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nonlinear_elasticity_global_rom.cpp
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// libROM MFEM Example: parametric ROM for nonlinear elasticity problem (adapted from ex10p.cpp)
//
// Compile with: make nonlinear_elasticity_global_rom
//
// Description: This examples solves a time dependent nonlinear elasticity
// problem of the form dv/dt = H(x) + S v, dx/dt = v, where H is a
// hyperelastic model and S is a viscosity operator of Laplacian
// type. The geometry of the domain is assumed to be as follows:
//
// +---------------------+
// boundary --->| |
// attribute 1 | |
// (fixed) +---------------------+
//
// The example demonstrates the use of hyper reduction to solve a
// nonlinear elasticity problem. Time integration is done with various
// explicit time integrator solvers. The basis for the velocity field
// is either constructed using a separate velocity basis or using the
// displacement basis. It is possible to set the initial condition in
// terms of either velocity or deformation. The velocity initial condition
// works better when both velocity and displacement bases are used. The
// deformation initial condition is better when only the displacement
// basis is used. The input flag -sc controls the scaling of the initial
// condition applied. This is what parameterizes the ROM. If the scaling
// factor is within the range +-10%, the results are generally accurate.
// =================================================================================
//
// Sample runs and results for parametric ROM using displacement basis, velocity basis
// and nonlinear term basis, with velocity initial condition:
//
// Offline phase:
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 0.9 -id 0
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 1.1 -id 1
//
// Merge phase:
// ./nonlinear_elasticity_global_rom -merge -ns 2 -dt 0.01 -tf 5.0
//
// Create FOM comparison data:
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 1.0 -id 2
// Output message:
// Elapsed time for time integration loop 9.17153
// Elapsed time for entire simulation 10.0001
//
// Online phase with full sampling:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype gnat -rvdim 40 -rxdim 10 -hdim 71 -nsr 1170 -sc 1.0
// Output message:
// Elapsed time for time integration loop 7.03877
// Relative error of ROM position (x) at t_final: 5 is 0.000231698
// Relative error of ROM velocity (v) at t_final: 5 is 0.466941
// Elapsed time for entire simulation 8.98334
//
// Online phase with strong hyper-reduction, using GNAT (over-sampled DEIM):
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype gnat -rvdim 40 -rxdim 10 -hdim 71 -nsr 100 -sc 1.0
// Output message:
// Elapsed time for time integration loop 4.18114
// Relative error of ROM position (x) at t_final: 5 is 0.00209877
// Relative error of ROM velocity (v) at t_final: 5 is 1.39472
// Elapsed time for entire simulation 4.52802
//
// Online phase with strong hyper-reduction, using QDEIM:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype qdeim -rvdim 40 -rxdim 10 -hdim 71 -nsr 100 -sc 1.0
// Output message:
// Elapsed time for time integration loop 4.2972
// Relative error of ROM position (x) at t_final: 5 is 0.00188458
// Relative error of ROM velocity (v) at t_final: 5 is 0.978726
// Elapsed time for entire simulation 5.33154
//
// Online phase with EQP hyper-reduction
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -eqp -ns 2 -ntw 50 -rvdim 40 -rxdim 10 -hdim 1 -sc 1.0
// Output message:
// Elapsed time for time integration loop 2.70006
// Relative error of ROM position (x) at t_final: 5 is 0.00169666
// Relative error of ROM velocity (v) at t_final: 5 is 17.71
// Elapsed time for entire simulation 831.216
//
// Online phase with EQP hyper-reduction and subsampling of snapshots
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -eqp -ns 2 -ntw 50 -rvdim 40 -rxdim 10 -hdim 1 -sc 1.0 -sbs 10
// Output message:
// Elapsed time for time integration loop 0.552546
// Relative error of ROM position (x) at t_final: 5 is 0.00247479
// Relative error of ROM velocity (v) at t_final: 5 is 1.33349
