Random Fields Generation Library

PRESENTATION

This library aims to generate random fields with prescribed first-order marginal distribution and correlation structure over structured grids or non-structured point arrays. Currently the library offers:

1. Random field generation using the spectral method by Shinozuka and Deodatis [1,2] and a variation suited for isotropic media.

This software is mainly developed at laboratoire MSSMat (Ecole Centrale Paris - CNRS).

• contact : Luciano de Carvalho Paludo
• contributors (by order of first commit): R. Cottereau, L. Paludo, V. Bouvier

It is developed in FORTRAN 90.

REFERENCES

Original references for the theory are:

1. Shinozuka, M. and Deodatis, G., Simulation of multi-dimensional Gaussian stochastic fields by spectral representation, App. Mech. Rev. 49 (1), 1996, pp. 29-53.
2. Shinozuka, M. and Deodatis, G., Simulation of stochastic processes by spectral representation, App. Mech. Rev. 44 (4), 1991, pp. 191-205.

INSTALLATION

Requirements

There are two libraries needed to build the Random Fields Generation Library:

HDF5 : www.hdfgroup.org is a library used to manage big size files MPI : a MPI library

The path to these libraries should be informed in the Makefile (LIBHDF5, INCLUDEHDF5, LIBMPI and INCLUDEMPI)

Compiling

Inside the folder randomField the command make will build the file "librandomfield.a" that will be file of the library that your makefile should point to.

USE

To create "N" realizations the inputs are:

• Points coordinates (xPoints)
• Correlation model
• First-order marginal law
• Correlation length
• Field average
• Field variance
• Number of realizations (N)
• Generation method

SYNTAX

The syntax to call the function is:

createStandardGaussianFieldUnstruct(xPoints, corrMod, margiFirst, corrL, fieldAvg, fieldVar, Nmc, method, randField)

It should be observed that all the variables should be allocated before the call Where:

xPoints - is a matrix where each column contains X, Y and Z coordinates (real numbers) for each point.

      |X1  X2  X3  ...... Xn|
      |Y1  Y2  Y3  ...... Yn|
      |Z1  Z2  Z3  ...... Zn|

corrMod - string containing the name of the correlation model. Only the "gaussian" option is implemented.

margiFirst - string containing the name of the first-order marginal law. The options are "gaussian" or "lognormal"

corrL - vector of positive real numbers containing the correlation length in each direction

      |Correlation Length in X|
      |Correlation Length in Y|
      |Correlation Length in Z|

fieldAvg - real number containing the field average

fieldVar - positive real number containing the field variance

Nmc - integer representing the number of realizations

method - generation method (integer). The options are "2" for Shinozuka and Deodatis method and "1" for the isotropic spectrum optimized version

randField - matrix tha will store the results. For a call with "xPoints" dimension 3xn and Nmc = N the size of the matrix is n x N.

      |A1 B1 C1 ... N1|
      |A2 B2 C2 ... N2|
      |A3 B3 C3 ... N3|
      | .  .  . .    .|
      | .  .  .   .  .|
      |An Bn Cn ... Nn|

Obs: Each realization is represented by a letter and each point by a number.