Example solution of a steady-state advection-diffusion-reaction equation with Dirichlet boundary conditon on a hexahedral mesh using nodal (Hgrad) elements and stabilization. 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_HGRAD_HEX_C1_FEM.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Intrepid_Utils.hpp"
#include "Sacado_No_Kokkos.hpp"
#include "Epetra_Time.h"
#include "Epetra_Map.h"
#include "Epetra_SerialComm.h"
#include "Epetra_FECrsMatrix.h"
#include "Epetra_FEVector.h"
#include "Epetra_Import.h"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_XMLParameterListHelpers.hpp"
#include "Teuchos_Assert.hpp"
#include "Shards_CellTopology.hpp"
#include "EpetraExt_RowMatrixOut.h"
#include "EpetraExt_MultiVectorOut.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_MultiLevelPreconditioner.h"
#include "ml_epetra_utils.h"
#include "map"

Include dependency graph for example_StabilizedADR.cpp:

Typedefs
typedef Sacado::Fad::SFad < double, 3 >	Fad3

typedef shards::CellTopology	ShardsCellTopology

typedef Intrepid::FunctionSpaceTools	IntrepidFSTools

typedef Intrepid::CellTools < double >	IntrepidCTools

typedef long long	int128

Functions
template<typename Scalar >
const Scalar	exactSolution (const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined exact solution. More...

template<typename Scalar >
void	diffusionTensor (Scalar diffusion[][3], const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined diffusion tensor. More...

template<typename Scalar >
void	advectiveVector (Scalar advection[3], const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined advective vector. More...

template<typename Scalar >
const Scalar	reactionTerm (const Scalar &x, const Scalar &y, const Scalar &z)
	User-defined reaction coefficient. More...

template<typename Scalar >
void	exactSolutionGrad (Scalar gradExact[3], const Scalar &x, const Scalar &y, const Scalar &z)
	Computes gradient of the exact solution. Requires user-defined exact solution. More...

template<typename Scalar >
const Scalar	sourceTerm (Scalar &x, Scalar &y, Scalar &z)
	Computes source term: f = -div(K.grad u - b.u) + c.u. Requires user-defined exact solution, diffusion tensor, advective vector and reaction coefficient. More...

template<class ArrayOut , class ArrayIn >
void	evaluateDiffusionTensor (ArrayOut &worksetDiffusionValues, const ArrayIn &evaluationPoints)
	Computation of the diffusion tensor at array of points in physical space. More...

template<class ArrayOut , class ArrayIn >
void	evaluateAdvectiveVector (ArrayOut &worksetAdvectionValues, const ArrayIn &evaluationPoints)
	Computation of the advective vector at array of points in physical space.. More...

template<class ArrayOut , class ArrayIn >
void	evaluateReactionCoefficient (ArrayOut &worksetReactionValues, const ArrayIn &evaluationPoints)
	Computation of the reaction coefficient at array of points in physical space.. More...

template<class ArrayOut , class ArrayIn >
void	evaluateSourceTerm (ArrayOut &sourceTermValues, const ArrayIn &evaluationPoints)
	Computation of the source term at array of points in physical space. More...

template<class ArrayOut , class ArrayIn >
void	evaluateExactSolution (ArrayOut &exactSolutionValues, const ArrayIn &evaluationPoints)
	Computation of the exact solution at array of points in physical space. More...

template<class ArrayOut , class ArrayIn >
void	evaluateExactSolutionGrad (ArrayOut &exactSolutionGradValues, const ArrayIn &evaluationPoints)
	Computation of the gradient of the exact solution at array of points in physical space. More...

int	TestMultiLevelPreconditioner (char ProblemType[], Teuchos::ParameterList &MLList, Epetra_CrsMatrix &A, const Epetra_MultiVector &xexact, Epetra_MultiVector &b, Epetra_MultiVector &uh, double &TotalErrorResidual, double &TotalErrorExactSol)

template<class Scalar >
void	getPamgenMesh (FieldContainer< Scalar > &localNodeCoordsFC, FieldContainer< long long > &localCellToNodeFC, FieldContainer< int > &nodeOnBoundaryFC, FieldContainer< bool > &nodeIsOwnedFC, FieldContainer< long long > &globalNodeIdsFC, const std::string &meshInput, const int &procRank, const int &numProcs, const Epetra_Comm &Comm, Epetra_Time &Time, const string &message, const int verbose=0)
	Pamgen wrapper. More...

void	getInputArguments (Teuchos::ParameterList &inputMeshList, std::string &meshInput, Teuchos::ParameterList &inputSolverList, int &argc, char *argv[], const Epetra_Comm &Comm, const std::string &inputMeshFile="ADR.xml", const std::string &intputSolverFile="ML_nonsym.xml")

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

Variables
double	g_advection [3] ={0.,0.,0.}

double	g_reaction

Detailed Description

Example solution of a steady-state advection-diffusion-reaction equation with Dirichlet boundary conditon on a hexahedral mesh using nodal (Hgrad) elements and stabilization.

    This example requires the following Trilinos packages:

Pamgen to generate a Hexahedral mesh;
Sacado to form the source term from user-specified manufactured solution, and diffusion, advection and reaction functions.
Intrepid to build the discretization matrix and right-hand side
ML to solve the linear system.

 Steady-state advection-diffusion boundary value problem in conservative form:

        -div (A.grad(u) - b.u) + c.u = f  in Omega
                                   u = 0  on Gamma
 where
        A   is a symmetric, positive definite diffusivity tensor
        b   is advective velocity vector which is not required to be divergence free
        c   is a reaction coefficient
        f   is a given source term

 The user must provide definitions for these quantities and definition for the exact solution


 Corresponding discrete linear system for nodal coefficients(x):

             Kx = d

        K - HGrad stiffness matrix
        d - right hand side vector

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

Remarks: Usage:
./TrilinosCouplings_examples_scaling_example_StabilizedADR.exe; Example requires Pamgen formatted mesh input file named ADR.xml.

Function Documentation

template<typename Scalar >

void advectiveVector	(	Scalar	advection[3],
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z
	)

User-defined advective vector.

Parameters

advection	[out] 3-dimensional advective vector evaluated at (x,y,z)
x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

Remarks: Advective vector is not required to be divergence-free

template<typename Scalar >

void diffusionTensor	(	Scalar	diffusion[][3],
		const Scalar &	x,
		const Scalar &	y,
		const Scalar &	z
	)

User-defined diffusion tensor.

Parameters

diffusion	[out] 3 x 3 diffusivity tensor evaluated at (x,y,z)
x	[in] x-coordinate of the evaluation point
y	[in] y-coordinate of the evaluation point
z	[in] z-coordinate of the evaluation point

Warning: Symmetric and positive definite tensor is required for every (x,y,z).