// Elapsed time for entire simulation 11.469
//
// =================================================================================
//
// Sample runs and results for parametric ROM using only displacement basis
// and nonlinear term basis:
// Offline phase:
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 0.9 -xbo -def-ic -id 0
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 1.1 -xbo -def-ic -id 1
//
// Merge phase:
// ./nonlinear_elasticity_global_rom -merge -ns 2 -dt 0.01 -tf 5.0 -xbo
//
// Create FOM comparison data:
// ./nonlinear_elasticity_global_rom -offline -dt 0.01 -tf 5.0 -s 14 -vs 100 -sc 1.0 -xbo -def-ic -id 2
// Output message:
// Elapsed time for time integration loop 9.61062
// Elapsed time for entire simulation 10.3806
//
// Online phase with full sampling:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype gnat -rxdim 57 -hdim 183 -nsr 1170 -sc 1.0 -xbo -def-ic
// Output message:
// Elapsed time for time integration loop 8.43858
// Relative error of ROM position (x) at t_final: 5 is 7.08272e-05
// Relative error of ROM velocity (v) at t_final: 5 is 0.00387647
// Elapsed time for entire simulation 24.7245
//
// Online phase with strong hyper reduction, using GNAT (over-sampled DEIM):
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype gnat -rxdim 2 -hdim 4 -nsr 10 -sc 1.0 -xbo -def-ic
// Output message:
// Elapsed time for time integration loop 0.507339
// Relative error of ROM position (x) at t_final: 5 is 0.0130818
// Relative error of ROM velocity (v) at t_final: 5 is 0.979978
// Elapsed time for entire simulation 0.583618
//
// Online phase with strong hyper reduction, using QDEIM:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -hyp -hrtype qdeim -rxdim 2 -hdim 4 -nsr 10 -sc 1.0 -xbo -def-ic
// Output message:
// Elapsed time for time integration loop 0.504657
// Relative error of ROM position (x) at t_final: 5 is 0.00883079
// Relative error of ROM velocity (v) at t_final: 5 is 1.26721
// Elapsed time for entire simulation 0.581446
//
// Online phase with EQP hyper reduction:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -eqp -ns 2 -rxdim 2 -hdim 1 -ntw 25 -sc 1.00 -xbo -def-ic
// Elapsed time for time integration loop 0.144368
// Relative error of ROM position (x) at t_final: 5 is 0.0189361
// Relative error of ROM velocity (v) at t_final: 5 is 0.830724
// Elapsed time for entire simulation 4.97996
//
// Online phase with EQP hyper reduction and subsampling of snapshots:
// ./nonlinear_elasticity_global_rom -online -dt 0.01 -tf 5.0 -s 14 -vs 100 -eqp -ns 2 -rxdim 2 -hdim 1 -ntw 25 -sc 1.00 -xbo -def-ic -sbs 10
// Elapsed time for time integration loop 0.0141128
// Relative error of ROM position (x) at t_final: 5 is 0.0243952
// Relative error of ROM velocity (v) at t_final: 5 is 0.986434
// Elapsed time for entire simulation 0.782108
//
// This example runs in parallel with MPI, by using the same number of MPI ranks
// in all phases (offline, merge, online).
#include "mfem.hpp"
#include "linalg/Vector.h"
#include "linalg/BasisGenerator.h"
#include "linalg/BasisReader.h"
#include "linalg/NNLS.h"
#include "hyperreduction/Hyperreduction.h"
#include "mfem/SampleMesh.hpp"
#include "mfem/Utilities.hpp"
#include <memory>
#include <cmath>
#include <limits>
using namespace std;
using namespace mfem;
#include "nonlinear_elasticity_global_rom_eqp.hpp"
class RomOperator : public TimeDependentOperator
{
private:
int rxdim, rvdim, hdim;
int nsamp_H;
double current_dt;
bool oversampling;
CAROM::Matrix *V_v_sp, *V_x_sp;
CAROM::Vector *V_xTv_0_sp;
CAROM::Matrix *V_xTV_v_sp;
CAROM::Matrix *V_v_sp_dist;
CAROM::Vector *psp_librom, *psp_v_librom;
CAROM::Vector *Vx_librom_temp;
Vector *psp;
Vector *psp_x;
Vector *psp_v;
Vector *Vx_temp;
mutable Vector zH;
mutable CAROM::Vector zX;
mutable Vector zX_MFEM;
mutable CAROM::Vector zN;
const CAROM::Matrix *Hsinv;
mutable CAROM::Vector *z_librom;
mutable Vector z;
mutable Vector z_x;
mutable Vector z_v;
CAROM::Vector *v0_fom_librom, *v0_librom, *V_xTv_0;
CAROM::Matrix *V_xTV_v;
bool hyperreduce;
bool x_base_only;
CAROM::Vector *pfom_librom, *pfom_v_librom;
Vector *pfom;
Vector *pfom_x;
Vector *pfom_v;
