|
Intrepid
|
00001 // @HEADER 00002 // ************************************************************************ 00003 // 00004 // Intrepid Package 00005 // Copyright (2007) Sandia Corporation 00006 // 00007 // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive 00008 // license for use of this work by or on behalf of the U.S. Government. 00009 // 00010 // This library is free software; you can redistribute it and/or modify 00011 // it under the terms of the GNU Lesser General Public License as 00012 // published by the Free Software Foundation; either version 2.1 of the 00013 // License, or (at your option) any later version. 00014 // 00015 // This library is distributed in the hope that it will be useful, but 00016 // WITHOUT ANY WARRANTY; without even the implied warranty of 00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00018 // Lesser General Public License for more details. 00019 // 00020 // You should have received a copy of the GNU Lesser General Public 00021 // License along with this library; if not, write to the Free Software 00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 00023 // USA 00024 // Questions? Contact Pavel Bochev (pbboche@sandia.gov), 00025 // Denis Ridzal (dridzal@sandia.gov), 00026 // Kara Peterson (kjpeter@sandia.gov). 00027 // 00028 // ************************************************************************ 00029 // @HEADER 00030 00036 #include "Intrepid_FieldContainer.hpp" 00037 #include "Intrepid_HGRAD_QUAD_C1_FEM.hpp" 00038 #include "Intrepid_DefaultCubatureFactory.hpp" 00039 #include "Intrepid_RealSpaceTools.hpp" 00040 #include "Intrepid_ArrayTools.hpp" 00041 #include "Intrepid_FunctionSpaceTools.hpp" 00042 #include "Intrepid_CellTools.hpp" 00043 #include "Teuchos_oblackholestream.hpp" 00044 #include "Teuchos_RCP.hpp" 00045 #include "Teuchos_GlobalMPISession.hpp" 00046 #include "Teuchos_SerialDenseMatrix.hpp" 00047 #include "Teuchos_SerialDenseVector.hpp" 00048 #include "Teuchos_LAPACK.hpp" 00049 00050 using namespace std; 00051 using namespace Intrepid; 00052 00053 void rhsFunc(FieldContainer<double> &, const FieldContainer<double> &, int, int); 00054 void neumann(FieldContainer<double> & , 00055 const FieldContainer<double> & , 00056 const FieldContainer<double> & , 00057 const shards::CellTopology & , 00058 int, int, int); 00059 void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int); 00060 00062 void rhsFunc(FieldContainer<double> & result, 00063 const FieldContainer<double> & points, 00064 int xd, 00065 int yd) { 00066 00067 int x = 0, y = 1; 00068 00069 // second x-derivatives of u 00070 if (xd > 1) { 00071 for (int cell=0; cell<result.dimension(0); cell++) { 00072 for (int pt=0; pt<result.dimension(1); pt++) { 00073 result(cell,pt) = - xd*(xd-1)*std::pow(points(cell,pt,x), xd-2) * std::pow(points(cell,pt,y), yd); 00074 } 00075 } 00076 } 00077 00078 // second y-derivatives of u 00079 if (yd > 1) { 00080 for (int cell=0; cell<result.dimension(0); cell++) { 00081 for (int pt=0; pt<result.dimension(1); pt++) { 00082 result(cell,pt) -= yd*(yd-1)*std::pow(points(cell,pt,y), yd-2) * std::pow(points(cell,pt,x), xd); 00083 } 00084 } 00085 } 00086 00087 // add u 00088 for (int cell=0; cell<result.dimension(0); cell++) { 00089 for (int pt=0; pt<result.dimension(1); pt++) { 00090 result(cell,pt) += std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00091 } 00092 } 00093 00094 } 00095 00096 00098 void neumann(FieldContainer<double> & result, 00099 const FieldContainer<double> & points, 00100 const FieldContainer<double> & jacs, 00101 const shards::CellTopology & parentCell, 00102 int sideOrdinal, int xd, int yd) { 00103 00104 int x = 0, y = 1; 00105 00106 int numCells = result.dimension(0); 00107 int numPoints = result.dimension(1); 00108 00109 FieldContainer<double> grad_u(numCells, numPoints, 2); 00110 FieldContainer<double> side_normals(numCells, numPoints, 2); 00111 FieldContainer<double> normal_lengths(numCells, numPoints); 00112 00113 // first x-derivatives of u 00114 if (xd > 0) { 00115 for (int cell=0; cell<numCells; cell++) { 00116 for (int pt=0; pt<numPoints; pt++) { 00117 grad_u(cell,pt,x) = xd*std::pow(points(cell,pt,x), xd-1) * std::pow(points(cell,pt,y), yd); 00118 } 00119 } 00120 } 00121 00122 // first y-derivatives of u 00123 if (yd > 0) { 00124 for (int cell=0; cell<numCells; cell++) { 00125 for (int pt=0; pt<numPoints; pt++) { 00126 grad_u(cell,pt,y) = yd*std::pow(points(cell,pt,y), yd-1) * std::pow(points(cell,pt,x), xd); 00127 } 00128 } 00129 } 00130 00131 CellTools<double>::getPhysicalSideNormals(side_normals, jacs, sideOrdinal, parentCell); 00132 00133 // scale normals 00134 RealSpaceTools<double>::vectorNorm(normal_lengths, side_normals, NORM_TWO); 00135 FunctionSpaceTools::scalarMultiplyDataData<double>(side_normals, normal_lengths, side_normals, true); 