TrilinosCouplings Development
Classes | Defines | Typedefs | Functions
example_CurlLSFEM.cpp File Reference

Example solution of a div-curl system on a hexahedral mesh using curl-conforming (edge) elements. More...

#include "Intrepid_FunctionSpaceTools.hpp"
#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_CellTools.hpp"
#include "Intrepid_ArrayTools.hpp"
#include "Intrepid_HCURL_HEX_I1_FEM.hpp"
#include "Intrepid_HGRAD_HEX_C1_FEM.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Intrepid_Utils.hpp"
#include "Epetra_Time.h"
#include "Epetra_Map.h"
#include "Epetra_SerialComm.h"
#include "Epetra_Import.h"
#include "Epetra_Export.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_LinearProblem.h"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_ArrayRCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Shards_CellTopology.hpp"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.h"
#include "EpetraExt_VectorOut.h"
#include "AztecOO.h"
#include "ml_MultiLevelPreconditioner.h"
#include "ml_RefMaxwell_11_Operator.h"
#include "ml_RefMaxwell.h"
#include "ml_EdgeMatrixFreePreconditioner.h"
#include "ml_epetra_utils.h"
#include "create_inline_mesh.h"
#include "im_exodusII_l.h"
#include "im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
Include dependency graph for example_CurlLSFEM.cpp:

Classes

struct  fecomp

Defines

#define ABS(x)   ((x)>0?(x):-(x))

Typedefs

typedef
Intrepid::FunctionSpaceTools 
IntrepidFSTools
typedef
Intrepid::RealSpaceTools
< double > 
IntrepidRSTools
typedef Intrepid::CellTools
< double > 
IntrepidCTools

Functions

void TestMultiLevelPreconditioner_CurlLSFEM (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &CurlCurl, Epetra_CrsMatrix &D0clean, Epetra_CrsMatrix &M0inv, Epetra_CrsMatrix &M1, Epetra_MultiVector &xh, Epetra_MultiVector &b, double &TotalErrorResidual, double &TotalErrorExactSol)
 ML Preconditioner.
int evalu (double &uExact0, double &uExact1, double &uExact2, double &x, double &y, double &z)
 Exact solution evaluation.
double evalDivu (double &x, double &y, double &z, double &mu)
 Divergence of exact solution.
int evalCurlu (double &curlu0, double &curlu1, double &curlu2, double &x, double &y, double &z, double &mu)
 Curl of exact solution.
int evalGradDivu (double &gradDivu0, double &gradDivu1, double &gradDivu2, double &x, double &y, double &z, double &mu)
 Gradient of Divergence of exact solution.
int main (int argc, char *argv[])
int Multiply_Ones (const Epetra_CrsMatrix &A, const Epetra_Vector &x, Epetra_Vector &y)
 Multiplies Ax = y, where all non-zero entries of A are replaced with the value 1.0.
void solution_test (string msg, const Epetra_Operator &A, const Epetra_MultiVector &lhs, const Epetra_MultiVector &rhs, const Epetra_MultiVector &xexact, Epetra_Time &Time, double &TotalErrorExactSol, double &TotalErrorResidual)
 Compute ML solution residual.

Detailed Description

Example solution of a div-curl system on a hexahedral mesh using curl-conforming (edge) elements.

This example uses the following Trilinos packages:

For more details on the formulation see


            Div-Curl System:

                       curl u = g  in Omega
                        div u = h  in Omega
                        u x n = 0  on Gamma

            Corresponding discrete linear system for edge element coeficients (x):

                      (Kc + Mc*Dg*MgInv*Dg'*Mc)x = b

                      Kc    - Hcurl stiffness matrix
                      Mc    - Hcurl mass matrix
                      Dg    - Node to edge incidence matrix
                      MgInv - Hgrad mass matrix inverse
                      b     - right hand side vector

    
Author:
Created by P. Bochev, D. Ridzal, K. Peterson, D. Hensinger, C. Siefert.
Remarks:
Usage

     ./TrilinosCouplings_examples_scaling_Example_CurlLSFEM.exe  inputfile.xml


        inputfile.xml (optional)  -  xml input file containing Pamgen mesh description
                                     and material parameters for each Pamgen block,
                                     if not present code attempts to read CurlLSFEMin.xml.
                                      
     

Input files available in Trilinos for use with the CurlLSFEM driver:


Function Documentation

int evalCurlu ( double &  curlu0,
double &  curlu1,
double &  curlu2,
double &  x,
double &  y,
double &  z,
double &  mu 
)

Curl of exact solution.

