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Intrepid
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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_HEX_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, int); 00054 void neumann(FieldContainer<double> & , 00055 const FieldContainer<double> & , 00056 const FieldContainer<double> & , 00057 const shards::CellTopology & , 00058 int, int, int, int); 00059 void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int, int); 00060 00062 void rhsFunc(FieldContainer<double> & result, 00063 const FieldContainer<double> & points, 00064 int xd, 00065 int yd, 00066 int zd) { 00067 00068 int x = 0, y = 1, z = 2; 00069 00070 // second x-derivatives of u 00071 if (xd > 1) { 00072 for (int cell=0; cell<result.dimension(0); cell++) { 00073 for (int pt=0; pt<result.dimension(1); pt++) { 00074 result(cell,pt) = - xd*(xd-1)*std::pow(points(cell,pt,x), xd-2) * 00075 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00076 } 00077 } 00078 } 00079 00080 // second y-derivatives of u 00081 if (yd > 1) { 00082 for (int cell=0; cell<result.dimension(0); cell++) { 00083 for (int pt=0; pt<result.dimension(1); pt++) { 00084 result(cell,pt) -= yd*(yd-1)*std::pow(points(cell,pt,y), yd-2) * 00085 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00086 } 00087 } 00088 } 00089 00090 // second z-derivatives of u 00091 if (zd > 1) { 00092 for (int cell=0; cell<result.dimension(0); cell++) { 00093 for (int pt=0; pt<result.dimension(1); pt++) { 00094 result(cell,pt) -= zd*(zd-1)*std::pow(points(cell,pt,z), zd-2) * 00095 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00096 } 00097 } 00098 } 00099 00100 // add u 00101 for (int cell=0; cell<result.dimension(0); cell++) { 00102 for (int pt=0; pt<result.dimension(1); pt++) { 00103 result(cell,pt) += std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00104 } 00105 } 00106 00107 } 00108 00109 00111 void neumann(FieldContainer<double> & result, 00112 const FieldContainer<double> & points, 00113 const FieldContainer<double> & jacs, 00114 const shards::CellTopology & parentCell, 00115 int sideOrdinal, int xd, int yd, int zd) { 00116 00117 int x = 0, y = 1, z = 2; 00118 00119 int numCells = result.dimension(0); 00120 int numPoints = result.dimension(1); 00121 00122 FieldContainer<double> grad_u(numCells, numPoints, 3); 00123 FieldContainer<double> side_normals(numCells, numPoints, 3); 00124 FieldContainer<double> normal_lengths(numCells, numPoints); 00125 00126 // first x-derivatives of u 00127 if (xd > 0) { 00128 for (int cell=0; cell<numCells; cell++) { 00129 for (int pt=0; pt<numPoints; pt++) { 00130 grad_u(cell,pt,x) = xd*std::pow(points(cell,pt,x), xd-1) * 00131 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00132 } 00133 } 00134 } 00135 00136 // first y-derivatives of u 00137 if (yd > 0) { 00138 for (int cell=0; cell<numCells; cell++) { 00139 for (int pt=0; pt<numPoints; pt++) { 00140 grad_u(cell,pt,y) = yd*std::pow(points(cell,pt,y), yd-1) * 00141 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00142 } 00143 } 00144 } 00145 00146 // first z-derivatives of u 00147 if (zd > 0) { 00148 for (int cell=0; cell<numCells; cell++) { 00149 for (int pt=0; pt<numPoints; pt++) { 00150 grad_u(cell,pt,z) = zd*std::pow(points(cell,pt,z), zd-1) * 00151 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00152 } 00153 } 00154 } 00155 00156 CellTools<double>::getPhysicalSideNormals(side_normals, jacs, sideOrdinal, parentCell); 00157 00158 // scale normals 00159 RealSpaceTools<double>::vectorNorm(normal_lengths, side_normals, NORM_TWO); 00160 FunctionSpaceTools::scalarMultiplyDataData<double>(side_normals, normal_lengths, side_normals, true); 00161 00162 FunctionSpaceTools::dotMultiplyDataData<double>(result, grad_u, side_normals); 00163 00164 } 00165 00167 void u_exact(FieldContainer<double> & result, const FieldContainer<double> & points, int xd, int yd, int zd) { 00168 int x = 0, y = 1, z = 2; 00169 for (int cell=0; cell<result.dimension(0); cell++) { 00170 for (int pt=0; pt<result.dimension(1); pt++) { 00171 result(cell,pt) = std::pow(points(pt,x), xd)*std::pow(points(pt,y), yd)*std::pow(points(pt,z), zd); 00172 } 00173 } 00174 } 00175 00176 00177 00178 00179 int main(int argc, char *argv[]) { 00180 00181 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00182 00183 // This little trick lets us print to std::cout only if 00184 // a (dummy) command-line argument is provided. 