00136 00137 FunctionSpaceTools::dotMultiplyDataData<double>(result, grad_u, side_normals); 00138 00139 } 00140 00142 void u_exact(FieldContainer<double> & result, const FieldContainer<double> & points, int xd, int yd) { 00143 int x = 0, y = 1; 00144 for (int cell=0; cell<result.dimension(0); cell++) { 00145 for (int pt=0; pt<result.dimension(1); pt++) { 00146 result(cell,pt) = std::pow(points(pt,x), xd)*std::pow(points(pt,y), yd); 00147 } 00148 } 00149 } 00150 00151 00152 00153 00154 int main(int argc, char *argv[]) { 00155 00156 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00157 00158 // This little trick lets us print to std::cout only if 00159 // a (dummy) command-line argument is provided. 00160 int iprint = argc - 1; 00161 Teuchos::RCP<std::ostream> outStream; 00162 Teuchos::oblackholestream bhs; // outputs nothing 00163 if (iprint > 0) 00164 outStream = Teuchos::rcp(&std::cout, false); 00165 else 00166 outStream = Teuchos::rcp(&bhs, false); 00167 00168 // Save the format state of the original std::cout. 00169 Teuchos::oblackholestream oldFormatState; 00170 oldFormatState.copyfmt(std::cout); 00171 00172 *outStream \ 00173 << "===============================================================================\n" \ 00174 << "| |\n" \ 00175 << "| Unit Test (Basis_HGRAD_QUAD_C1_FEM) |\n" \ 00176 << "| |\n" \ 00177 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00178 << "| for the Neumann problem on a physical parallelogram |\n" \ 00179 << "| AND a reference quad Omega with boundary Gamma. |\n" \ 00180 << "| |\n" \ 00181 << "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \ 00182 << "| |\n" \ 00183 << "| For a generic parallelogram, the basis recovers a complete |\n" \ 00184 << "| polynomial space of order 1. On a (scaled and/or translated) |\n" \ 00185 << "| reference quad, the basis recovers a complete tensor product |\n" \ 00186 << "| space of order 1 (i.e. incl. the xy term). |\n" \ 00187 << "| |\n" \ 00188 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00189 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00190 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00191 << "| |\n" \ 00192 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00193 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00194 << "| |\n" \ 00195 << "===============================================================================\n"\ 00196 << "| TEST 1: Patch test |\n"\ 00197 << "===============================================================================\n"; 00198 00199 00200 int errorFlag = 0; 00201 00202 outStream -> precision(16); 00203 00204 00205 try { 00206 00207 int max_order = 1; // max total order of polynomial solution 00208 DefaultCubatureFactory<double> cubFactory; // create cubature factory 00209 shards::CellTopology cell(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create parent cell topology 00210 shards::CellTopology side(shards::getCellTopologyData< shards::Line<> >()); // create relevant subcell (side) topology 00211 int cellDim = cell.getDimension(); 00212 int sideDim = side.getDimension(); 00213 00214 // Define array containing points at which the solution is evaluated, in reference cell. 00215 int numIntervals = 10; 00216 int numInterpPoints = (numIntervals + 1)*(numIntervals + 1); 00217 FieldContainer<double> interp_points_ref(numInterpPoints, 2); 00218 int counter = 0; 00219 for (int j=0; j<=numIntervals; j++) { 00220 for (int i=0; i<=numIntervals; i++) { 00221 interp_points_ref(counter,0) = i*(2.0/numIntervals)-1.0; 00222 interp_points_ref(counter,1) = j*(2.0/numIntervals)-1.0; 00223 counter++; 00224 } 00225 } 00226 00227 /* Parent cell definition. */ 00228 FieldContainer<double> cell_nodes[2]; 00229 cell_nodes[0].resize(1, 4, cellDim); 00230 cell_nodes[1].resize(1, 4, cellDim); 00231 00232 // Generic parallelogram. 00233 cell_nodes[0](0, 0, 0) = -5.0; 00234 cell_nodes[0](0, 0, 1) = -1.0; 00235 cell_nodes[0](0, 1, 0) = 4.0; 00236 cell_nodes[0](0, 1, 1) = 1.0; 00237 cell_nodes[0](0, 2, 0) = 8.0; 00238 cell_nodes[0](0, 2, 1) = 3.0; 00239 cell_nodes[0](0, 3, 0) = -1.0; 00240 cell_nodes[0](0, 3, 1) = 1.0; 00241 // Reference quad. 00242 cell_nodes[1](0, 0, 0) = -1.0; 00243 cell_nodes[1](0, 0, 1) = -1.0; 00244 cell_nodes[1](0, 1, 0) = 1.0; 00245 cell_nodes[1](0, 1, 1) = -1.0; 00246 cell_nodes[1](0, 2, 0) = 1.0; 00247 cell_nodes[1](0, 2, 1) = 1.0; 00248 cell_nodes[1](0, 3, 0) = -1.0; 00249 cell_nodes[1](0, 3, 1) = 1.0; 00250 00251 std::stringstream mystream[2]; 00252 mystream[0].str("\n>> Now testing basis on a generic parallelogram ...\n"); 00253 mystream[1].str("\n>> Now testing basis on the reference quad ...