m3.842283e-05\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m3.389920e-05\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m2.930210e-05\u001b[39m\n",
      "      5 Linear |R| = \u001b[33m2.795557e-05\u001b[39m\n",
      "      6 Linear |R| = \u001b[33m2.754196e-05\u001b[39m\n",
      "      7 Linear |R| = \u001b[33m2.706112e-05\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m2.671805e-05\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m2.671468e-05\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m2.671427e-05\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m2.663420e-05\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m2.646883e-05\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m2.642290e-05\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m2.625304e-05\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m2.510249e-05\u001b[39m\n",
      "     16 Linear |R| = \u001b[32m2.209128e-05\u001b[39m\n",
      "     17 Linear |R| = \u001b[32m1.734948e-05\u001b[39m\n",
      "     18 Linear |R| = \u001b[32m1.156796e-05\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m5.965815e-06\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m2.368576e-06\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m4.975610e-07\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m1.989943e-08\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m1.989911e-08\u001b[39m\n",
      " Iteration 1 eigenvalue = 0.3067117936\n",
      "      0 Linear |R| = \u001b[32m1.989911e-08\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m1.088202e-08\u001b[39m\n",
      "      2 Linear |R| = \u001b[32m4.920697e-09\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m4.068182e-09\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m3.605581e-09\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m3.262619e-09\u001b[39m\n",
      "      6 Linear |R| = \u001b[32m2.915870e-09\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m2.759658e-09\u001b[39m\n",
      "      8 Linear |R| = \u001b[33m2.664131e-09\u001b[39m\n",
      "      9 Linear |R| = \u001b[33m2.623122e-09\u001b[39m\n",
      "     10 Linear |R| = \u001b[33m2.604614e-09\u001b[39m\n",
      "     11 Linear |R| = \u001b[33m2.601068e-09\u001b[39m\n",
      "     12 Linear |R| = \u001b[33m2.598811e-09\u001b[39m\n",
      "     13 Linear |R| = \u001b[33m2.598468e-09\u001b[39m\n",
      "     14 Linear |R| = \u001b[33m2.597797e-09\u001b[39m\n",
      "     15 Linear |R| = \u001b[33m2.590935e-09\u001b[39m\n",
      "     16 Linear |R| = \u001b[33m2.576311e-09\u001b[39m\n",
      "     17 Linear |R| = \u001b[33m2.571331e-09\u001b[39m\n",
      "     18 Linear |R| = \u001b[33m2.561288e-09\u001b[39m\n",
      "     19 Linear |R| = \u001b[32m2.428330e-09\u001b[39m\n",
      "     20 Linear |R| = \u001b[32m1.511909e-09\u001b[39m\n",
      "     21 Linear |R| = \u001b[32m1.311711e-09\u001b[39m\n",
      "     22 Linear |R| = \u001b[32m1.005954e-10\u001b[39m\n",
      " 2 Nonlinear |R| = \u001b[32m1.006960e-10\u001b[39m\n",
      " Iteration 2 eigenvalue = 0.3067117929\n",
      "\u001b[32m Solve Converged!\u001b[39m\n",
      "\n",
      "Postprocessor Values:\n",
      "+----------------+----------------+\n",
      "| time           | u-normalized   |\n",
      "+----------------+----------------+\n",
      "|   0.000000e+00 |   1.000000e+00 |\n",
      "|   1.000000e+00 |   3.260390e+00 |\n",
      "+----------------+----------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!rm inputEigenProblem_out_eigenvalue-data_0001*.csv\n",
    "!./neutron__transport-opt -i inputEigenProblem_reflector.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicity factor for group-1 =  0    0.499887\n",
      "Name: eigen_values_real, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "df = pd.read_csv('inputEigenProblem_reflector_out_eigenvalue-data_0001.csv')\n",
    "lam =df[\"eigen_values_real\"]\n",
    "\n",
    "\n",
    "k=(v[0]*chi[0]*sigma_f[0])/(lam+sigma_a[0]-sigma_12)\n",
    "\n",
    "\n",
    "print('Multiplicity factor for group-1 = ',k)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('inputEigenProblem_reflector_out_x-data_0001.csv')\n",
    "df2 = pd.read_csv('inputEigenProblem_reflector_out.csv')\n",
    "unormal=df2[\"u-normalized\"]\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(df[\"x\"],df[\"u_r\"]/unormal[1],\"r-\")\n",
    "\n",