mutable Vector *zfom_x;
mutable Vector *zfom_v;
CAROM::Vector *zfom_x_librom;
CAROM::SampleMeshManager *smm;
CAROM::Vector *z_v_librom;
CAROM::Vector *z_x_librom;
// Data for EQP
bool eqp;
const IntegrationRule *ir_eqp;
std::vector<double> eqp_rw;
std::vector<int> eqp_qp;
Vector eqp_coef;
Vector eqp_DS_coef;
const bool fastIntegration = true;
ElemMatrices *em;
CAROM::Matrix eqp_lifting;
std::vector<int> eqp_liftDOFs;
mutable CAROM::Vector eqp_lifted;
int rank;
NeoHookeanModel *model;
protected:
CAROM::Matrix *S_hat;
CAROM::Vector *S_hat_v0;
Vector *S_hat_v0_temp;
CAROM::Vector *S_hat_v0_temp_librom;
CAROM::Matrix *M_hat;
CAROM::Matrix *M_hat_inv;
const std::shared_ptr<CAROM::Matrix> U_H;
HyperelasticOperator *fomSp;
CGSolver M_hat_solver; // Krylov solver for inverting the reduced mass matrix M_hat
HypreSmoother M_hat_prec; // Preconditioner for the reduced mass matrix M_hat
public:
HyperelasticOperator *fom;
RomOperator(HyperelasticOperator *fom_,
HyperelasticOperator *fomSp_, const int rvdim_, const int rxdim_,
const int hdim_, CAROM::SampleMeshManager *smm_, const Vector *v0_,
const Vector *x0_, const Vector v0_fom_,
const std::shared_ptr<CAROM::Matrix> V_v_,
const std::shared_ptr<CAROM::Matrix> V_x_,
const std::shared_ptr<CAROM::Matrix> U_H_,
const CAROM::Matrix *Hsinv_, const int myid, const bool oversampling_,
const bool hyperreduce_, const bool x_base_only_, const bool use_eqp,
CAROM::Vector *eqpSol,
const IntegrationRule *ir_eqp_, NeoHookeanModel *model_);
virtual void Mult(const Vector &y, Vector &dy_dt) const;
void Mult_Hyperreduced(const Vector &y, Vector &dy_dt) const;
void Mult_FullOrder(const Vector &y, Vector &dy_dt) const;
void SetEQP(CAROM::Vector *eqpSol);
CAROM::Matrix V_v, V_x, V_vTU_H;
const Vector *x0;
const Vector *v0;
Vector v0_fom;
virtual ~RomOperator();
};
/** Function representing the elastic energy density for the given hyperelastic
model+deformation. Used in HyperelasticOperator::GetElasticEnergyDensity. */
class ElasticEnergyCoefficient : public Coefficient
{
private:
HyperelasticModel &model;
const ParGridFunction &x;
DenseMatrix J;
public:
ElasticEnergyCoefficient(HyperelasticModel &m, const ParGridFunction &x_)
: model(m), x(x_) {}
virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
virtual ~ElasticEnergyCoefficient() {}
};
void InitialDeformationIC1(const Vector &x, Vector &y);
void InitialVelocityIC1(const Vector &x, Vector &v);
void InitialDeformationIC2(const Vector &x, Vector &y);
void InitialVelocityIC2(const Vector &x, Vector &v);
void visualize(ostream &out, ParMesh *mesh, ParGridFunction *deformed_nodes,
ParGridFunction *field, const char *field_name = NULL,
bool init_vis = false);
// TODO: move this to the library?
void MergeBasis(const int dimFOM, const int nparam, const int max_num_snapshots,
std::string name, bool squareSV)
{
MFEM_VERIFY(nparam > 0, "Must specify a positive number of parameter sets");
bool update_right_SV = false;
bool isIncremental = false;
CAROM::Options options(dimFOM, nparam * max_num_snapshots, 1, update_right_SV);
CAROM::BasisGenerator generator(options, isIncremental, "basis" + name);
for (int paramID = 0; paramID < nparam; ++paramID)
{
std::string snapshot_filename = "basis" + std::to_string(
paramID) + "_" + name + "_snapshot";
generator.loadSamples(snapshot_filename, "snapshot");
}
generator.endSamples(); // save the merged basis file
int cutoff = 0;
generator.finalSummary(1e-7, cutoff, "mergedSV_" + name + ".txt", 0, squareSV);
}
const CAROM::Matrix *GetSnapshotMatrix(const int dimFOM, const int nparam,
const int max_num_snapshots, std::string name)
{
MFEM_VERIFY(nparam > 0, "Must specify a positive number of parameter sets");
bool update_right_SV = false;
bool isIncremental = false;
CAROM::Options options(dimFOM, nparam * max_num_snapshots, 1, update_right_SV);
CAROM::BasisGenerator generator(options, isIncremental, "basis" + name);
for (int paramID = 0; paramID < nparam; ++paramID)
{
std::string snapshot_filename = "basis" + std::to_string(
paramID) + "_" + name + "_snapshot";
generator.loadSamples(snapshot_filename, "snapshot");
}
// TODO: this deep copy is inefficient, just to get around generator owning the matrix.