\n"); 00254 00255 for (int pcell = 0; pcell < 2; pcell++) { 00256 *outStream << mystream[pcell].str(); 00257 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00258 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes[pcell], cell); 00259 interp_points.resize(numInterpPoints, cellDim); 00260 00261 for (int x_order=0; x_order <= max_order; x_order++) { 00262 int max_y_order = max_order; 00263 if (pcell == 0) { 00264 max_y_order -= x_order; 00265 } 00266 for (int y_order=0; y_order <= max_y_order; y_order++) { 00267 00268 // evaluate exact solution 00269 FieldContainer<double> exact_solution(1, numInterpPoints); 00270 u_exact(exact_solution, interp_points, x_order, y_order); 00271 00272 int basis_order = 1; 00273 00274 // set test tolerance 00275 double zero = basis_order*basis_order*100*INTREPID_TOL; 00276 00277 //create basis 00278 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00279 Teuchos::rcp(new Basis_HGRAD_QUAD_C1_FEM<double,FieldContainer<double> >() ); 00280 int numFields = basis->getCardinality(); 00281 00282 // create cubatures 00283 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00284 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order); 00285 int numCubPointsCell = cellCub->getNumPoints(); 00286 int numCubPointsSide = sideCub->getNumPoints(); 00287 00288 /* Computational arrays. */ 00289 /* Section 1: Related to parent cell integration. */ 00290 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00291 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim); 00292 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00293 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim); 00294 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim); 00295 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell); 00296 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell); 00297 00298 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell); 00299 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00300 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00301 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim); 00302 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00303 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00304 FieldContainer<double> fe_matrix(1, numFields, numFields); 00305 00306 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell); 00307 FieldContainer<double> rhs_and_soln_vector(1, numFields); 00308 00309 /* Section 2: Related to subcell (side) integration. */ 00310 unsigned numSides = 4; 00311 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim); 00312 FieldContainer<double> cub_weights_side(numCubPointsSide); 00313 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim); 00314 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim); 00315 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim); 00316 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide); 00317 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide); 00318 00319 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide); 00320 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00321 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00322 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide); 00323 FieldContainer<double> neumann_fields_per_side(1, numFields); 00324 00325 /* Section 3: Related to global interpolant. */ 00326 FieldContainer<double> value_of_basis_at_interp_points(numFields, numInterpPoints); 00327 FieldContainer<double> transformed_value_of_basis_at_interp_points(1, numFields, numInterpPoints); 00328 FieldContainer<double> interpolant(1, numInterpPoints); 00329 00330 FieldContainer<int> ipiv(numFields); 00331 00332 00333 00334 /******************* START COMPUTATION ***********************/ 00335 00336 // get cubature points and weights 00337 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00338 00339 // compute geometric cell information 00340 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes[pcell], cell); 00341 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00342 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00343 00344 // compute weighted measure 00345 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00346 00348 // Computing mass matrices: 00349 // tabulate values of basis functions at (reference) cubature points 00350 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00351 00352 // transform values of basis functions 00353 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00354 value_of_basis_at_cub_points_cell); 00355 00356 // multiply with weighted measure 00357 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00358 weighted_measure_cell, 00359 transformed_value_of_basis_at_cub_points_cell); 00360 00361 // compute mass matrices 00362 FunctionSpaceTools::integrate<double>(fe_matrix, 00363 transformed_value_of_basis_at_cub_points_cell, 00364 weighted_transformed_value_of_basis_at_cub_points_cell, 00365 COMP_BLAS); 00367 00369 // Computing