    "u_values=df[\"u_r\"]/unormal[1]\n",
    "plt.grid()\n",
    "\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Normalized Neutron flux [N/cm^2]\")\n",
    "font = {'family' : 'DejaVu Sans',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 15}\n",
    "plt.rc('font', **font)\n",
    "\n",
    "plt.title(\"Partially Reflective Sphere Criticality\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicity factor for FDM =  \n",
      " 0.07312303616542802\n",
      "Multiplicity factor for FEM =  \n",
      " 0    0.499887\n",
      "Name: eigen_values_real, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nr= 50\n",
    "\n",
    "rn=3.44\n",
    "r0=0\n",
    "\n",
    "alpha = 0.1\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "h=(rn-r0)/(Nr-1)\n",
    "r = np.arange(r0,rn + h,h)\n",
    "\n",
    "A=np.zeros((Nr,Nr))\n",
    "B=np.zeros(Nr)\n",
    "\n",
    "\n",
    "A[0,0]=-2*D1/h**2\n",
    "A[0,1]=2*D1/h**2\n",
    "\n",
    "\n",
    "for i in range(1,Nr-1):\n",
    "    A[i,i-1]=(1-(h/r[i]))*D1/h**2  \n",
    "    A[i,i]=-2*D1/h**2\n",
    "    A[i,i+1]=(1+(h/r[i]))*D1/h**2\n",
    "\n",
    "\n",
    "#A[-1,-1]=(-2*D1/h**2-1/h-1/(rn))\n",
    "#A[-1,-2]=(2)*D1/h**2\n",
    "\n",
    "#Bare\n",
    "A[-1,-1]=-(2*D1/h**2+1/h+1/(rn))\n",
    "A[-1,-2]=(2)*D1/h**2\n",
    "\n",
    "#Albedo\n",
    "A[-1,-1]=((1-alpha)/(1+alpha))*(-2*D1/h**2-1/h-1/(rn))\n",
    "A[-1,-2]=(2)*D1/h**2\n",
    "D, V = LA.eig(A)\n",
    "\n",
    "\n",
    "eigen_value=D\n",
    "eigen_vec=V[:,1]\n",
    "c_star_vec=eigen_vec/LA.norm(eigen_vec[:][0])\n",
    "\n",
    "\n",
    "eigen_values = np.flip(np.sort(abs(D)))\n",
    "\n",
    "k_FDM=(v[0]*chi[0]*sigma_f[0])/(min(abs(D))+sigma_a[0]-sigma_12)\n",
    "\n",
    "\n",
    "k_FEM=(v[0]*chi[0]*sigma_f[0])/(lam+sigma_a[0]-sigma_12)\n",
    "\n",
    "print('Multiplicity factor for FDM =  \\n',k_FDM)\n",
    "print('Multiplicity factor for FEM =  \\n',k_FEM)\n",
    "\n",
    "DD = abs(c_star_vec)\n",
    "DD /= DD.max()\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(r,DD,label=\"FDM\")\n",
    "plt.plot(df[\"x\"],df[\"u_r\"]/unormal[1],\"r*\",label=\"FEM\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"Radius [cm]\")\n",
    "plt.ylabel(\"Normalized Neutron Flux\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "book_params = False\n",
    "openMC_xs = False\n",
    "\n",
    "x_a = 0.0\n",
    "x_interface = 3.44\n",
    "x_b = 10.0\n",
    "\n",
    "fdp_full = True\n",
    "\n",
    "if book_params:\n",
    "    diff_coeff_u1_c = 1.0\n",
    "    diff_coeff_u1_m = 1.0\n",
    "\n",
    "    fiss_u1_c = 0.057\n",
    "    #fiss_u1_c = 30\n",
    "\n",
    "    sigma_abs_u1_c = 0.001\n",
    "    sigma_abs_u1_m = 0.001\n",
    "    \n",
    "else:\n",
    "\n",
    "    diff_coeff_u1_c = 1.84\n",
    "    diff_coeff_u1_m = 1.64\n",
    "\n",
    "    fiss_u1_c = 0.174\n",
    "    #fiss_u1_c = 30\n",
    "\n",
    "    sigma_abs_u1_c = 0.0745\n",
    "    sigma_abs_u1_m = 0.00534\n",
    "    \n",
    "if openMC_xs:\n",
    "    diff_coeff_u1_c = 1.33\n",
    "    diff_coeff_u2_c = 0.0292\n",
    "\n",
    "    diff_coeff_u1_m = 7.25e-01\n",
    "    diff_coeff_u2_m = 4.52e-01\n",
    "\n",
    "    sigma_s12_c = 3.21e-07\n",
    "    sigma_s12_m = 3.74e-04\n",
    "\n",
    "    fiss_u1_c = 2.20e-01\n",
    "    #fiss_u1_c = 30\n",
    "\n",
    "    fiss_u2_c = 2.16e+01\n",
    "\n",
    "    sigma_abs_u1_c = 7.61e-02\n",
    "    sigma_abs_u2_c = 1.10e+01\n",
    "\n",
    "    sigma_abs_u1_m = 1.47e-03\n",
    "    sigma_abs_u2_m = 5.94e-04\n",
    "\n",
    "order = variable_order = 'second'\n",
    "flux_order = 'first'\n",
    "\n",
    "diffFlux_family = 'monomial_vec'\n",
    "diffFlux_r_family = 'monomial'\n",
    "\n",
    "#robin_u_ref = 0.0\n",
    "#robin_transfer_coeff = 10.0e+10\n",
    "\n",
    "n_felem_core = 300\n",
    "n_felem_reflector = 300\n",
    "\n",
    "u1_initial = 100000\n",
    "\n",
    "interfacial_transfer_coeff = 1000000000000000000.0\n",
    "interfacial_adsorption_coeff = 0\n",
    "\n",
    "u1_bc_left_neumann = 0\n",
    "u2_bc_left_neumann = 0\n",
    "\n",
    "u1_bc_right_robin_transfer_coeff = 10.0e+10\n",
    "\n",
    "n_plot_pts_core = 2*n_felem_core + 1\n",
    "n_plot_pts_reflector = 2*n_felem_reflector + 1\n",
    "\n",
    "flux_ref = 0.0   #u_ref for robin boundary condition\n",
    "\n",