CAROM::Matrix *s = new CAROM::Matrix(*generator.getSnapshotMatrix());
return s;
// return generator.getSnapshotMatrix(); // BUG: the matrix is deleted when generator goes out of scope.
}
// TODO: remove this by making online computation serial?
void BroadcastUndistributedRomVector(CAROM::Vector *v)
{
const int N = v->dim();
MFEM_VERIFY(N > 0, "");
double *d = new double[N];
MFEM_VERIFY(d != 0, "");
for (int i = 0; i < N; ++i)
d[i] = (*v)(i);
MPI_Bcast(d, N, MPI_DOUBLE, 0, MPI_COMM_WORLD);
for (int i = 0; i < N; ++i)
(*v)(i) = d[i];
delete[] d;
}
// Scaling factor for parameterization
double s = 1.0;
int main(int argc, char *argv[])
{
// 1. Initialize MPI.
int num_procs, myid;
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
// 2. Parse command-line options.
const char *mesh_file = "../data/beam-quad.mesh";
int ser_ref_levels = 2;
int par_ref_levels = 0;
int order = 2;
int ode_solver_type = 14; // RK4
int vis_steps = 1;
double t_final = 15.0;
double dt = 0.03;
double visc = 1e-2;
double mu = 0.25;
double K = 5.0;
bool adaptive_lin_rtol = true;
bool visualization = true;
bool visit = false;
bool def_ic = false;
// ROM parameters
bool offline = false;
bool merge = false;
bool online = false;
bool use_eqp = false;
bool writeSampleMesh = false;
bool hyperreduce = true;
bool x_base_only = false;
int num_samples_req = -1;
const char *samplingType = "gnat";
bool squareSV = true;
int nsets = 0;
int id_param = 0;
// Number of basis vectors to use
int rxdim = -1;
int rvdim = -1;
int hdim = -1;
bool preconditionNNLS = false;
double tolNNLS = 1.0e-14;
int maxNNLSnnz = 0;
// Number of time windows
int n_windows = 0;
// Subsampling steps
int snap_step = 1;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
"Number of times to refine the mesh uniformly in serial.");
args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
"Number of times to refine the mesh uniformly in parallel.");
args.AddOption(&order, "-o", "--order",
"Order (degree) of the finite elements.");
args.AddOption(&ode_solver_type, "-s", "--ode-solver",
"ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3,\n\t"
" 11 - Forward Euler, 12 - RK2,\n\t"
" 13 - RK3 SSP, 14 - RK4."
" 22 - Implicit Midpoint Method,\n\t"
" 23 - SDIRK23 (A-stable), 24 - SDIRK34");
args.AddOption(&t_final, "-tf", "--t-final",
"Final time; start time is 0.");
args.AddOption(&dt, "-dt", "--time-step",
"Time step.");
args.AddOption(&visc, "-v", "--viscosity",
"Viscosity coefficient.");
args.AddOption(&mu, "-mu", "--shear-modulus",
"Shear modulus in the Neo-Hookean hyperelastic model.");
args.AddOption(&K, "-K", "--bulk-modulus",
"Bulk modulus in the Neo-Hookean hyperelastic model.");
args.AddOption(&adaptive_lin_rtol, "-alrtol", "--adaptive-lin-rtol",
"-no-alrtol", "--no-adaptive-lin-rtol",
"Enable or disable adaptive linear solver rtol.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.AddOption(&visit, "-visit", "--visit-datafiles", "-no-visit",
"--no-visit-datafiles",
"Save data files for VisIt (visit.llnl.gov) visualization.");
args.AddOption(&vis_steps, "-vs", "--visualization-steps",
"Visualize every n-th timestep.");
args.AddOption(&nsets, "-ns", "--nset", "Number of parametric snapshot sets");
args.AddOption(&offline, "-offline", "--offline", "-no-offline", "--no-offline",
"Enable or disable the offline phase.");
args.AddOption(&online, "-online", "--online", "-no-online", "--no-online",
"Enable or disable the online phase.");
args.AddOption(&merge, "-merge", "--merge", "-no-merge", "--no-merge",
"Enable or disable the merge phase.");
args.AddOption(&squareSV, "-sqsv", "--square-sv", "-no-sqsv", "--no-square-sv",
"Use singular values squared in energy fraction.");
args.AddOption(&samplingType, "-hrtype", "--hrsamplingtype",
"Sampling type for hyperreduction.");
args.AddOption(&num_samples_req, "-nsr", "--nsr",
"number of samples we want to select for the sampling algorithm.");
args.AddOption(&rxdim, "-rxdim", "--rxdim",
