v0.9.0
quad_polynomial_approximation.cpp
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1 /** \file quad_polynomial_approximation.cpp
2  \example quad_polynomial_approximation.cpp
3  \brief Checking approximation functions for quad
4 
5 */
6 
7 /* This file is part of MoFEM.
8  * MoFEM is free software: you can redistribute it and/or modify it under
9  * the terms of the GNU Lesser General Public License as published by the
10  * Free Software Foundation, either version 3 of the License, or (at your
11  * option) any later version.
12  *
13  * MoFEM is distributed in the hope that it will be useful, but WITHOUT
14  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
15  * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16  * License for more details.
17  *
18  * You should have received a copy of the GNU Lesser General Public
19  * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
20 
21 #include <MoFEM.hpp>
22 
23 using namespace MoFEM;
24 
28 
29 static char help[] = "...\n\n";
30 
31 static constexpr int approx_order = 5;
32 struct ApproxFunction {
33  static inline double fun(double x, double y) {
34  double r = 1;
35  for (int o = 1; o <= approx_order; ++o) {
36  for (int i = 0; i <= o; ++i) {
37  int j = o - i;
38  if (j >= 0)
39  r += pow(x, i) * pow(y, j);
40  }
41  }
42  return r;
43  }
44 
45  static inline VectorDouble3 diff_fun(double x, double y) {
46  VectorDouble3 r(2);
47  r.clear();
48  for (int o = 1; o <= approx_order; ++o) {
49  for (int i = 0; i <= o; ++i) {
50  int j = o - i;
51  if (j >= 0) {
52  r[0] += i > 0 ? i * pow(x, i - 1) * pow(y, j) : 0;
53  r[1] += j > 0 ? j * pow(x, i) * pow(y, j - 1) : 0;
54  }
55  }
56  }
57  return r;
58  }
59 };
60 
61 struct QuadOpCheck : public OpEle {
62 
63  QuadOpCheck(boost::shared_ptr<VectorDouble> &field_vals,
64  boost::shared_ptr<MatrixDouble> &diff_field_vals);
65  MoFEMErrorCode doWork(int side, EntityType type,
67 
68 private:
69  boost::shared_ptr<VectorDouble> fieldVals;
70  boost::shared_ptr<MatrixDouble> diffFieldVals;
71 };
72 
73 struct QuadOpRhs : public OpEle {
74 
76  MoFEMErrorCode doWork(int side, EntityType type,
78 
79 private:
81 };
82 
83 struct QuadOpLhs : public OpEle {
84 
86  MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type,
87  EntityType col_type,
90 
91 private:
93 };
94 
95 int main(int argc, char *argv[]) {
96 
97  MoFEM::Core::Initialize(&argc, &argv, (char *)0, help);
98 
99  try {
100 
101  moab::Core mb_instance;
102  moab::Interface &moab = mb_instance;
103 
104  std::array<double, 12> one_quad_coords = {0, 0, 0,
105 
106  1, 0, 0,
107 
108  1, 1, 0,
109 
110  0, 1, 0};
111  std::array<EntityHandle, 4> one_quad_nodes;
112  for (int n = 0; n != 4; ++n)
113  CHKERR moab.create_vertex(&one_quad_coords[3 * n], one_quad_nodes[n]);
114  EntityHandle one_quad;
115  CHKERR moab.create_element(MBQUAD, one_quad_nodes.data(), 4, one_quad);
116  Range one_quad_range;
117  one_quad_range.insert(one_quad);
118  Range one_quad_adj_ents;
119  CHKERR moab.get_adjacencies(one_quad_range, 1, true, one_quad_adj_ents,
120  moab::Interface::UNION);
121 
122  MoFEM::Core core(moab);
123  MoFEM::Interface &m_field = core;
124 
125  BitRefLevel bit_level0 = BitRefLevel().set(0);
126  CHKERR m_field.getInterface<BitRefManager>()->setBitRefLevelByDim(
127  0, 2, bit_level0);
128 
129  // Fields
130  CHKERR m_field.add_field("FIELD1", H1, AINSWORTH_LEGENDRE_BASE, 1);
131  CHKERR m_field.add_ents_to_field_by_type(0, MBQUAD, "FIELD1");
132 
133  CHKERR m_field.set_field_order(0, MBVERTEX, "FIELD1", 1);
134  CHKERR m_field.set_field_order(0, MBEDGE, "FIELD1", approx_order);
135  CHKERR m_field.set_field_order(0, MBQUAD, "FIELD1", approx_order);
136  CHKERR m_field.build_fields();
137 
138  // FE
139  CHKERR m_field.add_finite_element("QUAD");
140 
141  // Define rows/cols and element data