    "inputFileName = \"input_2Domain.hit\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def write_input_file_1d_coupled(pjfnk=False,filename='input.hit'):\n",
    "    import pyhit\n",
    "    import moosetree\n",
    "    root = pyhit.load('')\n",
    "\n",
    "    prblm = root.insert(-1,'Problem')\n",
    "    prblm['type'] = 'FEProblem'\n",
    "    prblm['coord_type'] = 'RSPHERICAL'\n",
    "\n",
    "    mesh = root.insert(-1,'Mesh')\n",
    "    \n",
    "    omega1 = mesh.insert(-1,'omega1')\n",
    "    omega1['type'] = 'GeneratedMeshGenerator'\n",
    "    omega1['dim'] = 1\n",
    "    omega1['xmin'] = x_a\n",
    "    omega1['xmax'] = x_interface\n",
    "    omega1['nx'] = n_felem_core\n",
    "    omega1['boundary_name_prefix'] = 'omega_1'\n",
    "    if order == 'second':\n",
    "        omega1['elem_type'] = 'edge3'\n",
    "    \n",
    "    omega2 = mesh.insert(-1,'omega2')\n",
    "    omega2['type'] = 'GeneratedMeshGenerator'\n",
    "    omega2['dim'] = 1\n",
    "    omega2['xmin'] = x_interface\n",
    "    omega2['xmax'] = x_b\n",
    "    omega2['nx'] = n_felem_reflector\n",
    "    omega2['boundary_name_prefix'] = 'omega_2'\n",
    "    if order == 'second':\n",
    "        omega2['elem_type'] = 'edge3'\n",
    "\n",
    "    omega = mesh.insert(-1,'omega')\n",
    "    omega['type'] = 'StitchedMeshGenerator'\n",
    "    omega['inputs'] = \"'omega1 omega2'\"\n",
    "    omega['stitch_boundaries_pairs'] = \"'omega_1_right omega_2_left'\"\n",
    "    omega['clear_stitched_boundary_ids'] = 'true'\n",
    "    \n",
    "    mod1 = mesh.insert(-1,'mod1')\n",
    "    mod1['type'] = 'SubdomainBoundingBoxGenerator'\n",
    "    mod1['input'] = 'omega'\n",
    "    mod1['block_id'] = 1\n",
    "    mod1['block_name'] = 'omega_1'\n",
    "    mod1['bottom_left'] = str(x_a)+' 0 0'\n",
    "    mod1['top_right'] = str(x_interface)+' 1 0'\n",
    "    \n",
    "    mod2 = mesh.insert(-1,'mod2')\n",
    "    mod2['type'] = 'SubdomainBoundingBoxGenerator'\n",
    "    mod2['input'] = 'mod1'\n",
    "    mod2['block_id'] = 2\n",
    "    mod2['block_name'] = 'omega_2'\n",
    "    mod2['bottom_left'] = str(x_interface)+' 0 0'\n",
    "    mod2['top_right'] = str(x_b)+' 1 0'\n",
    "    \n",
    "    mod3 = mesh.insert(-1,'mod3')\n",
    "    mod3['type'] = 'SideSetsBetweenSubdomainsGenerator'\n",
    "    mod3['input'] = 'mod2'\n",
    "    mod3['primary_block'] = 'omega_1'\n",
    "    mod3['paired_block'] = 'omega_2' \n",
    "    mod3['new_boundary'] = 'interface_12'\n",
    "    \n",
    "    mod4 = mesh.insert(-1,'mod4')\n",
    "    mod4['type'] = 'SideSetsAroundSubdomainGenerator'\n",
    "    mod4['input'] = 'mod3'\n",
    "    mod4['block'] = 'omega_1'\n",
    "    mod4['normal'] = '-1 0 0'\n",
    "    mod4['new_boundary'] = 'omega_1_left'\n",
    "    \n",
    "    mod5 = mesh.insert(-1,'mod5')\n",
    "    mod5['type'] = 'SideSetsAroundSubdomainGenerator'\n",
    "    mod5['input'] = 'mod4'\n",
    "    mod5['block'] = 'omega_2'\n",
    "    mod5['normal'] = '1 0 0'\n",
    "    mod5['new_boundary'] = 'omega_2_right'\n",
    "    \n",
    "    vars = root.insert(-1,'Variables')\n",
    "    \n",
    "    u1_c = vars.insert(-1,'u1_c')\n",
    "    u1_c['block'] = 'omega_1'\n",
    "    u1_c['order'] = order\n",
    "    u1_c['family'] = 'lagrange'\n",
    "    u1_c['initial_condition'] = u1_initial\n",
    "    \n",
    "    u1_m = vars.insert(-1,'u1_m')\n",
    "    u1_m['block'] = 'omega_2'\n",
    "    u1_m['order'] = order\n",
    "    u1_m['family'] = 'lagrange'\n",
    "    u1_m['initial_condition'] = u1_initial\n",
    "    \n",
    "    aux_vars = root.insert(-1,'AuxVariables')\n",
    "    \n",
    "    diffFlux_u1_c = aux_vars.insert(-1,'diffFlux_u1_c')\n",
    "    diffFlux_u1_c['block'] = 'omega_1'\n",
    "    diffFlux_u1_c['order'] = flux_order\n",
    "    diffFlux_u1_c['family'] = diffFlux_family\n",
    "\n",
    "    diffFlux_u1_m = aux_vars.insert(-1,'diffFlux_u1_m')\n",
    "    diffFlux_u1_m['block'] = 'omega_2'\n",
    "    diffFlux_u1_m['order'] = flux_order\n",
    "    diffFlux_u1_m['family'] = diffFlux_family\n",
    "    \n",
    "    diffFlux_u1_c_r = aux_vars.insert(-1,'diffFlux_u1_c_r')\n",
    "    diffFlux_u1_c_r['block'] = 'omega_1'\n",
    "    diffFlux_u1_c_r['order'] = flux_order\n",
    "    diffFlux_u1_c_r['family'] = diffFlux_r_family\n",
    "\n",
    "    diffFlux_u1_m_r = aux_vars.insert(-1,'diffFlux_u1_m_r')\n",