"Basis dimension for displacement solution space.");
args.AddOption(&rvdim, "-rvdim", "--rvdim",
"Basis dimension for velocity solution space.");
args.AddOption(&hdim, "-hdim", "--hdim",
"Basis dimension for the nonlinear term.");
args.AddOption(&id_param, "-id", "--id", "Parametric index");
args.AddOption(&hyperreduce, "-hyp", "--hyperreduce", "-no-hyp",
"--no-hyperreduce", "Hyper reduce nonlinear term");
args.AddOption(&x_base_only, "-xbo", "--xbase-only", "-no-xbo",
"--not-xbase-only", "Use the displacement (X) basis to approximate velocity.");
args.AddOption(&def_ic, "-def-ic", "--deformation-ic", "-vel-ic",
"--velocity-ic",
"Use a deformation-, or velocity initial condition. Default is velocity IC.");
args.AddOption(&s, "-sc", "--scaling", "Scaling factor for initial condition.");
args.AddOption(&use_eqp, "-eqp", "--eqp", "-no-eqp", "--no-eqp",
"Use EQP instead of DEIM for the hyperreduction.");
args.AddOption(&writeSampleMesh, "-smesh", "--sample-mesh", "-no-smesh",
"--no-sample-mesh", "Write the sample mesh to file.");
args.AddOption(&preconditionNNLS, "-preceqp", "--preceqp", "-no-preceqp",
"--no-preceqp", "Precondition the NNLS system for EQP.");
args.AddOption(&tolNNLS, "-tolnnls", "--tol-nnls",
"Tolerance for NNLS solver.");
args.AddOption(&maxNNLSnnz, "-maxnnls", "--max-nnls",
"Maximum nnz for NNLS");
args.AddOption(&n_windows, "-ntw", "--n-time-windows",
"Number of time windows. Default is 0");
args.AddOption(&snap_step, "-sbs", "--subsampling-step",
"Subsamble every n-th snapshot. Default is 1, meaning no subsampling");
args.Parse();
if (!args.Good())
{
if (myid == 0)
{
args.PrintUsage(cout);
}
MPI_Finalize();
return 1;
}
if (myid == 0)
{
args.PrintOptions(cout);
}
const bool check = (offline && !merge && !online) || (!offline && merge
&& !online) || (!offline && !merge && online);
MFEM_VERIFY(check, "only one of offline, merge, or online must be true!");
StopWatch solveTimer, totalTimer;
totalTimer.Start();
// 3. Read the serial mesh from the given mesh file on all processors. We can
// handle triangular, quadrilateral, tetrahedral and hexahedral meshes
// with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
// 4. Define the ODE solver used for time integration. Several implicit
// singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
// explicit Runge-Kutta methods are available.
ODESolver *ode_solver;
switch (ode_solver_type)
{
// Implicit L-stable methods
// To be added...
// Explicit methods
case 11:
ode_solver = new ForwardEulerSolver;
break;
case 12:
ode_solver = new RK2Solver(0.5);
break; // midpoint method
case 13:
ode_solver = new RK3SSPSolver;
break;
case 14:
ode_solver = new RK4Solver;
break;
case 15:
ode_solver = new GeneralizedAlphaSolver(0.5);
break;
// Implicit A-stable methods (not L-stable)
// To be added...
default:
if (myid == 0)
{
cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
}
delete mesh;
MPI_Finalize();
return 3;
}
// 5. Refine the mesh in serial to increase the resolution. In this example
// we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
// a command-line parameter.
for (int lev = 0; lev < ser_ref_levels; lev++)
{
mesh->UniformRefinement();
}
// 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
// this mesh further in parallel to increase the resolution. Once the
// parallel mesh is defined, the serial mesh can be deleted.
ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
delete mesh;
for (int lev = 0; lev < par_ref_levels; lev++)
{
pmesh->UniformRefinement();
}
// 7. Define the parallel vector finite element spaces representing the mesh
// deformation x_gf, the velocity v_gf, and the initial configuration,
// x_ref. Define also the elastic energy density, w_gf, which is in a
// discontinuous higher-order space. Since x and v are integrated in time
// as a system, we group them together in block vector vx, on the unique
// parallel degrees of freedom, with offsets given by array true_offset.
