Richardson.cpp

/* ******************************************************************** */
/* See the file COPYRIGHT for a complete copyright notice, contact      */
/* person and disclaimer.                                               */
/* ******************************************************************** */

#include "ml_config.h"
#include "ml_common.h"

#if defined(HAVE_ML_MLAPI) && defined(HAVE_ML_GALERI)

#include "MLAPI_Space.h"
#include "MLAPI_Operator.h"
#include "MLAPI_MultiVector.h"
#include "MLAPI_Gallery.h"
#include "MLAPI_Expressions.h"
#include "MLAPI_MultiLevelSA.h"

using namespace Teuchos;
using namespace MLAPI;

// ============== //
// example driver //
// ============== //

int main(int argc, char *argv[])
{

#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
#endif

  try {

    // Initialize the workspace and set the output level

    Init();

    // global dimension of the problem

    int NumGlobalElements = 10000;

    // define the space for fine level vectors and operators.

    Space S(NumGlobalElements);

    // define the linear system matrix.

    Operator A = Gallery("Laplace2D", S);

    // set parameters for aggregation and smoothers
    // NOTE: only a limited subset of the parameters accepted by
    // class ML_Epetra::MultiLevelPreconditioner is supported
    // by MLAPI::MultiLevelSA

    Teuchos::ParameterList MLList;
    MLList.set("max levels",3);
    MLList.set("aggregation: type", "Uncoupled");
    MLList.set("aggregation: damping factor", 1.333);
    MLList.set("smoother: type","symmetric Gauss-Seidel");
    MLList.set("smoother: sweeps",1);
    MLList.set("smoother: damping factor",1.0);
    MLList.set("coarse: max size",3);
    MLList.set("coarse: type","Amesos-KLU");

    MultiLevelSA P(A, MLList);

    // Here we define a simple Richardson method for the
    // solution of A x = b. The preconditioner is P,
    // the exact solution (x_ex) is a random vector, the
    // starting solution (x) is the zero vector.

    MultiVector x_ex(S);
    MultiVector x(S);
    MultiVector b(S);
    MultiVector r(S);
    MultiVector z(S);

    x_ex.Random();
    b = A * x_ex;
    x = 0.0;

    double OldNorm   = 1.0;
    double Tolerance = 1e-13;
    int    MaxIters  = 30;

    // ================ //
    // Richardson cycle //
    // ================ //

    for (int i = 0 ; i < MaxIters ; ++i) {

      r = b - A * x; // new residual
      z = P * r;     // apply preconditioner with zero initial guess
      x = x + z;     // update solution

      // compute the A-norm of the error

      double NewNorm = sqrt((x - x_ex) * (A * (x - x_ex)));

      if (GetMyPID() == 0 && i) {
        std::cout << "||x - x_ex||_A = ";
        std::cout.width(15);
        std::cout << NewNorm << ", ";
        std::cout << "reduction = ";
        std::cout.width(15);
        std::cout << NewNorm / OldNorm << std::endl;
      }

      if (NewNorm < Tolerance)
        break;

      OldNorm = NewNorm;
    }

    // finalize the MLAPI workspace

    Finalize();

  }
  catch (const int e) {
    std::cout << "Caught integer exception, code = " << e << std::endl;
  }
  catch (...) {
    std::cout << "problems here..." << std::endl;
  }

#ifdef HAVE_MPI
  MPI_Finalize();
#endif

  return(0);

}

#else

#include "ml_include.h"

int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  MPI_Init(&argc,&argv);
#endif

  puts("This MLAPI example requires the following configuration options:");
  puts("\t--enable-epetra");
  puts("\t--enable-teuchos");
  puts("\t--enable-ifpack");
  puts("\t--enable-amesos");
  puts("\t--enable-galeri");
  puts("Please check your configure line.");

#ifdef HAVE_MPI
  MPI_Finalize();
#endif

  return(0);
}

#endif // if defined(HAVE_ML_MLAPI)