    "    diffFlux_u1_m_r['block'] = 'omega_2'\n",
    "    diffFlux_u1_m_r['order'] = flux_order\n",
    "    diffFlux_u1_m_r['family'] = diffFlux_r_family\n",
    "\n",
    "    kernels = root.insert(-1,'Kernels')\n",
    "    \n",
    "    diffusion_term_u1_c = kernels.insert(-1,'diffusion_term_u1_c')\n",
    "    diffusion_term_u1_c['type'] = 'DiffusionTerm'\n",
    "    diffusion_term_u1_c['block'] = 'omega_1'\n",
    "    diffusion_term_u1_c['variable'] = 'u1_c'\n",
    "    diffusion_term_u1_c['diffCoeff'] = diff_coeff_u1_c\n",
    "    \n",
    "    diffusion_term_u1_m = kernels.insert(-1,'diffusion_term_u1_m')\n",
    "    diffusion_term_u1_m['type'] = 'DiffusionTerm'\n",
    "    diffusion_term_u1_m['block'] = 'omega_2'\n",
    "    diffusion_term_u1_m['variable'] = 'u1_m'\n",
    "    diffusion_term_u1_m['diffCoeff'] = diff_coeff_u1_m\n",
    "    \n",
    "    fission_source_u1_c = kernels.insert(-1,'fission_source_u1_c')\n",
    "    fission_source_u1_c['type'] = 'FissionSource'\n",
    "    fission_source_u1_c['block'] = 'omega_1'\n",
    "    fission_source_u1_c['variable'] = 'u1_c'\n",
    "    fission_source_u1_c['Sigma_nu'] = fiss_u1_c\n",
    "    \n",
    "    abs_u1_c = kernels.insert(-1,'abs_u1_c')\n",
    "    abs_u1_c['type'] = 'SourceTermG1'\n",
    "    abs_u1_c['block'] = 'omega_1'\n",
    "    abs_u1_c['variable'] = 'u1_c'\n",
    "    abs_u1_c['sigma_sa'] = -sigma_abs_u1_c\n",
    "    \n",
    "    abs_u1_m = kernels.insert(-1,'abs_u1_m')\n",
    "    abs_u1_m['type'] = 'SourceTermG1'\n",
    "    abs_u1_m['block'] = 'omega_2'\n",
    "    abs_u1_m['variable'] = 'u1_m'\n",
    "    abs_u1_m['sigma_sa'] = -sigma_abs_u1_m\n",
    "    \n",
    "    interf_kernels = root.insert(-1,'InterfaceKernels')\n",
    "    \n",
    "    scalar_flux_continuity_u1 = interf_kernels.insert(-1,'scalar_flux_continuity_u1')\n",
    "    scalar_flux_continuity_u1['type'] = 'InterfaceDiffusion'\n",
    "    scalar_flux_continuity_u1['variable'] = 'u1_c'\n",
    "    scalar_flux_continuity_u1['neighbor_var'] = 'u1_m'\n",
    "    scalar_flux_continuity_u1['boundary'] = 'interface_12'\n",
    "    scalar_flux_continuity_u1['D'] = diff_coeff_u1_c\n",
    "    scalar_flux_continuity_u1['D_neighbor'] = diff_coeff_u1_m\n",
    "    \n",
    "    scalar_flux_jump_u1 = interf_kernels.insert(-1,'scalar_flux_jump_u1')\n",
    "    scalar_flux_jump_u1['type'] = 'InterfacePartition'\n",
    "    scalar_flux_jump_u1['variable'] = 'u1_c'\n",
    "    scalar_flux_jump_u1['neighbor_var'] = 'u1_m'\n",
    "    scalar_flux_jump_u1['boundary'] = 'interface_12'\n",
    "    scalar_flux_jump_u1['kCoeff'] = 1\n",
    "    \n",
    "    aux_kernels = root.insert(-1,'AuxKernels')\n",
    "    \n",
    "    diffusion_flux_u1_c = aux_kernels.insert(-1,'diffusion_flux_u1_c')\n",
    "    diffusion_flux_u1_c['type'] = 'HeatFlux'\n",
    "    diffusion_flux_u1_c['block'] = 'omega_1'\n",
    "    diffusion_flux_u1_c['field'] = 'u1_c'\n",
    "    diffusion_flux_u1_c['thCondCoeff'] = diff_coeff_u1_c\n",
    "    diffusion_flux_u1_c['variable'] = 'diffFlux_u1_c'\n",
    "    diffusion_flux_u1_c['execute_on'] = 'timestep_end'\n",
    "    \n",
    "    diffusion_flux_u1_m = aux_kernels.insert(-1,'diffusion_flux_u1_m')\n",
    "    diffusion_flux_u1_m['type'] = 'HeatFlux'\n",
    "    diffusion_flux_u1_m['block'] = 'omega_2'\n",
    "    diffusion_flux_u1_m['field'] = 'u1_m'\n",
    "    diffusion_flux_u1_m['thCondCoeff'] = diff_coeff_u1_m\n",
    "    diffusion_flux_u1_m['variable'] = 'diffFlux_u1_m'\n",
    "    diffusion_flux_u1_m['execute_on'] = 'timestep_end'\n",
    "  \n",
    "    diffusion_flux_u1_c_r = aux_kernels.insert(-1,'diffusion_flux_u1_c_r')\n",
    "    diffusion_flux_u1_c_r['type'] = 'VectorVariableComponentAux'\n",
    "    diffusion_flux_u1_c_r['block'] = 'omega_1'\n",
    "    diffusion_flux_u1_c_r['vector_variable'] = 'diffFlux_u1_c'\n",
    "    diffusion_flux_u1_c_r['component'] = \"x\"\n",
    "    diffusion_flux_u1_c_r['variable'] = 'diffFlux_u1_c_r'\n",
    "    diffusion_flux_u1_c_r['execute_on'] = 'timestep_end'\n",
    "\n",
    "    diffusion_flux_u1_m_r = aux_kernels.insert(-1,'diffusion_flux_u1_m_r')\n",
    "    diffusion_flux_u1_m_r['type'] = 'VectorVariableComponentAux'\n",
    "    diffusion_flux_u1_m_r['block'] = 'omega_2'\n",
    "    diffusion_flux_u1_m_r['vector_variable'] = 'diffFlux_u1_m'\n",