stiffness matrices: 00370 // tabulate gradients of basis functions at (reference) cubature points 00371 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00372 00373 // transform gradients of basis functions 00374 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00375 jacobian_inv_cell, 00376 grad_of_basis_at_cub_points_cell); 00377 00378 // multiply with weighted measure 00379 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00380 weighted_measure_cell, 00381 transformed_grad_of_basis_at_cub_points_cell); 00382 00383 // compute stiffness matrices and sum into fe_matrix 00384 FunctionSpaceTools::integrate<double>(fe_matrix, 00385 transformed_grad_of_basis_at_cub_points_cell, 00386 weighted_transformed_grad_of_basis_at_cub_points_cell, 00387 COMP_BLAS, 00388 true); 00390 00392 // Computing RHS contributions: 00393 // map cell (reference) cubature points to physical space 00394 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes[pcell], cell); 00395 00396 // evaluate rhs function 00397 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order); 00398 00399 // compute rhs 00400 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00401 rhs_at_cub_points_cell_physical, 00402 weighted_transformed_value_of_basis_at_cub_points_cell, 00403 COMP_BLAS); 00404 00405 // compute neumann b.c. contributions and adjust rhs 00406 sideCub->getCubature(cub_points_side, cub_weights_side); 00407 for (unsigned i=0; i<numSides; i++) { 00408 // compute geometric cell information 00409 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell); 00410 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes[pcell], cell); 00411 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell); 00412 00413 // compute weighted edge measure 00414 FunctionSpaceTools::computeEdgeMeasure<double>(weighted_measure_side_refcell, 00415 jacobian_side_refcell, 00416 cub_weights_side, 00417 i, 00418 cell); 00419 00420 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00421 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE); 00422 // transform 00423 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell, 00424 value_of_basis_at_cub_points_side_refcell); 00425 00426 // multiply with weighted measure 00427 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00428 weighted_measure_side_refcell, 00429 transformed_value_of_basis_at_cub_points_side_refcell); 00430 00431 // compute Neumann data 00432 // map side cubature points in reference parent cell domain to physical space 00433 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes[pcell], cell); 00434 // now compute data 00435 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell, 00436 cell, (int)i, x_order, y_order); 00437 00438 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00439 neumann_data_at_cub_points_side_physical, 00440 weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00441 COMP_BLAS); 00442 00443 // adjust RHS 00444 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00445 } 00447 00449 // Solution of linear system: 00450 int info = 0; 00451 Teuchos::LAPACK<int, double> solver; 00452 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00454 00456 // Building interpolant: 00457 // evaluate basis at interpolation points 00458 basis->getValues(value_of_basis_at_interp_points, interp_points_ref, OPERATOR_VALUE); 00459 // transform values of basis functions 00460 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points, 00461 value_of_basis_at_interp_points); 00462 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points); 00464 00465 /******************* END COMPUTATION ***********************/ 00466 00467 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00468 00469 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00470 << x_order << ", " << y_order << ") and finite element interpolant of order " << basis_order << ": " 00471 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00472 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00473 00474 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00475 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00476 *outStream << "\n\nPatch test failed for solution polynomial order (" 00477 << x_order << ", " << y_order << ") and basis order " << basis_order << "\n\n"; 00478 errorFlag++; 00479 } 00480 } // end for y_order 00481 } // end for x_order 00482 } // end for pcell 00483 00484 } 00485 // Catch unexpected errors 00486 catch (std::logic_error err) { 00487 *outStream << err.what() << "\n\n"; 00488 errorFlag = -1000; 00489 }; 00490 00491 if (errorFlag != 0) 00492 std::cout << "End Result: TEST FAILED\n"; 00493 else 00494 std::cout << "End Result: TEST PASSED\n"; 00495 00496 // reset format state of std::cout 00497 std::cout.copyfmt(oldFormatState); 00498 00499 return errorFlag; 00500 }
1.7.4