|
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_TRI_Cn_FEM_ORTH.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_TRI_Cn_FEM_ORTH) |\n" \ 00176 << "| |\n" \ 00177 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00178 << "| for the Neumann problem on a triangular patch |\n" \ 00179 << "| 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 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00184 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00185 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00186 << "| |\n" \ 00187 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00188 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00189 << "| |\n" \ 00190 << "===============================================================================\n"\ 00191 << "| TEST 1: Patch test |\n"\ 00192 << "===============================================================================\n"; 00193 00194 00195 int errorFlag = 0; 00196 00197 outStream -> precision(16); 00198 00199 00200 try { 00201 00202 int max_order = 10; // max total order of polynomial solution 00203 DefaultCubatureFactory<double> cubFactory; // create cubature factory 00204 shards::CellTopology cell(shards::getCellTopologyData< shards::Triangle<> >()); // create parent cell topology 00205 shards::CellTopology side(shards::getCellTopologyData< shards::Line<> >()); // create relevant subcell (side) topology 00206 int cellDim = cell.getDimension(); 00207 int sideDim = side.getDimension(); 00208 00209 // Define array containing points at which the solution is evaluated, in reference cell. 00210 int numIntervals = 10; 00211 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2))/2; 00212 FieldContainer<double> interp_points_ref(numInterpPoints, 2); 00213 int counter = 0; 00214 for (int j=0; j<=numIntervals; j++) { 00215 for (int i=0; i<=numIntervals; i++) { 00216 if (i <= numIntervals-j) { 00217 interp_points_ref(counter,0) = i*(1.0/numIntervals); 00218 interp_points_ref(counter,1) = j*(1.0/numIntervals); 00219 counter++; 00220 } 00221 } 00222 } 00223 00224 /* Parent cell definition. */ 00225 FieldContainer<double> cell_nodes(1, 3, cellDim); 00226 // Perturbed reference triangle. 00227 cell_nodes(0, 0, 0) = 0.1; 00228 cell_nodes(0, 0, 1) = -0.1; 00229 cell_nodes(0, 1, 0) = 1.1; 00230 cell_nodes(0, 1, 1) = -0.1; 00231 cell_nodes(0, 2, 0) = 0.1; 00232 cell_nodes(0, 2, 1) = 0.9; 00233 // Reference triangle. 00234 /*cell_nodes(0, 0, 0) = 0.0; 00235 cell_nodes(0, 0, 1) = 0.0; 00236 cell_nodes(0, 1, 0) = 1.0; 00237 cell_nodes(0, 1, 1) = 0.0; 00238 cell_nodes(0, 2, 0) = 0.0; 00239 cell_nodes(0, 2, 1) = 1.0;*/ 00240 00241 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00242 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell); 00243 interp_points.resize(numInterpPoints, cellDim); 00244 00245 for (int x_order=0; x_order <= max_order; x_order++) { 00246 for (int y_order=0; y_order <= max_order-x_order; y_order++) { 00247 00248 // evaluate exact solution 00249 FieldContainer<double> exact_solution(1, numInterpPoints); 00250 u_exact(exact_solution, interp_points, x_order, y_order); 00251 00252 int total_order = std::max(x_order + y_order, 1); 00253 00254 for (int basis_order=total_order; basis_order <= max_order; basis_order++) { 00255 00256 // set test tolerance 00257 double zero = basis_order*basis_order*100*INTREPID_TOL; 00258 00259 //create basis 00260 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00261 Teuchos::rcp(new Basis_HGRAD_TRI_Cn_FEM_ORTH<double,FieldContainer<double> >(basis_order) ); 00262 int numFields = basis->getCardinality(); 00263 00264 // create cubatures 00265 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00266 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order); 00267 int numCubPointsCell = cellCub->getNumPoints(); 00268 int numCubPointsSide = sideCub->getNumPoints(); 00269 00270 /* Computational arrays. */ 00271 /* Section 1: Related to parent cell integration. */ 00272 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00273 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim); 00274 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00275 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim); 00276 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim); 00277 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell); 00278 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell); 00279 00280 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell); 00281 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00282 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00283 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim); 00284 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00285 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00286 FieldContainer<double> fe_matrix(1, numFields, numFields); 00287 00288 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell); 00289 FieldContainer<double> rhs_and_soln_vector(1, numFields); 00290 00291 /* Section 2: Related to subcell (side) integration. */ 00292 unsigned numSides = 3; 00293 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim); 00294 FieldContainer<double> cub_weights_side(numCubPointsSide); 00295 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim); 00296 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim); 00297 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim); 00298 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide); 00299 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide); 00300 00301 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide); 00302 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00303 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00304 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide); 00305 FieldContainer<double> neumann_fields_per_side(1, numFields); 00306 00307 /* Section 3: Related to global interpolant. */ 00308 FieldContainer<double> value_of_basis_at_interp_points(numFields, numInterpPoints); 00309 FieldContainer<double> transformed_value_of_basis_at_interp_points(1, numFields, numInterpPoints); 00310 FieldContainer<double> interpolant(1, numInterpPoints); 