v0.14.0
analytical_poisson.cpp

For more information and detailed explain of this example see COR-2: Solving the Poisson equation

/**
* \file analytical_poisson.cpp
* \ingroup mofem_simple_interface
* \example analytical_poisson.cpp
*
* For more information and detailed explain of this
* example see \ref poisson_tut1
*
*
*/
#include <MoFEM.hpp>
static char help[] = "...\n\n";
/**
* \brief Function
*
* This is prescribed exact function. If this function is given by polynomial
* order of "p" and order of approximation is "p" or higher, solution of
* finite element method is exact (with machine precision).
*
* \f[
* u = 1+x^2+y^2+z^3
* \f]
*
*/
struct ExactFunction {
double operator()(const double x, const double y, const double z) const {
return 1 + x * x + y * y + z * z * z;
}
};
/**
* \brief Exact gradient
*/
FTensor::Tensor1<double, 3> operator()(const double x, const double y,
const double z) const {
grad(0) = 2 * x;
grad(1) = 2 * y;
grad(2) = 3 * z * z;
return grad;
}
};
/**
* \brief Laplacian of function.
*
* This is Laplacian of \f$u\f$, it is calculated using formula
* \f[
* \nabla^2 u(x,y,z) = \nabla \cdot \nabla u
* \frac{\partial^2 u}{\partial x^2}+
* \frac{\partial^2 u}{\partial y^2}+
* \frac{\partial^2 u}{\partial z^2}
* \f]
*
*/
double operator()(const double x, const double y, const double z) const {
return 4 + 6 * z;
}
};
int main(int argc, char *argv[]) {
// Initialize PETSc
MoFEM::Core::Initialize(&argc,&argv,(char *)0,help);
try {
// Create MoAB database
moab::Core moab_core; // create database
moab::Interface &moab = moab_core; // create interface to database
// Get command line options
int order = 3; // default approximation order
PetscBool flg_test = PETSC_FALSE; // true check if error is numerical error
CHKERR PetscOptionsBegin(PETSC_COMM_WORLD, "", "Poisson's problem options",
"none");
// Set approximation order
CHKERR PetscOptionsInt("-order", "approximation order", "", order, &order,
PETSC_NULL);
// Set testing (used by CTest)
CHKERR PetscOptionsBool("-test", "if true is ctest", "", flg_test,
&flg_test, PETSC_NULL);
ierr = PetscOptionsEnd();
// Create MoFEM database and link it to MoAB
MoFEM::Core mofem_core(moab); // create database
MoFEM::Interface &m_field = mofem_core; // create interface to database
// Register DM Manager
CHKERR DMRegister_MoFEM("DMMOFEM"); // register MoFEM DM in PETSc
// Create vector to store approximation global error
Vec global_error;
// First we crate elements, implementation of elements is problem independent,
// we do not know yet what fields are present in the problem, or
// even we do not decided yet what approximation base or spaces we
// are going to use. Implementation of element is free from
// those constrains and can be used in different context.
// Elements used by KSP & DM to assemble system of equations
boost::shared_ptr<ForcesAndSourcesCore> domain_lhs_fe; ///< Volume element for the matrix
boost::shared_ptr<ForcesAndSourcesCore> boundary_lhs_fe; ///< Boundary element for the matrix
boost::shared_ptr<ForcesAndSourcesCore> domain_rhs_fe; ///< Volume element to assemble vector
boost::shared_ptr<ForcesAndSourcesCore> boundary_rhs_fe; ///< Volume element to assemble vector
boost::shared_ptr<ForcesAndSourcesCore> domain_error; ///< Volume element evaluate error
boost::shared_ptr<PoissonExample::PostProcFE>
post_proc_volume; ///< Volume element to Post-process results
boost::shared_ptr<ForcesAndSourcesCore> null; ///< Null element do nothing
{
// Add problem specific operators the generic finite elements to calculate matrices and vectors.
boundary_lhs_fe, domain_rhs_fe, boundary_rhs_fe);
// Add problem specific operators the generic finite elements to calculate error on elements and global error
// in H1 norm
global_error, domain_error);
// Post-process results
.creatFEToPostProcessResults(post_proc_volume);
}
// Get simple interface is simplified version enabling quick and
// easy construction of problem.