    "    diffusion_flux_u1_m_r['component'] = \"x\"\n",
    "    diffusion_flux_u1_m_r['variable'] = 'diffFlux_u1_m_r'\n",
    "    diffusion_flux_u1_m_r['execute_on'] = 'timestep_end'\n",
    "    \n",
    "    \n",
    "    bcs = root.insert(-1,'BCs')\n",
    "    \n",
    "    entry_u1 = bcs.insert(-1,'entry_u1')\n",
    "    entry_u1['type'] = 'NeumannBC'\n",
    "    entry_u1['variable'] = 'u1_c'\n",
    "    entry_u1['boundary'] = 'omega_1_left'\n",
    "    entry_u1['value'] = u1_bc_left_neumann \n",
    "    \n",
    "    exit_u1 = bcs.insert(-1,'exit_u1')\n",
    "    exit_u1['type'] = 'VacuumBC'\n",
    "    exit_u1['variable'] = 'u1_m'\n",
    "    exit_u1['boundary'] = 'omega_2_right'\n",
    "    \n",
    "    functions = root.insert(-1,'Functions')\n",
    "    \n",
    "    ref_flux_func = functions.insert(-1, 'refFluxFunc')\n",
    "    ref_flux_func['type'] = 'ParsedFunction'\n",
    "    ref_flux_func['value'] = 'flux_ref'\n",
    "    ref_flux_func['vars'] = 'flux_ref'\n",
    "    ref_flux_func['vals'] = str(flux_ref)\n",
    "    \n",
    "    if pjfnk:\n",
    "        exe = root.insert(-1,'Executioner')\n",
    "        exe['type'] = 'Steady'\n",
    "        exe['solve_type']  = 'PJFNK'\n",
    "        exe['petsc_options_iname']  = '-pc_type -pc_hypre_type'\n",
    "        exe['petsc_options_value']  = 'hypre boomeramg'\n",
    "        exe['l_max_its']  = 20\n",
    "        exe['l_tol']  = 1e-5\n",
    "        exe['nl_max_its']  = 15\n",
    "        exe['nl_rel_tol']  = 1e-8\n",
    "        exe['nl_abs_tol']  = 1e-8\n",
    "    elif fdp_full:\n",
    "        pre = root.insert(-1, 'Preconditioning')\n",
    "        pre['active'] = 'fdp-newt-full'\n",
    "        \n",
    "        fdp = pre.insert(-1, 'fdp-newt-full')\n",
    "        fdp['type'] = 'FDP'\n",
    "        fdp['full'] = 'true'\n",
    "        fdp['solve_type'] = 'NEWTON'\n",
    "        fdp['petsc_options_iname'] = \"\"'-pc_type -mat_fd_coloring_err -mat_fd_type'\"\"\n",
    "        fdp['petsc_options_value'] = \"\"'lu  1e-8          ds'\"\"\n",
    "        \n",
    "        exe = root.insert(-1,'Executioner')\n",
    "        exe['type'] = 'Steady'\n",
    "\n",
    "    vp = root.insert(-1,'VectorPostprocessors')\n",
    "    \n",
    "    omega_1 = vp.insert(-1,'omega_1')\n",
    "    omega_1['type'] = 'LineValueSampler'\n",
    "    omega_1['execute_on'] = 'timestep_end final'\n",
    "    omega_1['variable'] = 'u1_c diffFlux_u1_c_r'  \n",
    "    omega_1['start_point'] = str(x_a)+' 0 0'\n",
    "    omega_1['end_point'] = str(x_interface*0.999)+' 0 0'\n",
    "    omega_1['num_points'] = n_plot_pts_core\n",
    "    omega_1['sort_by'] = 'id'\n",
    "    \n",
    "    omega_2 = vp.insert(-1,'omega_2')\n",
    "    omega_2['type'] = 'LineValueSampler'\n",
    "    omega_2['execute_on'] = 'timestep_end final'\n",
    "    omega_2['variable'] = 'u1_m diffFlux_u1_m_r'   \n",
    "    omega_2['start_point'] = str(x_interface*1.001)+' 0 0'\n",
    "    omega_2['end_point'] = str(x_b)+' 0 0'\n",
    "    omega_2['num_points'] = n_plot_pts_reflector\n",
    "    omega_2['sort_by'] = 'id'  \n",
    "\n",
    "    out = root.insert(-1,'Outputs')\n",
    "    out['console'] = 'true'\n",
    "    csv = out.insert(-1,'csv')\n",
    "    csv['type'] = 'CSV'\n",
    "    csv['file_base'] = 'output'\n",
    "    csv['execute_on'] = 'final'\n",
    "    \n",
    "    debug = root.insert(-1,'Debug')\n",
    "    debug['show_var_residual_norms'] = 'true'\n",
    "\n",
    "    pyhit.write(filename, root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Problem]\n",
      "  type = FEProblem\n",
      "  coord_type = RSPHERICAL\n",
      "[]\n",
      "[Mesh]\n",
      "  [omega1]\n",
      "    type = GeneratedMeshGenerator\n",
      "    dim = 1\n",
      "    xmin = 0.0\n",
      "    xmax = 3.44\n",
      "    nx = 300\n",
      "    boundary_name_prefix = omega_1\n",
      "    elem_type = edge3\n",
      "  []\n",
      "  [omega2]\n",
      "    type = GeneratedMeshGenerator\n",
      "    dim = 1\n",
      "    xmin = 3.44\n",
      "    xmax = 10.0\n",
      "    nx = 300\n",
      "    boundary_name_prefix = omega_2\n",
      "    elem_type = edge3\n",
      "  []\n",
      "  [omega]\n",
      "    type = StitchedMeshGenerator\n",
      "    inputs = 'omega1 omega2'\n",
      "    stitch_boundaries_pairs = 'omega_1_right omega_2_left'\n",
