v0.13.0
analytical_nonlinear_poisson.cpp

For more information and detailed explain of this example see COR-5: A nonlinear Poisson equation

/**
* \file analytical_nonlinear_poisson.cpp
* \ingroup mofem_simple_interface
* \example analytical_nonlinear_poisson.cpp
*
* example see \ref poisson_tut4
*
*
*/
/* This file is part of MoFEM.
* MoFEM is free software: you can redistribute it and/or modify it under
* Free Software Foundation, either version 3 of the License, or (at your
* option) any later version.
*
* MoFEM is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
*
* You should have received a copy of the GNU Lesser General Public
#include <BasicFiniteElements.hpp>
#include <PoissonOperators.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+2y+3z
* \f]
*
*/
struct ExactFunction {
double operator()(const double x, const double y, const double z) const {
return 1 + x + y + pow(z, 3);
}
};
/**
*/
FTensor::Tensor1<double, 3> operator()(const double x, const double y,
const double z) const {
grad(2) = 3 * z * z;
}
};
/**
* \brief Laplacian of function.
*
*/
double operator()(const double x, const double y, const double z) const {
return 0.4e1 + (double)(4 * x) + (double)(4 * y) + 0.4e1 * pow(z, 0.3e1) +
0.3e1 *
(0.6e1 * z * z + 0.6e1 * (double)x * z * z +
0.6e1 * (double)y * z * z + 0.6e1 * pow(z, 0.5e1)) *
z * z +
0.6e1 *
(0.2e1 + (double)(2 * x) + (double)(2 * y) +
0.2e1 * pow(z, 0.3e1) + (double)(x * x) + (double)(2 * x * y) +
0.2e1 * (double)x * pow(z, 0.3e1) + (double)(y * y) +
0.2e1 * (double)y * pow(z, 0.3e1) + pow(z, 0.6e1)) *
z;
}
};
struct FunA {
double operator()(const double u) { return 1 + u * u; }
};
struct DiffFunA {
double operator()(const double u) { return 2 * u; }
};
int operator()(int, int, int p) const { return 2 * (p + 1); }
};
int main(int argc, char *argv[]) {
// Initialize PETSc
MoFEM::Core::Initialize(&argc, &argv, (char *)0, help);
// Create MoAB database
moab::Core moab_core; // create database
moab::Interface &moab = moab_core; // create interface to database
try {
// 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<ForcesAndSourcesCore>
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.
domain_lhs_fe, 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
// 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.
1);
// Add Lagrange multiplier field on body boundary
// 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.
// 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();
}
// 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 SNES solver
CHKERR DMMoFEMSNESSetJacobian(dm, simple_interface->getDomainFEName(),
domain_lhs_fe, null, null);
CHKERR DMMoFEMSNESSetJacobian(dm, simple_interface->getBoundaryFEName(),
boundary_lhs_fe, null, null);
// Set calculation of the right hand side vector for KSP solver
CHKERR DMMoFEMSNESSetFunction(dm, simple_interface->getDomainFEName(),
domain_rhs_fe, null, null);
CHKERR DMMoFEMSNESSetFunction(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
SNES solver;
CHKERR SNESCreate(PETSC_COMM_WORLD, &solver);
CHKERR SNESSetFromOptions(solver);
CHKERR SNESSetDM(solver, dm);
// Set-up solver, is type of solver and pre-conditioners
CHKERR SNESSetUp(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 SNESSolve(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 SNESDestroy(&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
CHKERR boost::static_pointer_cast<PostProcVolumeOnRefinedMesh>(
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;
}
static Index< 'p', 3 > p
int main(int argc, char *argv[])
static char help[]
#define CATCH_ERRORS
Catch errors.
Definition: definitions.h:385
@ AINSWORTH_LEGENDRE_BASE
Ainsworth Cole (Legendre) approx. base .
Definition: definitions.h:73
@ L2
field with C-1 continuity
Definition: definitions.h:101
@ H1
continuous field
Definition: definitions.h:98
#define CHKERRG(n)
Check error code of MoFEM/MOAB/PETSc function.
Definition: definitions.h:496
#define CHKERR
Inline error check.
Definition: definitions.h:548
PetscErrorCode DMMoFEMSNESSetFunction(DM dm, const char fe_name[], MoFEM::FEMethod *method, MoFEM::BasicMethod *pre_only, MoFEM::BasicMethod *post_only)
set SNES residual evaluation function
Definition: DMMMoFEM.cpp:676
PetscErrorCode DMMoFEMSNESSetJacobian(DM dm, const char fe_name[], MoFEM::FEMethod *method, MoFEM::BasicMethod *pre_only, MoFEM::BasicMethod *post_only)
set SNES Jacobian evaluation function
Definition: DMMMoFEM.cpp:717
PetscErrorCode DMRegister_MoFEM(const char sname[])
Register MoFEM problem.
Definition: DMMMoFEM.cpp:59
PetscErrorCode DMoFEMLoopFiniteElements(DM dm, const char fe_name[], MoFEM::FEMethod *method, CacheTupleWeakPtr cache_ptr=CacheTupleSharedPtr())
Executes FEMethod for finite elements in DM.
Definition: DMMMoFEM.cpp:544
PetscErrorCode DMoFEMMeshToGlobalVector(DM dm, Vec g, InsertMode mode, ScatterMode scatter_mode)
set ghosted vector values on all existing mesh entities
Definition: DMMMoFEM.cpp:493
const FTensor::Tensor2< T, Dim, Dim > Vec
static MoFEMErrorCodeGeneric< PetscErrorCode > ierr
Definition: Exceptions.hpp:87
CoreTmp< 0 > Core
Definition: Core.hpp:1096
DeprecatedCoreInterface Interface
Definition: Interface.hpp:1965
const double D
diffusivity
double operator()(const double u)
FTensor::Tensor1< double, 3 > operator()(const double x, const double y, const double t) const
double operator()(const double x, const double y, const double t) const
double operator()(const double x, const double y, const double z) const
double operator()(const double u)
Core (interface) class.
Definition: Core.hpp:92
static MoFEMErrorCode Initialize(int *argc, char ***args, const char file[], const char help[])
Initializes the MoFEM database PETSc, MOAB and MPI.
Definition: Core.cpp:85
static MoFEMErrorCode Finalize()
Checks for options to be called at the conclusion of the program.
Definition: Core.cpp:125
Deprecated interface functions.
MoFEMErrorCode getInterface(IFACE *&iface) const
Get interface refernce to pointer of interface.
MoFEMErrorCode createGhostVec(Vec *ghost_vec) const
MoFEMErrorCode testError(Vec ghost_vec)
Test error.
MoFEMErrorCode assembleGhostVector(Vec ghost_vec) const
Assemble error vector.
MoFEMErrorCode printError(Vec ghost_vec)
Print error.
Create finite elements instances.
MoFEMErrorCode creatFEToPostProcessResults(boost::shared_ptr< ForcesAndSourcesCore > &post_proc_volume) const
Create finite element to post-process results.
MoFEMErrorCode createFEToAssembleMatrixAndVectorForNonlinearProblem(boost::function< double(const double, const double, const double)> f_u, boost::function< double(const double, const double, const double)> f_source, boost::function< double(const double)> a, boost::function< double(const double)> diff_a, 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, ForcesAndSourcesCore::RuleHookFun vol_rule, ForcesAndSourcesCore::RuleHookFun face_rule=FaceRule(), bool trans=true) const
Create finite element to calculate matrix and vectors.
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.
int operator()(int, int, int p) const