00311 00312 FieldContainer<int> ipiv(numFields); 00313 00314 00315 00316 /******************* START COMPUTATION ***********************/ 00317 00318 // get cubature points and weights 00319 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00320 00321 // compute geometric cell information 00322 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell); 00323 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00324 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00325 00326 // compute weighted measure 00327 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00328 00330 // Computing mass matrices: 00331 // tabulate values of basis functions at (reference) cubature points 00332 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00333 00334 // transform values of basis functions 00335 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00336 value_of_basis_at_cub_points_cell); 00337 00338 // multiply with weighted measure 00339 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00340 weighted_measure_cell, 00341 transformed_value_of_basis_at_cub_points_cell); 00342 00343 // compute mass matrices 00344 FunctionSpaceTools::integrate<double>(fe_matrix, 00345 transformed_value_of_basis_at_cub_points_cell, 00346 weighted_transformed_value_of_basis_at_cub_points_cell, 00347 COMP_BLAS); 00349 00351 // Computing stiffness matrices: 00352 // tabulate gradients of basis functions at (reference) cubature points 00353 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00354 00355 // transform gradients of basis functions 00356 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00357 jacobian_inv_cell, 00358 grad_of_basis_at_cub_points_cell); 00359 00360 // multiply with weighted measure 00361 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00362 weighted_measure_cell, 00363 transformed_grad_of_basis_at_cub_points_cell); 00364 00365 // compute stiffness matrices and sum into fe_matrix 00366 FunctionSpaceTools::integrate<double>(fe_matrix, 00367 transformed_grad_of_basis_at_cub_points_cell, 00368 weighted_transformed_grad_of_basis_at_cub_points_cell, 00369 COMP_BLAS, 00370 true); 00372 00374 // Computing RHS contributions: 00375 // map cell (reference) cubature points to physical space 00376 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell); 00377 00378 // evaluate rhs function 00379 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order); 00380 00381 // compute rhs 00382 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00383 rhs_at_cub_points_cell_physical, 00384 weighted_transformed_value_of_basis_at_cub_points_cell, 00385 COMP_BLAS); 00386 00387 // compute neumann b.c. contributions and adjust rhs 00388 sideCub->getCubature(cub_points_side, cub_weights_side); 00389 for (unsigned i=0; i<numSides; i++) { 00390 // compute geometric cell information 00391 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell); 00392 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell); 00393 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell); 00394 00395 // compute weighted edge measure 00396 FunctionSpaceTools::computeEdgeMeasure<double>(weighted_measure_side_refcell, 00397 jacobian_side_refcell, 00398 cub_weights_side, 00399 i, 00400 cell); 00401 00402 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00403 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE); 00404 // transform 00405 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell, 00406 value_of_basis_at_cub_points_side_refcell); 00407 00408 // multiply with weighted measure 00409 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00410 weighted_measure_side_refcell, 00411 transformed_value_of_basis_at_cub_points_side_refcell); 00412 00413 // compute Neumann data 00414 // map side cubature points in reference parent cell domain to physical space 00415 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell); 00416 // now compute data 00417 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell, 00418 cell, (int)i, x_order, y_order); 00419 00420 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00421 neumann_data_at_cub_points_side_physical, 00422 weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00423 COMP_BLAS); 00424 00425 // adjust RHS 00426 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00427 } 00429 00431 // Solution of linear system: 00432 int info = 0; 00433 Teuchos::LAPACK<int, double> solver; 00434 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00436 00438 // Building interpolant: 00439 // evaluate basis at interpolation points 00440 basis->getValues(value_of_basis_at_interp_points, interp_points_ref, OPERATOR_VALUE); 00441 // transform values of basis functions 00442 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points, 00443 value_of_basis_at_interp_points); 00444 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points); 00446 00447 /******************* END COMPUTATION ***********************/ 00448 00449 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00450 00451 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00452 << x_order << ", " << y_order << ") and finite element interpolant of order " << basis_order << ": " 00453 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00454 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00455 00456 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00457 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00458 *outStream << "\n\nPatch test failed for solution polynomial order (" 00459 << x_order << ", " << y_order << ") and basis order " << basis_order << "\n\n"; 00460 errorFlag++; 00461 } 00462 } // end for basis_order 00463 } // end for y_order 00464 } // end for x_order 00465 00466 } 00467 // Catch unexpected errors 00468 catch (std::logic_error err) { 00469 *outStream << err.what() << "\n\n"; 00470 errorFlag = -1000; 00471 }; 00472 00473 if (errorFlag != 0) 00474 std::cout << "End Result: TEST FAILED\n"; 00475 else 00476 std::cout << "End Result: TEST PASSED\n"; 00477 00478 // reset format state of std::cout 00479 std::cout.copyfmt(oldFormatState); 00480 00481 return errorFlag; 00482 }
1.7.4