      "    clear_stitched_boundary_ids = true\n",
      "  []\n",
      "  [mod1]\n",
      "    type = SubdomainBoundingBoxGenerator\n",
      "    input = omega\n",
      "    block_id = 1\n",
      "    block_name = omega_1\n",
      "    bottom_left = '0.0 0 0'\n",
      "    top_right = '3.44 1 0'\n",
      "  []\n",
      "  [mod2]\n",
      "    type = SubdomainBoundingBoxGenerator\n",
      "    input = mod1\n",
      "    block_id = 2\n",
      "    block_name = omega_2\n",
      "    bottom_left = '3.44 0 0'\n",
      "    top_right = '10.0 1 0'\n",
      "  []\n",
      "  [mod3]\n",
      "    type = SideSetsBetweenSubdomainsGenerator\n",
      "    input = mod2\n",
      "    primary_block = omega_1\n",
      "    paired_block = omega_2\n",
      "    new_boundary = interface_12\n",
      "  []\n",
      "  [mod4]\n",
      "    type = SideSetsAroundSubdomainGenerator\n",
      "    input = mod3\n",
      "    block = omega_1\n",
      "    normal = '-1 0 0'\n",
      "    new_boundary = omega_1_left\n",
      "  []\n",
      "  [mod5]\n",
      "    type = SideSetsAroundSubdomainGenerator\n",
      "    input = mod4\n",
      "    block = omega_2\n",
      "    normal = '1 0 0'\n",
      "    new_boundary = omega_2_right\n",
      "  []\n",
      "[]\n",
      "[Variables]\n",
      "  [u1_c]\n",
      "    block = omega_1\n",
      "    order = second\n",
      "    family = lagrange\n",
      "    initial_condition = 100000\n",
      "  []\n",
      "  [u1_m]\n",
      "    block = omega_2\n",
      "    order = second\n",
      "    family = lagrange\n",
      "    initial_condition = 100000\n",
      "  []\n",
      "[]\n",
      "[AuxVariables]\n",
      "  [diffFlux_u1_c]\n",
      "    block = omega_1\n",
      "    order = first\n",
      "    family = monomial_vec\n",
      "  []\n",
      "  [diffFlux_u1_m]\n",
      "    block = omega_2\n",
      "    order = first\n",
      "    family = monomial_vec\n",
      "  []\n",
      "  [diffFlux_u1_c_r]\n",
      "    block = omega_1\n",
      "    order = first\n",
      "    family = monomial\n",
      "  []\n",
      "  [diffFlux_u1_m_r]\n",
      "    block = omega_2\n",
      "    order = first\n",
      "    family = monomial\n",
      "  []\n",
      "[]\n",
      "[Kernels]\n",
      "  [diffusion_term_u1_c]\n",
      "    type = DiffusionTerm\n",
      "    block = omega_1\n",
      "    variable = u1_c\n",
      "    diffCoeff = 1.84\n",
      "  []\n",
      "  [diffusion_term_u1_m]\n",
      "    type = DiffusionTerm\n",
      "    block = omega_2\n",
      "    variable = u1_m\n",
      "    diffCoeff = 1.64\n",
      "  []\n",
      "  [fission_source_u1_c]\n",
      "    type = FissionSource\n",
      "    block = omega_1\n",
      "    variable = u1_c\n",
      "    Sigma_nu = 0.174\n",
      "  []\n",
      "  [abs_u1_c]\n",
      "    type = SourceTermG1\n",
      "    block = omega_1\n",
      "    variable = u1_c\n",
      "    sigma_sa = -0.0745\n",
      "  []\n",
      "  [abs_u1_m]\n",
      "    type = SourceTermG1\n",
      "    block = omega_2\n",
      "    variable = u1_m\n",
      "    sigma_sa = -0.00534\n",
      "  []\n",
      "[]\n",
      "[InterfaceKernels]\n",
      "  [scalar_flux_continuity_u1]\n",
      "    type = InterfaceDiffusion\n",
      "    variable = u1_c\n",
      "    neighbor_var = u1_m\n",
      "    boundary = interface_12\n",
      "    D = 1.84\n",
      "    D_neighbor = 1.64\n",
      "  []\n",
      "  [scalar_flux_jump_u1]\n",
      "    type = InterfacePartition\n",
      "    variable = u1_c\n",
      "    neighbor_var = u1_m\n",
      "    boundary = interface_12\n",
      "    kCoeff = 1\n",
      "  []\n",
      "[]\n",
      "[AuxKernels]\n",
      "  [diffusion_flux_u1_c]\n",
      "    type = HeatFlux\n",
      "    block = omega_1\n",
      "    field = u1_c\n",
      "    thCondCoeff = 1.84\n",
      "    variable = diffFlux_u1_c\n",
      "    execute_on = timestep_end\n",
      "  []\n",
      "  [diffusion_flux_u1_m]\n",
      "    type = HeatFlux\n",
      "    block = omega_2\n",
      "    field = u1_m\n",
      "    thCondCoeff = 1.64\n",
      "    variable = diffFlux_u1_m\n",
      "    execute_on = timestep_end\n",
      "  []\n",
      "  [diffusion_flux_u1_c_r]\n",
      "    type = VectorVariableComponentAux\n",
      "    block = omega_1\n",
      "    vector_variable = diffFlux_u1_c\n",
