VEC-6: Discountinous Galrekin for Kirchoff-Love Plate

Table of Contents

Prerequisites of this tutorial include SCL-11: Discountinous Galrekin for Poisson problem

Intended learning outcome:

Source code main code

* \file plate.cpp
* \example plate.cpp
* Implementation Kirchhoff-Love plate using Discointinous Galerkin (DG-Nitsche
* method)
#include <MoFEM.hpp>
using namespace MoFEM;
static char help[] = "...\n\n";
#include <BasicFiniteElements.hpp>
constexpr int BASE_DIM = 1; ///< dimension of base
constexpr int SPACE_DIM = 2; ///< dimension of space
constexpr int FIELD_DIM = 1; ///< dimension of approx. field
template <int DIM> struct ElementsAndOps {};
template <> struct ElementsAndOps<2> {
using DomainEleOp =
DomainEle::UserDataOperator; ///< Finire element operator type
using EntData = EntitiesFieldData::EntData; ///< Data on entities
GAUSS>::OpGradGradSymTensorGradGrad<1, 1, SPACE_DIM, 0>;
// Kronecker delta
// material parameters
constexpr double lambda = 1;
constexpr double mu = 1; ///< lame parameter
constexpr double t = 1; ///< plate stiffness
static double penalty = 1e6;
static double phi =
-1; // 1 - symmetric Nitsche, 0 - nonsymmetric, -1 antisymmetrica
static double nitsche = 1;
static int order = 4; // approximation order
auto source = [](const double x, const double y, const double) {
return cos(2 * x * M_PI) * sin(2 * y * M_PI);
* @brief get fourth-order constitutive tensor
auto plate_stiffness = []() {
constexpr auto a = (SPACE_DIM * (SPACE_DIM + 1)) / 2;
auto mat_D_ptr = boost::make_shared<MatrixDouble>(a * a, 1);
auto t_D = getFTensor4DdgFromMat<2, 2, 0>(*(mat_D_ptr));
constexpr double t3 = t * t * t;
constexpr double A = mu * t3 / 12;
constexpr double B = lambda * t3 / 12;
t_D(i, j, k, l) =
2 * B * ((t_kd(i, k) ^ t_kd(j, l)) / 4.) + A * t_kd(i, j) * t_kd(k, l);
// t_D(i, j, k, l) = (t_kd(i, k) ^ t_kd(j, l)) / 4.;
return mat_D_ptr;
// data for skeleton computation
std::array<std::vector<VectorInt>, 2>
indicesSideMap; ///< indices on rows for left hand-side
std::array<std::vector<MatrixDouble>, 2>
diffBaseSideMap; // first derivative of base functions
std::array<std::vector<MatrixDouble>, 2>
diff2BaseSideMap; // second derivative of base functions
std::array<double, 2> areaMap; // area/volume of elements on the side
std::array<int, 2> senseMap; // orientaton of local element edge/face in respect
// to global orientation of edge/face
* @brief Operator tp collect data from elements on the side of Edge/Face
OpCalculateSideData(std::string field_name, std::string col_field_name);
* @brief Operator the left hand side matrix
struct OpH1LhsSkeleton : public BoundaryEleOp {
* @brief Construct a new OpH1LhsSkeleton
* @param side_fe_ptr pointer to FE to evaluate side elements
OpH1LhsSkeleton(boost::shared_ptr<FaceSideEle> side_fe_ptr,
boost::shared_ptr<MatrixDouble> d_mat_ptr);
sideFEPtr; ///< pointer to element to get data on edge/face sides
MatrixDouble locMat; ///< local operator matrix
boost::shared_ptr<MatrixDouble> dMatPtr;
struct Plate {
Plate(MoFEM::Interface &m_field) : mField(m_field) {}
//! [Read mesh]
CHKERR simple->getOptions();
CHKERR simple->loadFile();
//! [Read mesh]
//! [Set up problem]
CHKERR PetscOptionsGetInt(PETSC_NULL, "", "-order", &order, PETSC_NULL);
CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-penalty", &penalty,
CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-phi", &phi, PETSC_NULL);
CHKERR PetscOptionsGetScalar(PETSC_NULL, "", "-nitsche", &nitsche,
MOFEM_LOG("WORLD", Sev::inform) << "Set order: " << order;
MOFEM_LOG("WORLD", Sev::inform) << "Set penalty: " << penalty;
