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example_DivLSFEM.cpp File Reference

Example solution of a div-curl system on a hexahedral mesh using div-conforming (face) 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_HDIV_HEX_I1_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_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_Vector.h"
#include "Epetra_LinearProblem.h"
#include "Epetra_Import.h"
#include "Epetra_Export.h"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.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 "EpetraExt_MatrixMatrix.h"
#include "create_inline_mesh.h"
#include "im_exodusII_l.h"
#include "im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
#include "AztecOO.h"
#include "ml_epetra_utils.h"
#include "ml_RefMaxwell_11_Operator.h"
#include "ml_FaceMatrixFreePreconditioner.h"
#include "ml_RefMaxwell.h"
Include dependency graph for example_DivLSFEM.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

int Multiply_Abs (const Epetra_CrsMatrix &A, const Epetra_Vector &x, Epetra_Vector &y)
 Multiplies abs(A)x = y, where all non-zero entries of A are replaced with their absolute values value.
void TestMultiLevelPreconditioner_DivLSFEM (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &GradDiv, Epetra_CrsMatrix &D0clean, Epetra_CrsMatrix &D1clean, Epetra_CrsMatrix &FaceNode, Epetra_CrsMatrix &M1, Epetra_CrsMatrix &M1inv, Epetra_CrsMatrix &M2, 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)
 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 evalCurlCurlu (double &curlCurlu0, double &curlCurlu1, double &curlCurlu2, double &x, double &y, double &z, double &mu)
 Curl of curl 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 div-conforming (face) elements.

This example uses Pamgen to generate a hexahedral mesh, Intrepid to build mass and stiffness matrices, and ML to solve.


           System

                       div v + \phi = f  in Omega
                       v+ A grad \phi = 0  in Omega
                       Dirichlet BC: \phi given  on Gamma

                       Omega is the box [0,1]^3

            where f is derived from a prescribed solution

            \phi(x,y,z)=-sin^2(\pi x)*sin^2(\pi y)*sin^2(\pi z)

            or other, discontinuous solution, aka "patch test"



    
Remarks:
Usage

     ./TrilinosCouplings_examples_scaling_Example_DivLSFEM.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 DivLSFEMin.xml.


     

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.n = 0  on Gamma

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

                      (Kd + Md*Dc*McInv*Dc'*Md)x = b

                      Kd    - Hdiv stiffness matrix
                      Md    - Hdiv mass matrix
                      Dc    - Edge to Face incidence matrix
                      McInv - 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_DivLSFEM.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 DivLSFEMin.xml.


     

Function Documentation

int evalCurlCurlu ( double &  curlCurlu0,
double &  curlCurlu1,
double &  curlCurlu2,
double &  x,
double &  y,
double &  z,
double &  mu 
)

Curl of curl of exact solution.

Parameters:
curlCurlu0[out] first component of curl curl of exact solution
curlCurlu1[out] second component of curl curl of exact solution
curlCurlu2[out] third component of curl curl of exact solution
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
mu[in] material parameter
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 
)

Divergence of exact solution.

Parameters:
x[in] x coordinate
y[in] y coordinate
z[in] z coordinate
Returns:
Value of the divergence of exact solution at (x,y,z)
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_Abs ( const Epetra_CrsMatrix &  A,
const Epetra_Vector &  x,
Epetra_Vector &  y 
)

Multiplies abs(A)x = y, where all non-zero entries of A are replaced with their absolute values value.

Parameters:
A[in] matrix
x[in] vector
y[out] vector
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
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(div) basis functions)
void TestMultiLevelPreconditioner_DivLSFEM ( char  ProblemType[],
Teuchos::ParameterList &  MLList,
Epetra_CrsMatrix &  GradDiv,
Epetra_CrsMatrix &  D0clean,
Epetra_CrsMatrix &  D1clean,
Epetra_CrsMatrix &  FaceNode,
Epetra_CrsMatrix &  M1,
Epetra_CrsMatrix &  M1inv,
Epetra_CrsMatrix &  M2,
Epetra_MultiVector &  xh,
Epetra_MultiVector &  b,
double &  TotalErrorResidual,
double &  TotalErrorExactSol 
)

ML Preconditioner.

Parameters:
ProblemType[in] problem type
MLList[in] ML parameter list
GradDiv[in] H(curl) stiffness matrix
D0clean[in] Edge to node incidence matrix
D1clean[in] Face to edge incidence matrix
FaceNode[in] Face to node incidence matrix
M1inv[in] H(curl) mass matrix inverse
M2[in] H(div) 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().

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