      "    component = x\n",
      "    variable = diffFlux_u1_c_r\n",
      "    execute_on = timestep_end\n",
      "  []\n",
      "  [diffusion_flux_u1_m_r]\n",
      "    type = VectorVariableComponentAux\n",
      "    block = omega_2\n",
      "    vector_variable = diffFlux_u1_m\n",
      "    component = x\n",
      "    variable = diffFlux_u1_m_r\n",
      "    execute_on = timestep_end\n",
      "  []\n",
      "[]\n",
      "[BCs]\n",
      "  [entry_u1]\n",
      "    type = NeumannBC\n",
      "    variable = u1_c\n",
      "    boundary = omega_1_left\n",
      "    value = 0\n",
      "  []\n",
      "  [exit_u1]\n",
      "    type = VacuumBC\n",
      "    variable = u1_m\n",
      "    boundary = omega_2_right\n",
      "  []\n",
      "[]\n",
      "[Functions]\n",
      "  [refFluxFunc]\n",
      "    type = ParsedFunction\n",
      "    value = flux_ref\n",
      "    vars = flux_ref\n",
      "    vals = 0.0\n",
      "  []\n",
      "[]\n",
      "[Executioner]\n",
      "  type = Steady\n",
      "  solve_type = PJFNK\n",
      "  petsc_options_iname = '-pc_type -pc_hypre_type'\n",
      "  petsc_options_value = 'hypre boomeramg'\n",
      "  l_max_its = 20\n",
      "  l_tol = 1e-05\n",
      "  nl_max_its = 15\n",
      "  nl_rel_tol = 1e-08\n",
      "  nl_abs_tol = 1e-08\n",
      "[]\n",
      "[VectorPostprocessors]\n",
      "  [omega_1]\n",
      "    type = LineValueSampler\n",
      "    execute_on = 'timestep_end final'\n",
      "    variable = 'u1_c diffFlux_u1_c_r'\n",
      "    start_point = '0.0 0 0'\n",
      "    end_point = '3.43656 0 0'\n",
      "    num_points = 601\n",
      "    sort_by = id\n",
      "  []\n",
      "  [omega_2]\n",
      "    type = LineValueSampler\n",
      "    execute_on = 'timestep_end final'\n",
      "    variable = 'u1_m diffFlux_u1_m_r'\n",
      "    start_point = '3.4434399999999994 0 0'\n",
      "    end_point = '10.0 0 0'\n",
      "    num_points = 601\n",
      "    sort_by = id\n",
      "  []\n",
      "[]\n",
      "[Outputs]\n",
      "  console = true\n",
      "  [csv]\n",
      "    type = CSV\n",
      "    file_base = output\n",
      "    execute_on = final\n",
      "  []\n",
      "[]\n",
      "[Debug]\n",
      "  show_var_residual_norms = true\n",
      "[]\n"
     ]
    }
   ],
   "source": [
    "write_input_file_1d_coupled(pjfnk=True,filename=inputFileName)\n",
    "!cat input_2Domain.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "In ReplicatedMesh::stitch_meshes:\n",
      "This mesh has 1 nodes on boundary 1.\n",
      "Other mesh has 1 nodes on boundary 0.\n",
      "Minimum edge length on both surfaces is 0.0114667.\n",
      "In ReplicatedMesh::stitch_meshes:\n",
      "Found 1 matching nodes.\n",
      "\n",
      "Framework Information:\n",
      "MOOSE Version:           git commit b98ea2c450 on 2021-09-23\n",
      "LibMesh Version:         \n",
      "PETSc Version:           3.15.1\n",
      "SLEPc Version:           3.15.1\n",
      "Current Time:            Mon May  9 11:31:43 2022\n",
      "Executable Timestamp:    Mon May  9 11:31:32 2022\n",
      "\n",
      "Parallelism:\n",
      "  Num Processors:          1\n",
      "  Num Threads:             1\n",
      "\n",
      "Mesh: \n",
      "  Parallel Type:           replicated\n",
      "  Mesh Dimension:          1\n",
      "  Spatial Dimension:       1\n",
      "  Nodes:                   1201\n",
      "  Elems:                   600\n",
      "  Num Subdomains:          2\n",
      "\n",
      "Nonlinear System:\n",
      "  Num DOFs:                1202\n",
      "  Num Local DOFs:          1202\n",
      "  Variables:               \"u1_c\" \"u1_m\" \n",
      "  Finite Element Types:    \"LAGRANGE\" \"LAGRANGE\" \n",
      "  Approximation Orders:    \"SECOND\" \"SECOND\" \n",
      "\n",
      "Auxiliary System:\n",
      "  Num DOFs:                2400\n",
      "  Num Local DOFs:          2400\n",
      "  Variables:               \"diffFlux_u1_c\" \"diffFlux_u1_m\" \"diffFlux_u1_c_r\" \"diffFlux_u1_m_r\" \n",
      "  Finite Element Types:    \"MONOMIAL_VEC\" \"MONOMIAL_VEC\" \"MONOMIAL\" \"MONOMIAL\" \n",
      "  Approximation Orders:    \"FIRST\" \"FIRST\" \"FIRST\" \"FIRST\" \n",
      "\n",
      "Execution Information:\n",
      "  Executioner:             Steady\n",
      "  Solver Mode:             Preconditioned JFNK\n",