MOFEM_LOG("WORLD", Sev::inform) << "Set phi: " << phi;
MOFEM_LOG("WORLD", Sev::inform) << "Set nitche: " << nitsche;
CHKERR simple->setFieldOrder("U", order);
CHKERR simple->setUp();
//! [Set up problem]
//! [Boundary condition]
// get edges and vertices on body skin
auto get_skin = [&]() {
Range body_ents;
mField.get_moab().get_entities_by_dimension(0, SPACE_DIM, body_ents));
Skinner skin(&mField.get_moab());
Range skin_ents;
MOAB_THROW(skin.find_skin(0, body_ents, false, skin_ents));
Range verts;
MOAB_THROW(mField.get_moab().get_connectivity(skin_ents, verts, true));
return skin_ents;
// remove dofs on skin edges from priblem
auto remove_dofs_from_problem = [&](Range &&skin) {
auto problem_mng = mField.getInterface<ProblemsManager>();
CHKERR problem_mng->removeDofsOnEntities(simple->getProblemName(), "U",
skin, 0, 1);
// it make plate simply supported
CHKERR remove_dofs_from_problem(get_skin());
//! [Boundary condition]
//! [Push operators to pipeline]
auto pipeline_mng = mField.getInterface<PipelineManager>();
auto rule_lhs = [](int, int, int p) -> int { return 2 * p; };
auto rule_rhs = [](int, int, int p) -> int { return 2 * p; };
auto rule_2 = [this](int, int, int) { return 2 * order; };
CHKERR pipeline_mng->setDomainLhsIntegrationRule(rule_lhs);
CHKERR pipeline_mng->setDomainRhsIntegrationRule(rule_rhs);
CHKERR pipeline_mng->setSkeletonLhsIntegrationRule(rule_2);
CHKERR pipeline_mng->setSkeletonRhsIntegrationRule(rule_2);
CHKERR pipeline_mng->setBoundaryLhsIntegrationRule(rule_2);
CHKERR pipeline_mng->setBoundaryRhsIntegrationRule(rule_2);
auto det_ptr = boost::make_shared<VectorDouble>();
auto jac_ptr = boost::make_shared<MatrixDouble>();
auto inv_jac_ptr = boost::make_shared<MatrixDouble>();
auto base_mass_ptr = boost::make_shared<MatrixDouble>();
auto data_l2_ptr = boost::make_shared<EntitiesFieldData>(MBENTITYSET);
auto mat_D_ptr = plate_stiffness();
auto push_ho_direcatives = [&](auto &pipeline) {
pipeline.push_back(new OpBaseDerivativesMass<BASE_DIM>(
base_mass_ptr, data_l2_ptr, AINSWORTH_LEGENDRE_BASE, L2));
pipeline.push_back(new OpBaseDerivativesNext<BASE_DIM>(
BaseDerivatives::SecondDerivative, base_mass_ptr, data_l2_ptr,
* @brief calculate jacobian
auto push_jacobian = [&](auto &pipeline) {
pipeline.push_back(new OpSetHOWeightsOnFace());
pipeline.push_back(new OpCalculateHOJac<SPACE_DIM>(jac_ptr));
new OpInvertMatrix<SPACE_DIM>(jac_ptr, det_ptr, inv_jac_ptr));
// push first base derivatives tp physical element shape
pipeline.push_back(new OpSetInvJacH1ForFace<1>(inv_jac_ptr));
// push second base directives tp physical element shape
pipeline.push_back(new OpSetInvJacH1ForFace<2>(inv_jac_ptr));
new OpDomainPlateStiffness("U", "U", mat_D_ptr));
// pipeline_mng->getOpDomainLhsPipeline().push_back(new OpDomainGradGrad(
// "U", "U", [](const double, const double, const double) { return 1; }));
// Push operators to the Pipeline for Skeleton
auto side_fe_ptr = boost::make_shared<FaceSideEle>(mField);
side_fe_ptr->getOpPtrVector().push_back(new OpCalculateSideData("U", "U"));
// Push operators to the Pipeline for Skeleton
new OpH1LhsSkeleton(side_fe_ptr, mat_D_ptr));
//! [Push operators to pipeline]
//! [Solve system]
auto pipeline_mng = mField.getInterface<PipelineManager>();
auto ksp_solver = pipeline_mng->createKSP();
CHKERR KSPSetFromOptions(ksp_solver);
CHKERR KSPSetUp(ksp_solver);
// Create RHS and solution vectors
auto dm = simple->getDM();
auto F = smartCreateDMVector(dm);
CHKERR KSPSolve(ksp_solver, F, D);
// Scatter result data on the mesh
//! [Solve system]
//! [Output results]