Simple *simple_interface;
// Query interface and get pointer to Simple interface
CHKERR m_field.getInterface(simple_interface);
// Build problem with simple interface
{
// Get options for simple interface from command line
CHKERR simple_interface->getOptions();
// Load mesh file to database
CHKERR simple_interface->loadFile();
// Add field on domain and boundary. Field is declared by space and base and rank. space
// can be H1. Hcurl, Hdiv and L2, base can be AINSWORTH_LEGENDRE_BASE, DEMKOWICZ_JACOBI_BASE and more,
// where rank is number of coefficients for dof.
//
// Simple interface assumes that there are four types of field; 1) defined
// on body domain, 2) fields defined on body boundary, 3) skeleton field defined
// on finite element skeleton. Finally data field is defined on body domain. Data field
// is not solved but used for post-process or to keep material parameters, etc. Here
// we using it to calculate approximation error on elements.
// Add domain filed "U" in space H1 and Legendre base, Ainsworth recipe is used
// to construct base functions.
CHKERR simple_interface->addDomainField("U",H1,AINSWORTH_LEGENDRE_BASE,1);
// Add Lagrange multiplier field on body boundary
CHKERR simple_interface->addBoundaryField("L",H1,AINSWORTH_LEGENDRE_BASE,1);
// Add error (data) field, we need only L2 norm. Later order is set to 0, so this
// is piecewise discontinuous constant approx., i.e. 1 DOF for element. You can use
// more DOFs and collate moments of error to drive anisotropic h/p-adaptivity, however
// this is beyond this example.
CHKERR simple_interface->addDataField("ERROR",L2,AINSWORTH_LEGENDRE_BASE,1);
// Set fields order domain and boundary fields.
CHKERR simple_interface->setFieldOrder("U",order); // to approximate function
CHKERR simple_interface->setFieldOrder("L",order); // to Lagrange multipliers
CHKERR simple_interface->setFieldOrder("ERROR",0); // approximation order for error
// Setup problem. At that point database is constructed, i.e. fields, finite elements and
// problem data structures with local and global indexing.
CHKERR simple_interface->setUp();
}
// Get access to PETSC-MoFEM DM manager.
// or more derails see <http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/index.html>
// Form that point internal MoFEM data structures are linked with PETSc interface. If
// DM functions contains string MoFEM is is MoFEM specific DM interface function,
// otherwise DM function part of standard PETSc interface.
DM dm;
// Get dm
CHKERR simple_interface->getDM(&dm);
// Set KSP context for DM. At that point only elements are added to DM operators.
// Calculations of matrices and vectors is executed by KSP solver. This part
// of the code makes connection between implementation of finite elements and
// data operators with finite element declarations in DM manager. From that
// point DM takes responsibility for executing elements, calculations of
// matrices and vectors, and solution of the problem.
{
// Set operators for KSP solver
dm, simple_interface->getDomainFEName(), domain_lhs_fe, null, null);
dm, simple_interface->getBoundaryFEName(), boundary_lhs_fe, null,
null);
// Set calculation of the right hand side vector for KSP solver
CHKERR DMMoFEMKSPSetComputeRHS(dm, simple_interface->getDomainFEName(),
domain_rhs_fe, null, null);
CHKERR DMMoFEMKSPSetComputeRHS(dm, simple_interface->getBoundaryFEName(),
boundary_rhs_fe, null, null);
}
// Solve problem, only PETEc interface here.
{
// Create the right hand side vector and vector of unknowns
Vec F,D;
CHKERR DMCreateGlobalVector(dm,&F);
// Create unknown vector by creating duplicate copy of F vector. only
// structure is duplicated no values.
CHKERR VecDuplicate(F,&D);
// Create solver and link it to DM
KSP solver;
CHKERR KSPCreate(PETSC_COMM_WORLD,&solver);
CHKERR KSPSetFromOptions(solver);
CHKERR KSPSetDM(solver,dm);
// Set-up solver, is type of solver and pre-conditioners
CHKERR KSPSetUp(solver);
// At solution process, KSP solver using DM creates matrices, Calculate
// values of the left hand side and the right hand side vector. then
// solves system of equations. Results are stored in vector D.