H1_FECollection fe_coll(order, dim);
ParFiniteElementSpace fespace(pmesh, &fe_coll, dim);
HYPRE_BigInt glob_size = fespace.GlobalTrueVSize();
if (myid == 0)
{
cout << "Number of velocity/deformation unknowns: " << glob_size << endl;
}
int true_size = fespace.TrueVSize();
Array<int> true_offset(3);
true_offset[0] = 0;
true_offset[1] = true_size;
true_offset[2] = 2 * true_size;
BlockVector vx(true_offset);
ParGridFunction v_gf, x_gf;
// Associate a FiniteElementSpace and true-dof data with the GridFunctions.
v_gf.MakeTRef(&fespace, vx, true_offset[0]);
x_gf.MakeTRef(&fespace, vx, true_offset[1]);
ParGridFunction x_ref(&fespace);
pmesh->GetNodes(x_ref);
L2_FECollection w_fec(order + 1, dim);
ParFiniteElementSpace w_fespace(pmesh, &w_fec);
ParGridFunction w_gf(&w_fespace);
// Basis params
bool update_right_SV = false;
bool isIncremental = false;
const std::string basisFileName = "basis" + std::to_string(id_param);
int max_num_snapshots = int(t_final / dt) + 2;
// The merge phase
if (merge)
{
totalTimer.Clear();
totalTimer.Start();
// Merge bases
if (x_base_only == false)
{
MergeBasis(true_size, nsets, max_num_snapshots, "V", squareSV);
}
MergeBasis(true_size, nsets, max_num_snapshots, "X", squareSV);
MergeBasis(true_size, nsets, max_num_snapshots, "H", squareSV);
totalTimer.Stop();
if (myid == 0)
{
printf("Elapsed time for merging and building ROM basis: %e second\n",
totalTimer.RealTime());
}
MPI_Finalize();
return 0;
}
// 8. Set the initial conditions for v_gf, x_gf and vx, and define the
// boundary conditions on a beam-like mesh (see description above).
VectorFunctionCoefficient *velo = 0;
VectorFunctionCoefficient *deform = 0;
if (def_ic)
{
velo = new VectorFunctionCoefficient(dim, InitialVelocityIC2);
}
else
{
velo = new VectorFunctionCoefficient(dim, InitialVelocityIC1);
}
v_gf.ProjectCoefficient(*velo);
v_gf.SetTrueVector();
if (def_ic)
{
deform = new VectorFunctionCoefficient(dim, InitialDeformationIC2);
}
else
{
deform = new VectorFunctionCoefficient(dim, InitialDeformationIC1);
}
x_gf.ProjectCoefficient(*deform);
x_gf.SetTrueVector();
v_gf.SetFromTrueVector();
x_gf.SetFromTrueVector();
Array<int> ess_bdr(fespace.GetMesh()->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed
Array<int> ess_tdof_list;
fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
// Store initial vx
BlockVector vx0 = BlockVector(vx);
BlockVector vx_diff = BlockVector(vx);
// Reduced order solution
Vector *wMFEM = 0;
CAROM::Vector *w = 0;
CAROM::Vector *w_v = 0;
CAROM::Vector *w_x = 0;
// Initialize reconstructed solution
Vector *v_rec = new Vector(v_gf.GetTrueVector());
Vector *x_rec = new Vector(x_gf.GetTrueVector());
CAROM::Vector *v_rec_librom = new CAROM::Vector(v_rec->GetData(), v_rec->Size(),
true, false);
CAROM::Vector *x_rec_librom = new CAROM::Vector(x_rec->GetData(), x_rec->Size(),
true, false);
// 9. Initialize the hyperelastic operator, the GLVis visualization and print
// the initial energies.