00185 int iprint = argc - 1; 00186 Teuchos::RCP<std::ostream> outStream; 00187 Teuchos::oblackholestream bhs; // outputs nothing 00188 if (iprint > 0) 00189 outStream = Teuchos::rcp(&std::cout, false); 00190 else 00191 outStream = Teuchos::rcp(&bhs, false); 00192 00193 // Save the format state of the original std::cout. 00194 Teuchos::oblackholestream oldFormatState; 00195 oldFormatState.copyfmt(std::cout); 00196 00197 *outStream \ 00198 << "===============================================================================\n" \ 00199 << "| |\n" \ 00200 << "| Unit Test (Basis_HGRAD_HEX_C1_FEM) |\n" \ 00201 << "| |\n" \ 00202 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00203 << "| for the Neumann problem on a physical parallelepiped |\n" \ 00204 << "| AND a reference hex Omega with boundary Gamma. |\n" \ 00205 << "| |\n" \ 00206 << "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \ 00207 << "| |\n" \ 00208 << "| For a generic parallelepiped, the basis recovers a complete |\n" \ 00209 << "| polynomial space of order 1. On a (scaled and/or translated) |\n" \ 00210 << "| reference hex, the basis recovers a complete tensor product |\n" \ 00211 << "| space of order 1 (i.e. incl. xy, xz, yz, xyz term). |\n" \ 00212 << "| |\n" \ 00213 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00214 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00215 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00216 << "| |\n" \ 00217 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00218 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00219 << "| |\n" \ 00220 << "===============================================================================\n"\ 00221 << "| TEST 1: Patch test |\n"\ 00222 << "===============================================================================\n"; 00223 00224 00225 int errorFlag = 0; 00226 00227 outStream -> precision(16); 00228 00229 00230 try { 00231 00232 int max_order = 1; // max total order of polynomial solution 00233 DefaultCubatureFactory<double> cubFactory; // create factory 00234 shards::CellTopology cell(shards::getCellTopologyData< shards::Hexahedron<> >()); // create parent cell topology 00235 shards::CellTopology side(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology 00236 int cellDim = cell.getDimension(); 00237 int sideDim = side.getDimension(); 00238 unsigned numSides = 6; 00239 00240 // Define array containing points at which the solution is evaluated, on the reference tet. 00241 int numIntervals = 10; 00242 int numInterpPoints = (numIntervals + 1)*(numIntervals + 1)*(numIntervals + 1); 00243 FieldContainer<double> interp_points_ref(numInterpPoints, 3); 00244 int counter = 0; 00245 for (int k=0; k<=numIntervals; k++) { 00246 for (int j=0; j<=numIntervals; j++) { 00247 for (int i=0; i<=numIntervals; i++) { 00248 interp_points_ref(counter,0) = i*(1.0/numIntervals)-1.0; 00249 interp_points_ref(counter,1) = j*(1.0/numIntervals)-1.0; 00250 interp_points_ref(counter,2) = k*(1.0/numIntervals)-1.0; 00251 counter++; 00252 } 00253 } 00254 } 00255 00256 /* Parent cell definition. */ 00257 FieldContainer<double> cell_nodes[2]; 00258 cell_nodes[0].resize(1, 8, cellDim); 00259 cell_nodes[1].resize(1, 8, cellDim); 00260 00261 // Generic parallelepiped. 00262 cell_nodes[0](0, 0, 0) = -5.0; 00263 cell_nodes[0](0, 0, 1) = -1.0; 00264 cell_nodes[0](0, 0, 2) = 0.0; 00265 cell_nodes[0](0, 1, 0) = 4.0; 00266 cell_nodes[0](0, 1, 1) = 1.0; 00267 cell_nodes[0](0, 1, 2) = 1.0; 00268 cell_nodes[0](0, 2, 0) = 8.0; 00269 cell_nodes[0](0, 2, 1) = 3.0; 00270 cell_nodes[0](0, 2, 2) = 1.0; 00271 cell_nodes[0](0, 3, 0) = -1.0; 00272 cell_nodes[0](0, 3, 1) = 1.0; 00273 cell_nodes[0](0, 3, 2) = 0.0; 00274 cell_nodes[0](0, 4, 0) = 5.0; 00275 cell_nodes[0](0, 4, 1) = 9.0; 00276 cell_nodes[0](0, 4, 2) = 1.0; 00277 cell_nodes[0](0, 5, 0) = 14.0; 00278 cell_nodes[0](0, 5, 1) = 11.0; 00279 cell_nodes[0](0, 5, 2) = 2.0; 00280 cell_nodes[0](0, 6, 0) = 18.0; 00281 cell_nodes[0](0, 6, 1) = 13.0; 00282 cell_nodes[0](0, 6, 2) = 2.0; 00283 cell_nodes[0](0, 7, 0) = 9.0; 00284 cell_nodes[0](0, 7, 1) = 11.0; 00285 cell_nodes[0](0, 7, 2) = 1.0; 00286 // Reference hex. 00287 cell_nodes[1](0, 0, 0) = -1.0; 00288 cell_nodes[1](0, 0, 1) = -1.0; 00289 cell_nodes[1](0, 0, 2) = -1.0; 00290 cell_nodes[1](0, 1, 0) = 1.0; 00291 cell_nodes[1](0, 1, 1) = -1.0; 00292 cell_nodes[1](0, 1, 2) = -1.0; 00293 cell_nodes[1](0, 2, 0) = 1.0; 00294 cell_nodes[1](0, 2, 1) = 1.0; 00295 cell_nodes[1](0, 2, 2) = -1.0; 00296 cell_nodes[1](0, 3, 0) = -1.0; 00297 cell_nodes[1](0, 3, 1) = 1.0; 00298 cell_nodes[1](0, 3, 2) = -1.0; 00299 cell_nodes[1](0, 4, 0) = -1.0; 00300 cell_nodes[1](0, 4, 1) = -1.0; 00301 cell_nodes[1](0, 4, 2) = 1.0; 00302 cell_nodes[1](0, 5, 0) = 1.0; 00303 cell_nodes[1](0, 5, 1) = -1.0; 00304 cell_nodes[1](0, 5, 2) = 1.0; 00305 cell_nodes[1](0, 6, 0) = 1.0; 00306 cell_nodes[1](0, 6, 1) = 1.0; 00307 cell_nodes[1](0, 6, 2) = 1.0; 00308 cell_nodes[1](0, 7, 0) = -1.0; 00309 cell_nodes[1](0, 7, 1) = 1.0; 00310 cell_nodes[1](0, 7, 2) = 1.0; 00311 00312 std::stringstream mystream[2]; 00313 mystream[0].str("\n>> Now testing basis on a generic parallelepiped ...\n"); 00314 mystream[1].str("\n>> Now testing basis on the reference hex ...