      "  PETSc Preconditioner:    hypre boomeramg \n",
      "\n",
      "\n",
      "\u001b[33m\n",
      "*** Warning ***\n",
      "/home/andrew/projects/neutron__transport/input_2Domain.hit:158: unused parameter 'AuxKernels/diffusion_flux_u1_c/thCondCoeff'\n",
      "/home/andrew/projects/neutron__transport/input_2Domain.hit:166: unused parameter 'AuxKernels/diffusion_flux_u1_m/thCondCoeff'\n",
      "\u001b[39m\n",
      " 0 Nonlinear |R| = \u001b[32m6.283209e+07\u001b[39m\n",
      "    |residual|_2 of individual variables:\n",
      "                       u1_c: 171227\n",
      "                       u1_m: 6.28319e+07\n",
      "      0 Linear |R| = \u001b[32m6.283209e+07\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m1.596180e+07\u001b[39m\n",
      "      2 Linear |R| = \u001b[32m7.912929e+06\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m5.832635e+06\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m5.334618e+05\u001b[39m\n",
      "      5 Linear |R| = \u001b[32m1.002458e+05\u001b[39m\n",
      "      6 Linear |R| = \u001b[32m3.591284e+03\u001b[39m\n",
      "      7 Linear |R| = \u001b[32m2.933574e+02\u001b[39m\n",
      " 1 Nonlinear |R| = \u001b[32m8.750396e+06\u001b[39m\n",
      "    |residual|_2 of individual variables:\n",
      "                       u1_c: 1.96558e+06\n",
      "                       u1_m: 8.52678e+06\n",
      "      0 Linear |R| = \u001b[32m8.750396e+06\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m5.459400e+04\u001b[39m\n",
      "      2 Linear |R| = \u001b[33m5.196767e+04\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m1.592378e+03\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m5.479529e+01\u001b[39m\n",
      " 2 Nonlinear |R| = \u001b[32m1.803688e+03\u001b[39m\n",
      "    |residual|_2 of individual variables:\n",
      "                       u1_c: 1077.17\n",
      "                       u1_m: 1446.72\n",
      "      0 Linear |R| = \u001b[32m1.803688e+03\u001b[39m\n",
      "      1 Linear |R| = \u001b[32m8.343264e+01\u001b[39m\n",
      "      2 Linear |R| = \u001b[32m1.699492e+01\u001b[39m\n",
      "      3 Linear |R| = \u001b[32m1.299450e+00\u001b[39m\n",
      "      4 Linear |R| = \u001b[32m7.975608e-03\u001b[39m\n",
      " 3 Nonlinear |R| = \u001b[32m1.829598e-02\u001b[39m\n",
      "    |residual|_2 of individual variables:\n",
      "                       u1_c: 0.0122271\n",
      "                       u1_m: 0.0136103\n",
      "\u001b[32m Solve Converged!\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "!./neutron__transport-opt -i input_2Domain.hit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Show FEM Solution'''\n",
    "\n",
    "import pandas as pd\n",
    "df1 = pd.read_csv('output_omega_1_0002.csv')\n",
    "df2 = pd.read_csv('output_omega_2_0002.csv')\n",
    "df_list = [df1,df2]\n",
    "save_name = \"2Domain.png\"\n",
    "\n",
    "#display(df1)\n",
    "#display(df2)\n",
    "\n",
    "x_list = [df1[\"x\"],df2[\"x\"]]\n",
    "y_list = [[df1[\"diffFlux_u1_c_r\"],df1[\"u1_c\"]],\n",
    "          [df2[\"diffFlux_u1_m_r\"],df2[\"u1_m\"]]]\n",
    "labels = [\"u1'\",\"u1\"]\n",
    "domain = [\"core\",\"reflector\"]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "for i in range(1):\n",
    "    for j,domain in enumerate([\"c\",\"m\"]):\n",
    "        field = \"u\"+str(i+1)+\"_\"\n",
    "        plt.plot(df_list[j][\"x\"],df_list[j][field+domain],label=field+domain)\n",
    "        \n",
    "    for j,domain in enumerate([\"c\",\"m\"]):\n",
    "        field = \"u\"+str(i+1)+\"_\"\n",
    "        plt.plot(df_list[j][\"x\"],df_list[j][\"diffFlux_u\"+str(i+1)+\"_\"+domain+\"_r\"],label=field+\"'\"+domain)\n",
    "        \n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.xlabel(\"r [cm]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "x_total = pd.concat([df1[\"x\"], df2[\"x\"]])\n",
    "u1 = pd.concat([df1[\"u1_c\"] ,df2[\"u1_m\"]])\n",
    "u1_prime = pd.concat([df1[\"diffFlux_u1_c_r\"] , df2[\"diffFlux_u1_m_r\"]])\n",
    "\n",
    "data_list = [u1,u1_prime]\n",
    "labels = [\"u1\",\"q1\"]\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "for i,data in enumerate(data_list):\n",
    "    plt.plot(x_total,data,label=labels[i])\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.xlabel(\"r [cm]\")\n",
    "plt.savefig(\"1Group.png\",dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}