HyperelasticOperator oper(fespace, ess_tdof_list, visc, mu, K);
NeoHookeanModel *model = new NeoHookeanModel(mu, K);
HyperelasticOperator *soper = 0;
// Fill dvdt and dxdt
Vector dvxdt(true_size * 2);
Vector dvdt(dvxdt.GetData() + 0, true_size);
Vector dxdt(dvxdt.GetData() + true_size, true_size);
socketstream vis_v, vis_w;
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
vis_v.open(vishost, visport);
vis_v.precision(8);
visualize(vis_v, pmesh, &x_gf, &v_gf, "Velocity", true);
// Make sure all ranks have sent their 'v' solution before initiating
// another set of GLVis connections (one from each rank)
MPI_Barrier(pmesh->GetComm());
vis_w.open(vishost, visport);
if (vis_w)
{
oper.GetElasticEnergyDensity(x_gf, w_gf);
vis_w.precision(8);
visualize(vis_w, pmesh, &x_gf, &w_gf, "Elastic energy density", true);
}
}
// Create data collection for solution output: either VisItDataCollection for
// ascii data files, or SidreDataCollection for binary data files.
DataCollection *dc = NULL;
if (visit)
{
if (offline)
dc = new VisItDataCollection("nlelast-fom", pmesh);
else
dc = new VisItDataCollection("nlelast-rom", pmesh);
dc->SetPrecision(8);
// To save the mesh using MFEM's parallel mesh format:
// dc->SetFormat(DataCollection::PARALLEL_FORMAT);
dc->RegisterField("x", &x_gf);
dc->RegisterField("v", &v_gf);
dc->SetCycle(0);
dc->SetTime(0.0);
dc->Save();
}
double ee0 = oper.ElasticEnergy(x_gf);
double ke0 = oper.KineticEnergy(v_gf);
if (myid == 0)
{
cout << "initial elastic energy (EE) = " << ee0 << endl;
cout << "initial kinetic energy (KE) = " << ke0 << endl;
cout << "initial total energy (TE) = " << (ee0 + ke0) << endl;
}
// 10. Create pROM object.
CAROM::BasisGenerator *basis_generator_v = 0;
CAROM::BasisGenerator *basis_generator_x = 0;
CAROM::BasisGenerator *basis_generator_H = 0;
if (offline)
{
CAROM::Options options(fespace.GetTrueVSize(), max_num_snapshots, 1,
update_right_SV);
if (x_base_only == false)
{
basis_generator_v = new CAROM::BasisGenerator(options, isIncremental,
basisFileName + "_V");
}
basis_generator_x = new CAROM::BasisGenerator(options, isIncremental,
basisFileName + "_X");
basis_generator_H = new CAROM::BasisGenerator(options, isIncremental,
basisFileName + "_H");
}
RomOperator *romop = 0;
std::shared_ptr<CAROM::Matrix> BV_librom;
std::shared_ptr<CAROM::Matrix> BX_librom;
std::shared_ptr<CAROM::Matrix> H_librom;
const CAROM::Matrix *Hsinv = 0;
int nsamp_H = -1;
CAROM::SampleMeshManager *smm = nullptr;
CAROM::Vector *eqpSol = nullptr;
CAROM::Vector *eqpSol_S = nullptr;
CAROM::Vector *window_ids = nullptr;
CAROM::Vector *load_eqpsol = new CAROM::Vector(1,
false); // Will be resized later
// 11. Initialize ROM operator
// I guess most of this should be done on id =0
if (online)
{
// Read bases
CAROM::BasisReader *readerV = 0;
if (x_base_only)
{
// The basis for v uses the x basis instead.
readerV = new CAROM::BasisReader("basisX");
rvdim = rxdim;
}
else
readerV = new CAROM::BasisReader("basisV");
BV_librom = readerV->getSpatialBasis();
if (rvdim == -1) // Change rvdim
rvdim = BV_librom->numColumns();
else
BV_librom = BV_librom->getFirstNColumns(rvdim);
MFEM_VERIFY(BV_librom->numRows() == true_size, "");
if (myid == 0)
printf("reduced V dim = %d\n", rvdim);
CAROM::BasisReader readerX("basisX");
BX_librom = readerX.getSpatialBasis();
if (rxdim == -1) // Change rxdim
rxdim = BX_librom->numColumns();
else
BX_librom = BX_librom->getFirstNColumns(rxdim);
MFEM_VERIFY(BX_librom->numRows() == true_size, "");
if (myid == 0)
printf("reduced X dim = %d\n", rxdim);
// Hyper reduce H
CAROM::BasisReader readerH("basisH");
H_librom = readerH.getSpatialBasis();
// Compute sample points
if (hdim == -1)
{
hdim = H_librom->numColumns();
}
CAROM::Matrix *Hsinv = new CAROM::Matrix(hdim, hdim, false);
MFEM_VERIFY(H_librom->numColumns() >= hdim, "");
if (H_librom->numColumns() > hdim)
H_librom = H_librom->getFirstNColumns(hdim);
if (myid == 0)
printf("reduced H dim = %d\n", hdim);
// Setup hyperreduction, using either EQP or sampled DOFs and a sample mesh.