Parameters:
curlu0[out] first component of curl of exact solution
curlu1[out] second component of curl of exact solution
curlu2[out] third component of curl of exact solution
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
mu[in] material parameter
double evalDivu ( double &  x,
double &  y,
double &  z,
double &  mu 
)

Divergence of exact solution.

Parameters:
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
mu[in] material parameter
Returns:
Value of the divergence of exact solution at (x,y,z)
int evalGradDivu ( double &  gradDivu0,
double &  gradDivu1,
double &  gradDivu2,
double &  x,
double &  y,
double &  z,
double &  mu 
)

Gradient of Divergence of exact solution.

Parameters:
gradDivu0[out] first (x) component of grad div of exact solution
gradDivu1[out] second (y) component of grad div of exact solution
gradDivu2[out] third (z) component of grad div of exact solution
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
mu[in] material parameter
int evalu ( double &  uExact0,
double &  uExact1,
double &  uExact2,
double &  x,
double &  y,
double &  z 
)

Exact solution evaluation.

Parameters:
uExact0[out] first component of exact solution at (x,y,z)
uExact1[out] second component of exact solution at (x,y,z)
uExact2[out] third component of exact solution at (x,y,z)
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
int Multiply_Ones ( const Epetra_CrsMatrix &  A,
const Epetra_Vector &  x,
Epetra_Vector &  y 
)

Multiplies Ax = y, where all non-zero entries of A are replaced with the value 1.0.

Parameters:
A[in] matrix
x[in] vector
y[in] vector

Referenced by TestMultiLevelPreconditioner_CurlLSFEM(), and TestMultiLevelPreconditioner_DivLSFEM().

void solution_test ( string  msg,
const Epetra_Operator &  A,
const Epetra_MultiVector &  lhs,
const Epetra_MultiVector &  rhs,
const Epetra_MultiVector &  xexact,
Epetra_Time &  Time,
double &  TotalErrorExactSol,
double &  TotalErrorResidual 
)

Compute ML solution residual.

Parameters:
A[in] discrete operator
lhs[in] solution vector
rhs[in] right hand side vector
Time[in] elapsed time for output
TotalErrorResidual[out] error residual
TotalErrorExactSol[out] error in xh (not an appropriate measure for H(curl) basis functions)

Referenced by TestMultiLevelPreconditioner_CurlLSFEM(), and TestMultiLevelPreconditioner_DivLSFEM().

void TestMultiLevelPreconditioner_CurlLSFEM ( char  ProblemType[],
Teuchos::ParameterList &  MLList,
Epetra_CrsMatrix &  CurlCurl,
Epetra_CrsMatrix &  D0clean,
Epetra_CrsMatrix &  M0inv,
Epetra_CrsMatrix &  M1,
Epetra_MultiVector &  xh,
Epetra_MultiVector &  b,
double &  TotalErrorResidual,
double &  TotalErrorExactSol 
)

ML Preconditioner.

Parameters:
ProblemType[in] problem type
MLList[in] ML parameter list
CurlCurl[in] H(curl) stiffness matrix
D0clean[in] Edge to node stiffness matrix
M0inv[in] H(grad) mass matrix inverse
M1[in] H(curl) mass matrix
xh[out] solution vector
b[in] right-hand-side vector
TotalErrorResidual[out] error residual
TotalErrorExactSol[out] error in xh

References Multiply_Ones(), and solution_test().

 All Classes Files Functions