Example solution of the eddy current Maxwell's equations using curl-conforming (edge) elements.
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#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_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_CrsMatrix.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_LinearProblem.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 "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 "pamgen_im_exodusII_l.h"
#include "pamgen_im_ne_nemesisI_l.h"
#include "pamgen_extras.h"
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#define | ABS(x) ((x)>0?(x):-(x)) |
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typedef Intrepid::FunctionSpaceTools | IntrepidFSTools |
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typedef Intrepid::RealSpaceTools< double > | IntrepidRSTools |
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typedef Intrepid::CellTools< double > | IntrepidCTools |
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void | TestMultiLevelPreconditioner_Maxwell (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. More...
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int | evalu (double &uExact0, double &uExact1, double &uExact2, double &x, double &y, double &z) |
| Exact solution evaluation. More...
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int | evalCurlu (double &curlu0, double &curlu1, double &curlu2, double &x, double &y, double &z, double &mu) |
| Curl of exact solution. More...
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int | evalCurlCurlu (double &curlcurlu0, double &curlcurlu1, double &curlcurlu2, double &x, double &y, double &z, double &mu) |
| CurlCurl of exact solution. More...
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int | main (int argc, char *argv[]) |
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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...
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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...
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Example solution of the eddy current Maxwell's equations using curl-conforming (edge) elements.
This example uses the following Trilinos packages:
- Pamgen to generate a Hexahedral mesh.
- Intrepid to build the discretization matrices and right-hand side.
- Epetra to handle the global matrix and vector.
- ML to solve the linear system.
Maxwell System:
curl x mu^{-1} curl E + sigma E = f
Corresponding discrete linear system for edge element coeficients (x):
(Kc + Mc)x = b
Kc - Hcurl stiffness matrix
Mc - Hcurl mass matrix
b - right hand side vector
- Author
- Created by P. Bochev, D. Ridzal, K. Peterson, D. Hensinger, C. Siefert.
Input files available in Trilinos for use with the Maxwell driver:
- Maxwell.xml - basic input file with box mesh and one mesh block
- Ninja.xml - input file with distorted mesh (shaped like Ninja star) and one mesh block
- Maxwell_in_block.xml - input file with box mesh with a center block with different material values.
◆ evalCurlCurlu()
int evalCurlCurlu |
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double & |
curlcurlu0, |
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double & |
curlcurlu1, |
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double & |
curlcurlu2, |
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double & |
x, |
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double & |
y, |
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double & |
z, |
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double & |
mu |
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CurlCurl of exact solution.
- Parameters
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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 |
◆ evalCurlu()
int evalCurlu |
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double & |
curlu0, |
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double & |
curlu1, |
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double & |
curlu2, |
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double & |
x, |
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double & |
y, |
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double & |
z, |
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double & |
mu |
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Curl of exact solution.
- Parameters
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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 |
◆ evalu()
int evalu |
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double & |
uExact0, |
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double & |
uExact1, |
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double & |
uExact2, |
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double & |
x, |
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double & |
y, |
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double & |
z |
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Exact solution evaluation.
- Parameters
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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 |
◆ Multiply_Ones()
int Multiply_Ones |
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const Epetra_CrsMatrix & |
A, |
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const Epetra_Vector & |
x, |
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Epetra_Vector & |
y |
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Multiplies Ax = y, where all non-zero entries of A are replaced with the value 1.0.
- Parameters
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A | [in] matrix |
x | [in] vector |
y | [in] vector |
◆ solution_test()
void solution_test |
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string |
msg, |
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const Epetra_Operator & |
A, |
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const Epetra_MultiVector & |
lhs, |
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const Epetra_MultiVector & |
rhs, |
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const Epetra_MultiVector & |
xexact, |
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Epetra_Time & |
Time, |
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double & |
TotalErrorExactSol, |
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double & |
TotalErrorResidual |
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Compute ML solution residual.
- Parameters
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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_Maxwell().
◆ TestMultiLevelPreconditioner_Maxwell()
void TestMultiLevelPreconditioner_Maxwell |
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char |
ProblemType[], |
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Teuchos::ParameterList & |
MLList, |
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Epetra_CrsMatrix & |
CurlCurl, |
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Epetra_CrsMatrix & |
D0clean, |
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Epetra_CrsMatrix & |
M0inv, |
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Epetra_CrsMatrix & |
M1, |
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Epetra_MultiVector & |
xh, |
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Epetra_MultiVector & |
b, |
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double & |
TotalErrorResidual, |
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double & |
TotalErrorExactSol |
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ML Preconditioner.
- Parameters
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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 solution_test().