ParFiniteElementSpace *sp_XV_space;
const IntegrationRule *ir0 = NULL;
if (ir0 == NULL)
{
const FiniteElement &fe = *fespace.GetFE(0);
ir0 = &(IntRules.Get(fe.GetGeomType(), 2 * fe.GetOrder() + 3));
}
// Timewindowing setup for EQP
int n_step = int(t_final / dt);
if (n_windows > 1)
{
window_ids = new CAROM::Vector(n_windows + 1, false);
get_window_ids(n_step, n_windows, window_ids);
}
if (use_eqp)
{
// EQP setup
eqpSol = new CAROM::Vector(ir0->GetNPoints() * fespace.GetNE(), true);
SetupEQP_snapshots(ir0, myid, &fespace, nsets, BV_librom.get(),
GetSnapshotMatrix(fespace.GetTrueVSize(), nsets, max_num_snapshots, "X"),
vx0.GetBlock(0),
preconditionNNLS, tolNNLS, maxNNLSnnz, model, *eqpSol, window_ids, snap_step);
if (writeSampleMesh)
WriteMeshEQP(pmesh, myid, ir0->GetNPoints(), *eqpSol);
}
else
{
vector<int> num_sample_dofs_per_proc(num_procs);
if (num_samples_req != -1)
{
nsamp_H = num_samples_req;
}
else
{
nsamp_H = hdim;
}
Hsinv->setSize(nsamp_H, hdim);
vector<int> sample_dofs(nsamp_H);
// Setup hyperreduction using DEIM, GNAT, or S-OPT
CAROM::Hyperreduction hr(samplingType);
hr.ComputeSamples(H_librom,
hdim,
sample_dofs,
num_sample_dofs_per_proc,
*Hsinv,
myid,
num_procs,
nsamp_H);
// Construct sample mesh
const int nspaces = 1;
std::vector<ParFiniteElementSpace *> spfespace(nspaces);
spfespace[0] = &fespace;
smm = new CAROM::SampleMeshManager(spfespace);
vector<int> sample_dofs_empty;
vector<int> num_sample_dofs_per_proc_empty;
num_sample_dofs_per_proc_empty.assign(num_procs, 0);
smm->RegisterSampledVariable("V", 0, sample_dofs,
num_sample_dofs_per_proc);
smm->RegisterSampledVariable("X", 0, sample_dofs,
num_sample_dofs_per_proc);
smm->RegisterSampledVariable("H", 0, sample_dofs,
num_sample_dofs_per_proc);
smm->ConstructSampleMesh();
}
w = new CAROM::Vector(rxdim + rvdim, false);
w_v = new CAROM::Vector(rvdim, false);
w_x = new CAROM::Vector(rxdim, false);
*w = 0.0;
// Note that some of this could be done only on the ROM solver process,
// but it is tricky, since RomOperator assembles Bsp in parallel.
wMFEM = new Vector(&((*w)(0)), rxdim + rvdim);
// Initial conditions
Vector *w_v0 = 0;
Vector *w_x0 = 0;
int sp_size = 0;
Array<int> ess_tdof_list_sp; // Initialize sample essential boundary conditions
if (myid == 0 && !use_eqp)
{
sp_XV_space = smm->GetSampleFESpace(0);
sp_size = sp_XV_space->TrueVSize();
Array<int> sp_offset(3);
sp_offset[0] = 0;
sp_offset[1] = sp_size;
sp_offset[2] = 2 * sp_size;
// Initialize sp_p with initial conditions.
BlockVector sp_vx(sp_offset);
ParGridFunction sp_v_gf, sp_x_gf;
// 12. Set the initial conditions for v_gf, x_gf and vx, and define the
// boundary conditions on a beam-like mesh (see description above).
// Associate a FiniteElementSpace and true-dof data with the GridFunctions.
sp_v_gf.MakeTRef(sp_XV_space, sp_vx, sp_offset[0]);
sp_x_gf.MakeTRef(sp_XV_space, sp_vx, sp_offset[1]);
VectorFunctionCoefficient *velo = 0;
VectorFunctionCoefficient *deform = 0;
if (def_ic)
{
velo = new VectorFunctionCoefficient(dim, InitialVelocityIC2);
}
else
{
velo = new VectorFunctionCoefficient(dim, InitialVelocityIC1);
}
sp_v_gf.ProjectCoefficient(*velo);
sp_v_gf.SetTrueVector();