auto pipeline_mng = mField.getInterface<PipelineManager>();
auto post_proc_fe = boost::make_shared<PostProcEle>(mField);
auto u_ptr = boost::make_shared<VectorDouble>();
new OpCalculateScalarFieldValues("U", u_ptr));
new OpPPMap(post_proc_fe->getPostProcMesh(),
{{"U", u_ptr}},
{}, {}, {}
pipeline_mng->getDomainRhsFE() = post_proc_fe;
CHKERR pipeline_mng->loopFiniteElements();
CHKERR post_proc_fe->writeFile("out_result.h5m");
//! [Output results]
//! [Run program]
// CHKERR checkResults();
//! [Run program]
int main(int argc, char *argv[]) {
// Initialisation of MoFEM/PETSc and MOAB data structures
const char param_file[] = "param_file.petsc";
// Add logging channel for example
auto core_log = logging::core::get();
core_log->add_sink(LogManager::createSink(LogManager::getStrmWorld(), "PL"));
MOFEM_LOG_TAG("PL", "plate");
try {
//! [Register MoFEM discrete manager in PETSc]
DMType dm_name = "DMMOFEM";
//! [Register MoFEM discrete manager in PETSc
//! [Create MoAB]
moab::Core mb_instance; ///< mesh database
moab::Interface &moab = mb_instance; ///< mesh database interface
//! [Create MoAB]
//! [Create MoFEM]
MoFEM::Core core(moab); ///< finite element database
MoFEM::Interface &m_field = core; ///< finite element database insterface
//! [Create MoFEM]
//! [Plate]
Plate ex(m_field);
CHKERR ex.runProblem();
//! [Plate]
OpCalculateSideData::OpCalculateSideData(std::string row_field_name,
std::string col_field_name)
: FaceSideOp(row_field_name, col_field_name, FaceSideOp::OPROW) {}
EntData &data) {
const auto nb_in_loop = getFEMethod()->nInTheLoop;
auto clear = [](auto nb) {
if (type == MBVERTEX) {
areaMap[nb_in_loop] = getMeasure();
senseMap[nb_in_loop] = getEdgeSense();
if (!nb_in_loop) {
areaMap[1] = 0;
senseMap[1] = 0;
const auto nb_dofs = data.getIndices().size();
if (nb_dofs) {
template <typename T> inline auto get_ntensor(T &base_mat) {
template <typename T> inline auto get_ntensor(T &base_mat, int gg, int bb) {
double *ptr = &base_mat(gg, bb);
template <typename T> inline auto get_diff_ntensor(T &base_mat) {
double *ptr = &*base_mat.data().begin();
return getFTensor1FromPtr<2>(ptr);
template <typename T>
inline auto get_diff_ntensor(T &base_mat, int gg, int bb) {
double *ptr = &base_mat(gg, 2 * bb);
return getFTensor1FromPtr<2>(ptr);
template <typename T> inline auto get_diff2_ntensor(T &base_mat) {
double *ptr = &*base_mat.data().begin();
template <typename T>
inline auto get_diff2_ntensor(T &base_mat, int gg, int bb) {
double *ptr = &base_mat(gg, 4 * bb);
* @brief Construct a new OpH1LhsSkeleton
* @param side_fe_ptr pointer to FE to evaluate side elements
OpH1LhsSkeleton::OpH1LhsSkeleton(boost::shared_ptr<FaceSideEle> side_fe_ptr,
boost::shared_ptr<MatrixDouble> mat_d_ptr)
: BoundaryEleOp(NOSPACE, BoundaryEleOp::OPSPACE), sideFEPtr(side_fe_ptr),
dMatPtr(mat_d_ptr) {}
// Collect data from side domian elements
CHKERR loopSideFaces("dFE", *sideFEPtr);
const auto in_the_loop =
sideFEPtr->nInTheLoop; // return number of elements on the side
// calculate penalty
const double s = getMeasure() / (areaMap[0] + areaMap[1]);
const double p = penalty * s;
// get normal of the face or edge
auto t_normal = getFTensor1Normal();
// Elastic stiffness tensor (4th rank tensor with minor and major
// symmetry)
auto t_D = getFTensor4DdgFromMat<SPACE_DIM, SPACE_DIM, 0>(*dMatPtr);
// get number of integration points on face
const size_t nb_integration_pts = getGaussPts().size2();
// beta paramter is zero, when penalty method is used, also, takes value 1,
// when boundary edge/face is evaluated, and 2 when is skeleton edge/face.