142  CHKERR m_field.modify_finite_element_add_field_row("QUAD", "FIELD1");
143  CHKERR m_field.modify_finite_element_add_field_col("QUAD", "FIELD1");
144  CHKERR m_field.modify_finite_element_add_field_data("QUAD", "FIELD1");
145  CHKERR m_field.add_ents_to_finite_element_by_type(0, MBQUAD, "QUAD");
146 
147  // build finite elemnts
148  CHKERR m_field.build_finite_elements();
149  // //build adjacencies
150  CHKERR m_field.build_adjacencies(bit_level0);
151 
152  // Problem
153  CHKERR m_field.add_problem("TEST_PROBLEM");
154 
155  // set finite elements for problem
156  CHKERR m_field.modify_problem_add_finite_element("TEST_PROBLEM", "QUAD");
157  // set refinement level for problem
158  CHKERR m_field.modify_problem_ref_level_add_bit("TEST_PROBLEM", bit_level0);
159 
160  // build problem
161  ProblemsManager *prb_mng_ptr;
162  CHKERR m_field.getInterface(prb_mng_ptr);
163  CHKERR prb_mng_ptr->buildProblem("TEST_PROBLEM", true);
164  // partition
165  CHKERR prb_mng_ptr->partitionSimpleProblem("TEST_PROBLEM");
166  CHKERR prb_mng_ptr->partitionFiniteElements("TEST_PROBLEM");
167  // what are ghost nodes, see Petsc Manual
168  CHKERR prb_mng_ptr->partitionGhostDofs("TEST_PROBLEM");
169 
170  // Create matrices
173  ->createMPIAIJWithArrays<PetscGlobalIdx_mi_tag>("TEST_PROBLEM", A);
175  CHKERR m_field.getInterface<VecManager>()->vecCreateGhost("TEST_PROBLEM",
176  ROW, F);
178  CHKERR m_field.getInterface<VecManager>()->vecCreateGhost("TEST_PROBLEM",
179  COL, D);
180 
181  auto rule = [&](int, int, int p) { return 2 * (p + 1); };
182 
183  auto assemble_matrices_and_vectors = [&]() {
185  Ele fe(m_field);
186  fe.getRuleHook = rule;
187  MatrixDouble inv_jac;
188  fe.getOpPtrVector().push_back(new OpCalculateInvJacForFace(inv_jac));
189  fe.getOpPtrVector().push_back(new OpSetInvJacH1ForFace(inv_jac));
190  fe.getOpPtrVector().push_back(new QuadOpRhs(F));
191  fe.getOpPtrVector().push_back(new QuadOpLhs(A));
192  CHKERR VecZeroEntries(F);
193  CHKERR MatZeroEntries(A);
194  CHKERR m_field.loop_finite_elements("TEST_PROBLEM", "QUAD", fe);
195  CHKERR VecAssemblyBegin(F);
196  CHKERR VecAssemblyEnd(F);
197  CHKERR MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
198  CHKERR MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
200  };
201 
202  auto solve_problem = [&] {
204  auto solver = createKSP(PETSC_COMM_WORLD);
205  CHKERR KSPSetOperators(solver, A, A);
206  CHKERR KSPSetFromOptions(solver);
207  CHKERR KSPSetUp(solver);
208  CHKERR KSPSolve(solver, F, D);
209  CHKERR VecGhostUpdateBegin(D, INSERT_VALUES, SCATTER_FORWARD);
210  CHKERR VecGhostUpdateEnd(D, INSERT_VALUES, SCATTER_FORWARD);
211  CHKERR m_field.getInterface<VecManager>()->setLocalGhostVector(
212  "TEST_PROBLEM", COL, D, INSERT_VALUES, SCATTER_REVERSE);
214  };
215 
216  auto check_solution = [&] {
218  Ele fe(m_field);
219  fe.getRuleHook = rule;
220  boost::shared_ptr<VectorDouble> field_vals_ptr(new VectorDouble());
221  boost::shared_ptr<MatrixDouble> diff_field_vals_ptr(new MatrixDouble());
222  MatrixDouble inv_jac;
223  fe.getOpPtrVector().push_back(new OpCalculateInvJacForFace(inv_jac));
224  fe.getOpPtrVector().push_back(new OpSetInvJacH1ForFace(inv_jac));
225  fe.getOpPtrVector().push_back(
226  new OpCalculateScalarFieldValues("FIELD1", field_vals_ptr));
227  fe.getOpPtrVector().push_back(
228  new OpCalculateScalarFieldGradient<2>("FIELD1", diff_field_vals_ptr));
229  fe.getOpPtrVector().push_back(
230  new QuadOpCheck(field_vals_ptr, diff_field_vals_ptr));
231  CHKERR m_field.loop_finite_elements("TEST_PROBLEM", "QUAD", fe);
233  };
234 
235  CHKERR assemble_matrices_and_vectors();
237  CHKERR check_solution();
238  }
239  CATCH_ERRORS;
240 
242  return 0;
243 }
244 
245 QuadOpCheck::QuadOpCheck(boost::shared_ptr<VectorDouble> &field_vals,
246  boost::shared_ptr<MatrixDouble> &diff_field_vals)