\n"); 00315 00316 00317 for (int pcell = 0; pcell < 2; pcell++) { 00318 *outStream << mystream[pcell].str(); 00319 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00320 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes[pcell], cell); 00321 interp_points.resize(numInterpPoints, cellDim); 00322 00323 for (int x_order=0; x_order <= max_order; x_order++) { 00324 int max_y_order = max_order; 00325 if (pcell == 0) { 00326 max_y_order -= x_order; 00327 } 00328 for (int y_order=0; y_order <= max_y_order; y_order++) { 00329 int max_z_order = max_order; 00330 if (pcell == 0) { 00331 max_z_order -= x_order; 00332 max_z_order -= y_order; 00333 } 00334 for (int z_order=0; z_order <= max_z_order; z_order++) { 00335 00336 // evaluate exact solution 00337 FieldContainer<double> exact_solution(1, numInterpPoints); 00338 u_exact(exact_solution, interp_points, x_order, y_order, z_order); 00339 00340 int basis_order = 1; 00341 00342 // set test tolerance; 00343 double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL; 00344 00345 //create basis 00346 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00347 Teuchos::rcp(new Basis_HGRAD_HEX_C1_FEM<double,FieldContainer<double> >() ); 00348 int numFields = basis->getCardinality(); 00349 00350 // create cubatures 00351 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00352 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order); 00353 int numCubPointsCell = cellCub->getNumPoints(); 00354 int numCubPointsSide = sideCub->getNumPoints(); 00355 00356 /* Computational arrays. */ 00357 /* Section 1: Related to parent cell integration. */ 00358 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00359 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim); 00360 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00361 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim); 00362 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim); 00363 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell); 00364 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell); 00365 00366 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell); 00367 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00368 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00369 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim); 00370 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00371 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00372 FieldContainer<double> fe_matrix(1, numFields, numFields); 00373 00374 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell); 00375 FieldContainer<double> rhs_and_soln_vector(1, numFields); 00376 00377 /* Section 2: Related to subcell (side) integration. */ 00378 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim); 00379 FieldContainer<double> cub_weights_side(numCubPointsSide); 00380 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim); 00381 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim); 00382 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim); 00383 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide); 00384 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide); 00385 00386 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide); 00387 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00388 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00389 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide); 00390 FieldContainer<double> neumann_fields_per_side(1, numFields); 00391 00392 /* Section 3: Related to global interpolant. */ 00393 FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints); 00394 FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints); 00395 FieldContainer<double> interpolant(1, numInterpPoints); 00396 00397 FieldContainer<int> ipiv(numFields); 00398 00399 00400 00401 /******************* START COMPUTATION ***********************/ 00402 00403 // get cubature points and weights 00404 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00405 00406 // compute geometric cell information 00407 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes[pcell], cell); 00408 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00409 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00410 00411 // compute weighted measure 00412 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00413 00415 // Computing mass matrices: 00416 // tabulate values of basis functions at (reference) cubature points 00417 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00418 00419 // transform values of basis functions 00420 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00421 value_of_basis_at_cub_points_cell); 00422 00423 // multiply with weighted measure 00424 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00425 weighted_measure_cell, 00426 transformed_value_of_basis_at_cub_points_cell); 00427 00428 // compute mass matrices 00429 FunctionSpaceTools::integrate<double>(fe_matrix, 00430 transformed_value_of_basis_at_cub_points_cell, 00431 