CHKERR KSPSolve(solver,F,D);
// Scatter solution on the mesh. Stores unknown vector on field on the mesh.
CHKERR DMoFEMMeshToGlobalVector(dm,D,INSERT_VALUES,SCATTER_REVERSE);
// Clean data. Solver and vector are not needed any more.
CHKERR KSPDestroy(&solver);
CHKERR VecDestroy(&D);
CHKERR VecDestroy(&F);
}
// Calculate error
{
// Loop over all elements in mesh, and run users operators on each element.
CHKERR DMoFEMLoopFiniteElements(dm, simple_interface->getDomainFEName(),
domain_error);
global_error);
if (flg_test == PETSC_TRUE) {
}
}
{
// Loop over all elements in the mesh and for each execute post_proc_volume
// element and operators on it.
CHKERR DMoFEMLoopFiniteElements(dm, simple_interface->getDomainFEName(),
post_proc_volume);
// Write results
post_proc_volume->writeFile("out_vol.h5m");
}
// Destroy DM, no longer needed.
CHKERR DMDestroy(&dm);
// Destroy ghost vector
CHKERR VecDestroy(&global_error);
}
// finish work cleaning memory, getting statistics, etc.
return 0;
}
PoissonExample::AuxFunctions
Definition: AuxPoissonFunctions.hpp:14
MoFEM::UnknownInterface::getInterface
MoFEMErrorCode getInterface(IFACE *&iface) const
Get interface reference to pointer of interface.
Definition: UnknownInterface.hpp:93
MoFEM::CoreTmp< 0 >
Core (interface) class.
Definition: Core.hpp:82
H1
@ H1
continuous field
Definition: definitions.h:85
MoFEM::DMMoFEMKSPSetComputeRHS
PetscErrorCode DMMoFEMKSPSetComputeRHS(DM dm, const char fe_name[], MoFEM::FEMethod *method, MoFEM::BasicMethod *pre_only, MoFEM::BasicMethod *post_only)
set KSP right hand side evaluation function
Definition: DMMoFEM.cpp:637
FTensor::Tensor1< double, 3 >
AuxPoissonFunctions.hpp
L2
@ L2
field with C-1 continuity
Definition: definitions.h:88
MoFEM.hpp
MoFEM::CoreTmp< 0 >::Finalize
static MoFEMErrorCode Finalize()
Checks for options to be called at the conclusion of the program.
Definition: Core.cpp:112
PoissonExample::CreateFiniteElements
Create finite elements instances.
Definition: PoissonOperators.hpp:861
MoFEM::DMMoFEMKSPSetComputeOperators
PetscErrorCode DMMoFEMKSPSetComputeOperators(DM dm, const char fe_name[], MoFEM::FEMethod *method, MoFEM::BasicMethod *pre_only, MoFEM::BasicMethod *post_only)
Set KSP operators and push mofem finite element methods.
Definition: DMMoFEM.cpp:678
ExactFunctionGrad
Exact gradient.
Definition: analytical_nonlinear_poisson.cpp:43
order
constexpr int order
Definition: dg_projection.cpp:18
MoFEM::DeprecatedCoreInterface
Deprecated interface functions.
Definition: DeprecatedCoreInterface.hpp:16
MoFEM::Interface
DeprecatedCoreInterface Interface
Definition: Interface.hpp:2010
PoissonExample::AuxFunctions::createGhostVec
MoFEMErrorCode createGhostVec(Vec *ghost_vec) const
Definition: AuxPoissonFunctions.hpp:30
ExactLaplacianFunction::operator()
double operator()(const double x, const double y, const double z) const
Definition: analytical_nonlinear_poisson.cpp:59
ExactFunction::operator()
double operator()(const double x, const double y, const double z) const
Definition: analytical_nonlinear_poisson.cpp:35
CHKERR
#define CHKERR
Inline error check.
Definition: definitions.h:548
PoissonExample::CreateFiniteElements::creatFEToPostProcessResults
MoFEMErrorCode creatFEToPostProcessResults(boost::shared_ptr< PostProcFE > &post_proc_volume) const
Create finite element to post-process results.
Definition: PoissonOperators.hpp:947
ExactLaplacianFunction
Laplacian of function.