const double beta = static_cast<double>(nitsche) / (in_the_loop + 1);
auto integrate = [&](auto sense_row, auto &row_ind, auto &row_diff,
auto &row_diff2, auto sense_col, auto &col_ind,
auto &col_diff, auto &col_diff2) {
// number of dofs, for homogenous approximation this value is
// constant.
const auto nb_rows = row_ind.size();
const auto nb_cols = col_ind.size();
const auto nb_row_base_functions = row_diff.size2() / SPACE_DIM;
if (nb_cols) {
// resize local element matrix
locMat.resize(nb_rows, nb_cols, false);
// get base functions, and integration weights
auto t_diff_row_base = get_diff_ntensor(row_diff);
auto t_diff2_row_base = get_diff2_ntensor(row_diff2);
// iterate integration points on face/edge
for (size_t gg = 0; gg != nb_integration_pts; ++gg) {
// t_w is integration weight, and measure is element area, or
// volume, depending if problem is in 2d/3d.
const double alpha = getMeasure() * t_w;
auto t_mat = locMat.data().begin();
// iterate rows
size_t rr = 0;
for (; rr != nb_rows; ++rr) {
t_mv(i, j) = t_D(i, j, k, l) * t_diff2_row_base(k, l);
// calculate tetting function
t_vn_plus(i, j) = beta * (phi * t_mv(i, j) / p);
t_vn(i, j) = (t_diff_row_base(j) * (t_normal(i) * sense_row)) -
t_vn_plus(i, j);
// get base functions on columns
auto t_diff_col_base = get_diff_ntensor(col_diff, gg, 0);
auto t_diff2_col_base = get_diff2_ntensor(col_diff2, gg, 0);
// iterate columns
for (size_t cc = 0; cc != nb_cols; ++cc) {
t_mu(i, j) = t_D(i, j, k, l) * t_diff2_col_base(k, l);
// // calculate variance of tested function
t_un(i, j) = -p * ((t_diff_col_base(j) * (t_normal(i) * sense_col) -
beta * t_mu(i, j) / p));
// assemble matrix
*t_mat -= alpha * (t_vn(i, j) * t_un(i, j));
*t_mat -= alpha * (t_vn_plus(i, j) * (beta * t_mu(i, j)));
// move to next column base and element of matrix
// move to next row base
// this is obsolete for this particular example, we keep it for
// generality. in case of multi-physcis problems diffrent fields
// can chare hierarchical base but use diffrent approx. order,
// so is possible to have more base functions than DOFs on
// element.
for (; rr < nb_row_base_functions; ++rr) {
// assemble system
CHKERR ::MatSetValues(getKSPB(), nb_rows, &*row_ind.begin(),
col_ind.size(), &*col_ind.begin(),
&*locMat.data().begin(), ADD_VALUES);
// iterate the sides rows
for (auto s0 : {LEFT_SIDE, RIGHT_SIDE}) {
const auto sense_row = senseMap[s0];
for (auto x0 = 0; x0 != indicesSideMap[s0].size(); ++x0) {
for (auto s1 : {LEFT_SIDE, RIGHT_SIDE}) {
const auto sense_col = senseMap[s1];
for (auto x1 = 0; x1 != indicesSideMap[s1].size(); ++x1) {
CHKERR integrate(sense_row, indicesSideMap[s0][x0],
sense_col, indicesSideMap[s1][x1],
static Index< 'p', 3 > p
std::string param_file
ForcesAndSourcesCore::UserDataOperator UserDataOperator
void simple(double P1[], double P2[], double P3[], double c[], const int N)
Definition: acoustic.cpp:69
static char help[]
constexpr double a
MoFEM::FaceElementForcesAndSourcesCore FaceEle
EntitiesFieldData::EntData EntData
constexpr int SPACE_DIM
constexpr int FIELD_DIM
ElementsAndOps< SPACE_DIM >::DomainEle DomainEle
ElementsAndOps< SPACE_DIM >::BoundaryEle BoundaryEle
Kronecker Delta class symmetric.