weighted_transformed_value_of_basis_at_cub_points_cell, 00432 COMP_BLAS); 00434 00436 // Computing stiffness matrices: 00437 // tabulate gradients of basis functions at (reference) cubature points 00438 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00439 00440 // transform gradients of basis functions 00441 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00442 jacobian_inv_cell, 00443 grad_of_basis_at_cub_points_cell); 00444 00445 // multiply with weighted measure 00446 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00447 weighted_measure_cell, 00448 transformed_grad_of_basis_at_cub_points_cell); 00449 00450 // compute stiffness matrices and sum into fe_matrix 00451 FunctionSpaceTools::integrate<double>(fe_matrix, 00452 transformed_grad_of_basis_at_cub_points_cell, 00453 weighted_transformed_grad_of_basis_at_cub_points_cell, 00454 COMP_BLAS, 00455 true); 00457 00459 // Computing RHS contributions: 00460 // map cell (reference) cubature points to physical space 00461 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes[pcell], cell); 00462 00463 // evaluate rhs function 00464 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order); 00465 00466 // compute rhs 00467 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00468 rhs_at_cub_points_cell_physical, 00469 weighted_transformed_value_of_basis_at_cub_points_cell, 00470 COMP_BLAS); 00471 00472 // compute neumann b.c. contributions and adjust rhs 00473 sideCub->getCubature(cub_points_side, cub_weights_side); 00474 for (unsigned i=0; i<numSides; i++) { 00475 // compute geometric cell information 00476 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell); 00477 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes[pcell], cell); 00478 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell); 00479 00480 // compute weighted face measure 00481 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell, 00482 jacobian_side_refcell, 00483 cub_weights_side, 00484 i, 00485 cell); 00486 00487 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00488 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE); 00489 // transform 00490 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell, 00491 value_of_basis_at_cub_points_side_refcell); 00492 00493 // multiply with weighted measure 00494 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00495 weighted_measure_side_refcell, 00496 transformed_value_of_basis_at_cub_points_side_refcell); 00497 00498 // compute Neumann data 00499 // map side cubature points in reference parent cell domain to physical space 00500 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes[pcell], cell); 00501 // now compute data 00502 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell, 00503 cell, (int)i, x_order, y_order, z_order); 00504 00505 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00506 neumann_data_at_cub_points_side_physical, 00507 weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00508 COMP_BLAS); 00509 00510 // adjust RHS 00511 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00512 } 00514 00516 // Solution of linear system: 00517 int info = 0; 00518 Teuchos::LAPACK<int, double> solver; 00519 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00521 00523 // Building interpolant: 00524 // evaluate basis at interpolation points 00525 basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE); 00526 // transform values of basis functions 00527 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref, 00528 value_of_basis_at_interp_points_ref); 00529 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref); 00531 00532 /******************* END COMPUTATION ***********************/ 00533 00534 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00535 00536 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00537 << x_order << ", " << y_order << ", " << z_order 00538 << ") and finite element interpolant of order " << basis_order << ": " 00539 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00540 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00541 00542 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00543 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00544 *outStream << "\n\nPatch test failed for solution polynomial order (" 00545 << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n"; 00546 errorFlag++; 00547 } 00548 } // end for z_order 00549 } // end for y_order 00550 } // end for x_order 00551 } // end for pcell 00552 00553 } 00554 // Catch unexpected errors 00555 catch (std::logic_error err) { 00556 *outStream << err.what() << "\n\n"; 00557 errorFlag = -1000; 00558 }; 00559 00560 if (errorFlag != 0) 00561 std::cout << "End Result: TEST FAILED\n"; 00562 else 00563 std::cout << "End Result: TEST PASSED\n"; 00564 00565 // reset format state of std::cout 00566 std::cout.copyfmt(oldFormatState); 00567 00568 return errorFlag; 00569 }
1.7.4