Definition: analytical_nonlinear_poisson.cpp:58
PoissonExample::AuxFunctions::testError
MoFEMErrorCode testError(Vec ghost_vec)
Test error.
Definition: AuxPoissonFunctions.hpp:73
MoFEM::DMoFEMMeshToGlobalVector
PetscErrorCode DMoFEMMeshToGlobalVector(DM dm, Vec g, InsertMode mode, ScatterMode scatter_mode)
set ghosted vector values on all existing mesh entities
Definition: DMMoFEM.cpp:535
MoFEM::DMRegister_MoFEM
PetscErrorCode DMRegister_MoFEM(const char sname[])
Register MoFEM problem.
Definition: DMMoFEM.cpp:43
PoissonExample::AuxFunctions::printError
MoFEMErrorCode printError(Vec ghost_vec)
Print error.
Definition: AuxPoissonFunctions.hpp:60
main
int main(int argc, char *argv[])
Definition: analytical_poisson.cpp:70
ExactFunction
Function.
Definition: analytical_nonlinear_poisson.cpp:34
MoFEM::CoreTmp< 0 >::Initialize
static MoFEMErrorCode Initialize(int *argc, char ***args, const char file[], const char help[])
Initializes the MoFEM database PETSc, MOAB and MPI.
Definition: Core.cpp:72
CATCH_ERRORS
#define CATCH_ERRORS
Catch errors.
Definition: definitions.h:385
help
static char help[]
Definition: analytical_poisson.cpp:18
PoissonOperators.hpp
MoFEM::Core
CoreTmp< 0 > Core
Definition: Core.hpp:1148
PoissonExample::CreateFiniteElements::createFEToEvaluateError
MoFEMErrorCode createFEToEvaluateError(boost::function< double(const double, const double, const double)> f_u, boost::function< FTensor::Tensor1< double, 3 >(const double, const double, const double)> g_u, Vec global_error, boost::shared_ptr< ForcesAndSourcesCore > &domain_error) const
Create finite element to calculate error.
Definition: PoissonOperators.hpp:911
MoFEM::Exceptions::ierr
static MoFEMErrorCodeGeneric< PetscErrorCode > ierr
Definition: Exceptions.hpp:76
AINSWORTH_LEGENDRE_BASE
@ AINSWORTH_LEGENDRE_BASE
Ainsworth Cole (Legendre) approx. base .
Definition: definitions.h:60
EigenMatrix::Vec
const FTensor::Tensor2< T, Dim, Dim > Vec
Definition: MatrixFunction.hpp:66
ReactionDiffusionEquation::D
const double D
diffusivity
Definition: reaction_diffusion.cpp:20
PoissonExample::CreateFiniteElements::createFEToAssembleMatrixAndVector
MoFEMErrorCode createFEToAssembleMatrixAndVector(boost::function< double(const double, const double, const double)> f_u, boost::function< double(const double, const double, const double)> f_source, boost::shared_ptr< ForcesAndSourcesCore > &domain_lhs_fe, boost::shared_ptr< ForcesAndSourcesCore > &boundary_lhs_fe, boost::shared_ptr< ForcesAndSourcesCore > &domain_rhs_fe, boost::shared_ptr< ForcesAndSourcesCore > &boundary_rhs_fe, bool trans=true) const
Create finite element to calculate matrix and vectors.
Definition: PoissonOperators.hpp:868
MoFEM::DMoFEMLoopFiniteElements
PetscErrorCode DMoFEMLoopFiniteElements(DM dm, const char fe_name[], MoFEM::FEMethod *method, CacheTupleWeakPtr cache_ptr=CacheTupleSharedPtr())
Executes FEMethod for finite elements in DM.
Definition: DMMoFEM.cpp:586
CHKERRG
#define CHKERRG(n)
Check error code of MoFEM/MOAB/PETSc function.
Definition: definitions.h:496
PoissonExample::AuxFunctions::assembleGhostVector
MoFEMErrorCode assembleGhostVector(Vec ghost_vec) const
Assemble error vector.
Definition: AuxPoissonFunctions.hpp:43
F
@ F
Definition: free_surface.cpp:394
ExactFunctionGrad::operator()
FTensor::Tensor1< double, 3 > operator()(const double x, const double y, const double z) const
Definition: analytical_nonlinear_poisson.cpp:44