MoFEM::EdgeElementForcesAndSourcesCore EdgeEle
int main(int argc, char *argv[])
Catch errors.
Definition: definitions.h:372
Ainsworth Cole (Legendre) approx. base .
Definition: definitions.h:60
#define MOAB_THROW(err)
Check error code of MoAB function and throw MoFEM exception.
Definition: definitions.h:541
#define MoFEMFunctionReturnHot(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:447
@ L2
field with C-1 continuity
Definition: definitions.h:88
@ H1
continuous field
Definition: definitions.h:85
Definition: definitions.h:83
#define MoFEMFunctionBegin
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:346
#define MoFEMFunctionReturn(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:416
#define CHKERR
Inline error check.
Definition: definitions.h:535
#define MoFEMFunctionBeginHot
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:440
auto get_diff_ntensor(T &base_mat)
auto get_ntensor(T &base_mat)
std::array< double, 2 > areaMap
std::array< int, 2 > senseMap
ElementsAndOps< SPACE_DIM >::FaceSideEle FaceSideEle
static double phi
constexpr double lambda
constexpr auto t_kd
PetscErrorCode DMoFEMMeshToLocalVector(DM dm, Vec l, InsertMode mode, ScatterMode scatter_mode)
set local (or ghosted) vector values on mesh for partition only
Definition: DMMMoFEM.cpp:470
PetscErrorCode DMRegister_MoFEM(const char sname[])
Register MoFEM problem.
Definition: DMMMoFEM.cpp:47
auto smartCreateDMVector(DM dm)
Get smart vector from DM.
Definition: DMMoFEM.hpp:965
#define MOFEM_LOG(channel, severity)
Definition: LogManager.hpp:301
#define MOFEM_LOG_TAG(channel, tag)
Tag channel.
Definition: LogManager.hpp:332
constexpr int BASE_DIM
FTensor::Index< 'i', SPACE_DIM > i
FormsIntegrators< DomainEleOp >::Assembly< PETSC >::BiLinearForm< GAUSS >::OpGradGrad< 1, 1, SPACE_DIM > OpDomainGradGrad
Definition: helmholtz.cpp:27
FTensor::Index< 'l', 3 > l
FTensor::Index< 'j', 3 > j
FTensor::Index< 'k', 3 > k
const double T
PetscErrorCode MoFEMErrorCode
MoFEM/PETSc error code.
Definition: Exceptions.hpp:56
UBlasMatrix< double > MatrixDouble
Definition: Types.hpp:77
implementation of Data Operators for Forces and Sources
Definition: MoFEM.hpp:24
PetscErrorCode PetscOptionsGetInt(PetscOptions *, const char pre[], const char name[], PetscInt *ivalue, PetscBool *set)
PetscErrorCode PetscOptionsGetScalar(PetscOptions *, const char pre[], const char name[], PetscScalar *dval, PetscBool *set)
FTensor::Tensor2_symmetric< FTensor::PackPtr< double *, 4 >, 2 > getFTensor2SymmetricLowerFromPtr< 2 >(double *ptr)
Definition: Templates.hpp:839
SmartPetscObj< Vec > smartVectorDuplicate(SmartPetscObj< Vec > &vec)
Create duplicate vector of smart vector.