247  : OpEle("FIELD1", "FIELD1", ForcesAndSourcesCore::UserDataOperator::OPROW),
248  fieldVals(field_vals), diffFieldVals(diff_field_vals) {}
249 
250 MoFEMErrorCode QuadOpCheck::doWork(int side, EntityType type,
253 
254  if (type == MBVERTEX) {
255  const int nb_gauss_pts = data.getN().size1();
256  auto t_coords = getFTensor1CoordsAtGaussPts();
257  for (int gg = 0; gg != nb_gauss_pts; ++gg) {
258  double f = ApproxFunction::fun(t_coords(0), t_coords(1));
259  constexpr double eps = 1e-6;
260  if (std::abs(f - (*fieldVals)[gg]) > eps)
261  SETERRQ2(PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
262  "Wrong value %6.4e != %6.4e", f, (*fieldVals)[gg]);
263  VectorDouble3 diff_f = ApproxFunction::diff_fun(t_coords(0), t_coords(1));
264 
265  std::cout << f - (*fieldVals)[gg] << " : ";
266  for (auto d : {0, 1})
267  std::cout << diff_f[d] - (*diffFieldVals)(d, gg) << " ";
268  std::cout << std::endl;
269 
270  for (auto d : {0, 1})
271  if (std::abs(diff_f[d] - (*diffFieldVals)(d, gg)) > eps)
272  SETERRQ2(PETSC_COMM_SELF, MOFEM_ATOM_TEST_INVALID,
273  "Wrong directive value (%d) %6.4e != %6.4e", diff_f[d],
274  (*diffFieldVals)(d, gg));
275 
276 
277  ++t_coords;
278  }
279  }
281 }
282 
284  : OpEle("FIELD1", "FIELD1", ForcesAndSourcesCore::UserDataOperator::OPROW),
285  F(f) {}
286 
287 MoFEMErrorCode QuadOpRhs::doWork(int side, EntityType type,
290  const int nb_dofs = data.getN().size2();
291  if (nb_dofs) {
292  const int nb_gauss_pts = data.getN().size1();
293  VectorDouble nf(nb_dofs);
294  nf.clear();
295  auto t_base = data.getFTensor0N();
296  auto t_coords = getFTensor1CoordsAtGaussPts();
297  auto t_w = getFTensor0IntegrationWeight();
298  double vol = getArea();
299  for (int gg = 0; gg != nb_gauss_pts; ++gg) {
300  double f = ApproxFunction::fun(t_coords(0), t_coords(1));
301  double v = t_w * vol * f;
302  double *val = &*nf.begin();
303  for (int bb = 0; bb != nb_dofs; ++bb) {
304  *val += v * t_base;
305  ++t_base;
306  ++val;
307  }
308  ++t_coords;
309  ++t_w;
310  }
311  CHKERR VecSetValues(F, data, &*nf.data().begin(), ADD_VALUES);
312  }
314 }
315 
317  : OpEle("FIELD1", "FIELD1",
319  A(a) {
320  // FIXME: Can be symmetric, is not for simplicity
321  sYmm = false;
322 }
323 
324 MoFEMErrorCode QuadOpLhs::doWork(int row_side, int col_side,
325  EntityType row_type, EntityType col_type,
329  const int row_nb_dofs = row_data.getN().size2();
330  const int col_nb_dofs = col_data.getN().size2();
331  if (row_nb_dofs && col_nb_dofs) {
332  const int nb_gauss_pts = row_data.getN().size1();
333  MatrixDouble m(row_nb_dofs, col_nb_dofs);
334  m.clear();
335  auto t_w = getFTensor0IntegrationWeight();
336  double vol = getArea();
337  double *row_base_ptr = &*row_data.getN().data().begin();
338  double *col_base_ptr = &*col_data.getN().data().begin();
339  for (int gg = 0; gg != nb_gauss_pts; ++gg) {
340 
341  double v = t_w * vol;
342  cblas_dger(CblasRowMajor, row_nb_dofs, col_nb_dofs, v, row_base_ptr, 1,
343  col_base_ptr, 1, &*m.data().begin(), col_nb_dofs);
344 
345  row_base_ptr += row_nb_dofs;
346  col_base_ptr += col_nb_dofs;
347  ++t_w;
348  }
349  CHKERR MatSetValues(A, row_data, col_data, &*m.data().begin(), ADD_VALUES);
350  }
352 }
QuadOpLhs(SmartPetscObj< Mat > &a)
static double fun(double x, double y)
virtual MoFEMErrorCode modify_finite_element_add_field_col(const std::string &fe_name, const std::string &name_row)=0
set field col which finite element use
QuadOpCheck(boost::shared_ptr< VectorDouble > &field_vals, boost::shared_ptr< MatrixDouble > &diff_field_vals)
virtual MoFEMErrorCode add_ents_to_finite_element_by_type(const EntityHandle entities, const EntityType type, const std::string &name, const bool recursive=true)=0
add entities to finite element
Problem manager is used to build and partition problems.
