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example_GradDiv.cpp File Reference

Example solution grad-div diffusion system with div-conforming (face) elements. More...

#include "TrilinosCouplings_config.h"
#include "TrilinosCouplings_Pamgen_Utils.hpp"
#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 "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
#include "AztecOO.h"
#include "ml_epetra_utils.h"
#include "ml_GradDiv.h"
Include dependency graph for example_GradDiv.cpp:

Classes

struct  fecomp
 

Macros

#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. More...
 
void TestMultiLevelPreconditioner_GradDiv (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. More...
 
int evalu (double &uExact0, double &uExact1, double &uExact2, double &x, double &y, double &z)
 Exact solution evaluation. More...
 
double evalDivu (double &x, double &y, double &z)
 Divergence of exact solution. More...
 
int evalGradDivu (double &gradDivu0, double &gradDivu1, double &gradDivu2, double &x, double &y, double &z, double &kappa)
 Grad of Div of exact solution. More...
 
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. More...
 
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. More...
 
int evalCurlu (double &curlu0, double &curlu1, double &curlu2, double &x, double &y, double &z, double &mu)
 

Detailed Description

Example solution grad-div diffusion system with div-conforming (face) elements.

This example uses the following Trilinos packages:

For more details on the formulation see

Grad-Div System:

grad kappa div F + mu F  = g  in Omega

Corresponding discrete linear system for edge element coeficients (x):
(Kc + Mc)x = b

Kd    - Hdiv stiffness matrix
Md    - Hcdiv mass matrix
b    - right hand side vector
Author
Created by P. Bochev, D. Ridzal, K. Peterson, D. Hensinger, C. Siefert.
Remarks
Usage
./TrilinosCouplings_examples_scaling_Example_GradDiv.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

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 evalGradDivu ( double &  gradDivu0,
double &  gradDivu1,
double &  gradDivu2,
double &  x,
double &  y,
double &  z,
double &  kappa 
)

Grad of Div of exact solution.

Parameters
gradDivu0[out] first component of grad div of exact solution
gradDivu1[out] second component of grad div of exact solution
gradDivu2[out] third 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_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_GradDiv ( 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 solution_test().