CoreTmp< 0 > Core
Definition: Core.hpp:1086
DeprecatedCoreInterface Interface
Definition: Interface.hpp:1955
FTensor::Tensor1< FTensor::PackPtr< double *, 2 >, 2 > getFTensor1FromPtr< 2 >(double *ptr)
Definition: Templates.hpp:726
const double D
double A
std::array< std::vector< MatrixDouble >, 2 > diff2BaseSideMap
Definition: plate.cpp:101
FormsIntegrators< DomainEleOp >::Assembly< PETSC >::BiLinearForm< GAUSS >::OpGradGradSymTensorGradGrad< 1, 1, SPACE_DIM, 0 > OpDomainPlateStiffness
Definition: plate.cpp:49
std::array< std::vector< MatrixDouble >, 2 > diffBaseSideMap
Definition: plate.cpp:99
auto plate_stiffness
get fourth-order constitutive tensor
Definition: plate.cpp:80
std::array< std::vector< VectorInt >, 2 > indicesSideMap
indices on rows for left hand-side
Definition: plate.cpp:97
constexpr double t
plate stiffness
Definition: plate.cpp:59
FormsIntegrators< DomainEleOp >::Assembly< PETSC >::LinearForm< GAUSS >::OpSource< BASE_DIM, FIELD_DIM > OpDomainPlateLoad
Definition: plate.cpp:51
auto get_diff2_ntensor(T &base_mat)
Definition: plate.cpp:490
static double nitsche
constexpr auto field_name
constexpr double mu
constexpr double penalty
virtual moab::Interface & get_moab()=0
Core (interface) class.
Definition: Core.hpp:82
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
static MoFEMErrorCode Finalize()
Checks for options to be called at the conclusion of the program.
Definition: Core.cpp:112
Deprecated interface functions.
Data on single entity (This is passed as argument to DataOperator::doWork)
MatrixDouble & getN(const FieldApproximationBase base)
get base functions this return matrix (nb. of rows is equal to nb. of Gauss pts, nb....
const VectorInt & getIndices() const
Get global indices of dofs on entity.
Base face element used to integrate on skeleton.
auto getFTensor0IntegrationWeight()
Get integration weights.
MatrixDouble & getGaussPts()
matrix of integration (Gauss) points for Volume Element
Get value at integration points for scalar field.
Post post-proc data at points from hash maps.
Definition: PostProc.hpp:166
Modify integration weights on face to take in account higher-order geometry.
PipelineManager interface.
boost::shared_ptr< FEMethod > & getDomainLhsFE()
Definition: PostProc.hpp:120
Problem manager is used to build and partition problems.
Simple interface for fast problem set-up.
Definition: Simple.hpp:26
MoFEMErrorCode getInterface(IFACE *&iface) const
Get interface refernce to pointer of interface.
Operator tp collect data from elements on the side of Edge/Face.
OpCalculateSideData(std::string field_name, std::string col_field_name, UserDataOperator::OpType type)
MoFEMErrorCode doWork(int side, EntityType type, EntData &data)
Operator the left hand side matrix.
Definition: plate.cpp:121
boost::shared_ptr< MatrixDouble > dMatPtr
Definition: plate.cpp:138
boost::shared_ptr< FaceSideEle > sideFEPtr
pointer to element to get data on edge/face sides
Definition: plate.cpp:136
MatrixDouble locMat
local operator matrix
Definition: plate.cpp:137
MoFEMErrorCode doWork(int side, EntityType type, EntitiesFieldData::EntData &data)
Operator for linear form, usually to calculate values on right hand side.
Definition: plate.cpp:511
OpH1LhsSkeleton(boost::shared_ptr< FaceSideEle > side_fe_ptr, boost::shared_ptr< MatrixDouble > d_mat_ptr)
Construct a new OpH1LhsSkeleton.
Definition: plate.cpp:506
Definition: plate.cpp:141
MoFEMErrorCode setupProblem()
[Read mesh]
Definition: plate.cpp:171
MoFEM::Interface & mField
Definition: plate.cpp:155
MoFEMErrorCode runProblem()
[Output results]
Definition: plate.cpp:376
MoFEMErrorCode boundaryCondition()
[Set up problem]
Definition: plate.cpp:200
MoFEMErrorCode outputResults()
[Solve system]
Definition: plate.cpp:336
MoFEMErrorCode solveSystem()
[Push operators to pipeline]
Definition: plate.cpp:309
MoFEMErrorCode assembleSystem()
[Boundary condition]
Definition: plate.cpp:235
Plate(MoFEM::Interface &m_field)
Definition: plate.cpp:143
MoFEMErrorCode readMesh()
[Read mesh]
Definition: plate.cpp:159