virtual MoFEMErrorCode build_adjacencies(const Range &ents, int verb=DEFAULT_VERBOSITY)=0
build adjacencies
static char help[]
MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type, EntityType col_type, DataForcesAndSourcesCore::EntData &row_data, DataForcesAndSourcesCore::EntData &col_data)
Operator for bi-linear form, usually to calculate values on left hand side.
MoFEMErrorCode doWork(int side, EntityType type, DataForcesAndSourcesCore::EntData &data)
Operator for linear form, usually to calculate values on right hand side.
ublas::matrix< double, ublas::row_major, DoubleAllocator > MatrixDouble
Definition: Types.hpp:74
virtual MoFEMErrorCode modify_problem_add_finite_element(const std::string &name_problem, const std::string &fe_name)=0
add finite element to problem, this add entities assigned to finite element to a particular problem
MoFEMErrorCode buildProblem(const std::string name, const bool square_matrix, int verb=VERBOSE)
build problem data structures
#define MoFEMFunctionReturn(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:477
virtual MoFEMErrorCode add_field(const std::string &name, const FieldSpace space, const FieldApproximationBase base, const FieldCoefficientsNumber nb_of_coefficients, const TagType tag_type=MB_TAG_SPARSE, const enum MoFEMTypes bh=MF_EXCL, int verb=DEFAULT_VERBOSITY)=0
Add field.
void cblas_dger(const enum CBLAS_ORDER order, const int M, const int N, const double alpha, const double *X, const int incX, const double *Y, const int incY, double *A, const int lda)
Definition: cblas_dger.c:12
virtual MoFEMErrorCode set_field_order(const EntityHandle meshset, const EntityType type, const std::string &name, const ApproximationOrder order, int verb=DEFAULT_VERBOSITY)=0
Set order approximation of the entities in the field.
Core (interface) class.
Definition: Core.hpp:50
static double fun(double x, double y, double z)
implementation of Data Operators for Forces and Sources
Definition: Common.hpp:21
static constexpr int approx_order
SmartPetscObj< Vec > F
static MoFEMErrorCode Initialize(int *argc, char ***args, const char file[], const char help[])
Initializes the MoFEM database PETSc, MOAB and MPI.
Definition: Core.cpp:51
static VectorDouble3 diff_fun(double x, double y)
PetscErrorCode solve_problem(MoFEM::Interface &m_field, const string &problem_name, const string &fe_name, const string &re_field, const string &im_field, InsertMode mode, FUNEVAL &fun_evaluator, PetscBool is_partitioned)
MoFEMErrorCode getInterface(const MOFEMuuid &uuid, IFACE *&iface) const
Get interface by uuid and return reference to pointer of interface.
bool sYmm
If true assume that matrix is symmetric structure.
const Tensor1_Expr< const dTensor0< T, Dim, i >, typename promote< T, double >::V, Dim, i > d(const Tensor0< T * > &a, const Index< i, Dim > index, const Tensor1< int, Dim > &d_ijk, const Tensor1< double, Dim > &d_xyz)
Definition: dTensor0.hpp:27
Calculate inverse of jacobian for face element.
DataForcesAndSourcesCore::EntData EntData
virtual MoFEMErrorCode add_ents_to_field_by_type(const Range &ents, const EntityType type, const std::string &name, int verb=DEFAULT_VERBOSITY)=0
Add entities to field meshset.
PetscErrorCode MoFEMErrorCode
MoFEM/PETSc error code.
Definition: Exceptions.hpp:66
QuadOpRhs(SmartPetscObj< Vec > &f)
auto getFTensor0IntegrationWeight()
Get integration weights.
static VectorDouble3 diff_fun(double x, double y, double z)
Managing BitRefLevels.
Ainsworth Cole (Legendre) approx. base .
Definition: definitions.h:146
MoFEMErrorCode MatSetValues(Mat M, const DataForcesAndSourcesCore::EntData &row_data, const DataForcesAndSourcesCore::EntData &col_data, const double *ptr, InsertMode iora)
Assemble PETSc matrix.
virtual MoFEMErrorCode modify_problem_ref_level_add_bit(const std::string &name_problem, const BitRefLevel &bit)=0
add ref level to problem
Vector manager is used to create vectors \mofem_vectors.
Definition: VecManager.hpp:36
MoFEMErrorCode VecSetValues(Vec V, const DataForcesAndSourcesCore::EntData &data, const double *ptr, InsertMode iora)
Assemble PETSc vector.
virtual MoFEMErrorCode add_finite_element(const std::string &fe_name, enum MoFEMTypes bh=MF_EXCL, int verb=DEFAULT_VERBOSITY)=0
add finite element
#define CHKERR
Inline error check.
Definition: definitions.h:596
virtual MoFEMErrorCode modify_finite_element_add_field_data(const std::string &fe_name, const std::string &name_filed)=0
set finite element field data
Transform local reference derivatives of shape functions to global derivatives.
MoFEMErrorCode partitionGhostDofs(const std::string name, int verb=VERBOSE)
determine ghost nodes
boost::shared_ptr< VectorDouble > fieldVals
ForcesAndSourcesCore::UserDataOperator UserDataOperator
VectorBoundedArray< double, 3 > VectorDouble3
Definition: Types.hpp:85
std::bitset< BITREFLEVEL_SIZE > BitRefLevel
Bit structure attached to each entity identifying to what mesh entity is attached.
Definition: Types.hpp:51
virtual MoFEMErrorCode build_fields(int verb=DEFAULT_VERBOSITY)=0
auto createKSP
Definition: AuxPETSc.hpp:241
SmartPetscObj< Mat > A
MoFEMErrorCode doWork(int side, EntityType type, DataForcesAndSourcesCore::EntData &data)
Operator for linear form, usually to calculate values on right hand side.
virtual MoFEMErrorCode add_problem(const std::string &name, enum MoFEMTypes bh=MF_EXCL, int verb=DEFAULT_VERBOSITY)=0
Add problem.
Get field gradients at integration pts for scalar filed rank 0, i.e. vector field.
Data on single entity (This is passed as argument to DataOperator::doWork)
MoFEMErrorCode partitionFiniteElements(const std::string name, bool part_from_moab=false, int low_proc=-1, int hi_proc=-1, int verb=VERBOSE)
partition finite elementsFunction which partition finite elements based on dofs partitioning....
structure to get information form mofem into DataForcesAndSourcesCore
virtual MoFEMErrorCode modify_finite_element_add_field_row(const std::string &fe_name, const std::string &name_row)=0
set field row which finite element use
#define MoFEMFunctionBegin
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:407
#define CATCH_ERRORS
Catch errors.
Definition: definitions.h:433
continuous field
Definition: definitions.h:171
static const double eps
int main(int argc, char *argv[])
ublas::vector< double, DoubleAllocator > VectorDouble
Definition: Types.hpp:72
MatrixDouble & getN(const FieldApproximationBase base)
get base functions this return matrix (nb. of rows is equal to nb. of Gauss pts, nb....
boost::shared_ptr< MatrixDouble > diffFieldVals
FaceElementForcesAndSourcesCoreSwitch< 0 > FaceElementForcesAndSourcesCore
Face finite element default.
Get value at integration points for scalar field.
MoFEMErrorCode partitionSimpleProblem(const std::string name, int verb=VERBOSE)
partition problem dofs
virtual MoFEMErrorCode build_finite_elements(int verb=DEFAULT_VERBOSITY)=0
Build finite elementsBuild finite element data structures. Have to be run before problem and adjacenc...
Matrix manager is used to build and partition problems.
FTensor::Tensor0< FTensor::PackPtr< double *, 1 > > getFTensor0N(const FieldApproximationBase base)
Get base function as Tensor0.
static MoFEMErrorCode Finalize()
Checks for options to be called at the conclusion of the program.
Definition: Core.cpp:61
DEPRECATED MoFEMErrorCode loop_finite_elements(const Problem *problem_ptr, const std::string &fe_name, FEMethod &method, int lower_rank, int upper_rank, MoFEMTypes bh, int verb=DEFAULT_VERBOSITY)