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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 // Redistribution and use in source and binary forms, with or without 00011 // modification, are permitted provided that the following conditions are 00012 // met: 00013 // 00014 // 1. Redistributions of source code must retain the above copyright 00015 // notice, this list of conditions and the following disclaimer. 00016 // 00017 // 2. Redistributions in binary form must reproduce the above copyright 00018 // notice, this list of conditions and the following disclaimer in the 00019 // documentation and/or other materials provided with the distribution. 00020 // 00021 // 3. Neither the name of the Corporation nor the names of the 00022 // contributors may be used to endorse or promote products derived from 00023 // this software without specific prior written permission. 00024 // 00025 // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY 00026 // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 00027 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 00028 // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE 00029 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 00030 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 00031 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 00032 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 00033 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 00034 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 00035 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 00036 // 00037 // Questions? Contact Pavel Bochev (pbboche@sandia.gov) 00038 // Denis Ridzal (dridzal@sandia.gov), or 00039 // Kara Peterson (kjpeter@sandia.gov) 00040 // 00041 // ************************************************************************ 00042 // @HEADER 00043 00049 #include "Intrepid_FieldContainer.hpp" 00050 #include "Intrepid_HGRAD_TET_Cn_FEM.hpp" 00051 #include "Intrepid_DefaultCubatureFactory.hpp" 00052 #include "Intrepid_RealSpaceTools.hpp" 00053 #include "Intrepid_ArrayTools.hpp" 00054 #include "Intrepid_FunctionSpaceTools.hpp" 00055 #include "Intrepid_CellTools.hpp" 00056 #include "Teuchos_oblackholestream.hpp" 00057 #include "Teuchos_RCP.hpp" 00058 #include "Teuchos_GlobalMPISession.hpp" 00059 #include "Teuchos_SerialDenseMatrix.hpp" 00060 #include "Teuchos_SerialDenseVector.hpp" 00061 #include "Teuchos_LAPACK.hpp" 00062 00063 using namespace std; 00064 using namespace Intrepid; 00065 00066 void rhsFunc(FieldContainer<double> &, const FieldContainer<double> &, int, int, int); 00067 void neumann(FieldContainer<double> & , 00068 const FieldContainer<double> & , 00069 const FieldContainer<double> & , 00070 const shards::CellTopology & , 00071 int, int, int, int); 00072 void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int, int); 00073 00075 void rhsFunc(FieldContainer<double> & result, 00076 const FieldContainer<double> & points, 00077 int xd, 00078 int yd, 00079 int zd) { 00080 00081 int x = 0, y = 1, z = 2; 00082 00083 // second x-derivatives of u 00084 if (xd > 1) { 00085 for (int cell=0; cell<result.dimension(0); cell++) { 00086 for (int pt=0; pt<result.dimension(1); pt++) { 00087 result(cell,pt) = - xd*(xd-1)*std::pow(points(cell,pt,x), xd-2) * 00088 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00089 } 00090 } 00091 } 00092 00093 // second y-derivatives of u 00094 if (yd > 1) { 00095 for (int cell=0; cell<result.dimension(0); cell++) { 00096 for (int pt=0; pt<result.dimension(1); pt++) { 00097 result(cell,pt) -= yd*(yd-1)*std::pow(points(cell,pt,y), yd-2) * 00098 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00099 } 00100 } 00101 } 00102 00103 // second z-derivatives of u 00104 if (zd > 1) { 00105 for (int cell=0; cell<result.dimension(0); cell++) { 00106 for (int pt=0; pt<result.dimension(1); pt++) { 00107 result(cell,pt) -= zd*(zd-1)*std::pow(points(cell,pt,z), zd-2) * 00108 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00109 } 00110 } 00111 } 00112 00113 // add u 00114 for (int cell=0; cell<result.dimension(0); cell++) { 00115 for (int pt=0; pt<result.dimension(1); pt++) { 00116 result(cell,pt) += std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00117 } 00118 } 00119 00120 } 00121 00122 00124 void neumann(FieldContainer<double> & result, 00125 const FieldContainer<double> & points, 00126 const FieldContainer<double> & jacs, 00127 const shards::CellTopology & parentCell, 00128 int sideOrdinal, int xd, int yd, int zd) { 00129 00130 int x = 0, y = 1, z = 2; 00131 00132 int numCells = result.dimension(0); 00133 int numPoints = result.dimension(1); 00134 00135 FieldContainer<double> grad_u(numCells, numPoints, 3); 00136 FieldContainer<double> side_normals(numCells, numPoints, 3); 00137 FieldContainer<double> normal_lengths(numCells, numPoints); 00138 00139 // first x-derivatives of u 00140 if (xd > 0) { 00141 for (int cell=0; cell<numCells; cell++) { 00142 for (int pt=0; pt<numPoints; pt++) { 00143 grad_u(cell,pt,x) = xd*std::pow(points(cell,pt,x), xd-1) * 00144 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00145 } 00146 } 00147 } 00148 00149 // first y-derivatives of u 00150 if (yd > 0) { 00151 for (int cell=0; cell<numCells; cell++) { 00152 for (int pt=0; pt<numPoints; pt++) { 00153 grad_u(cell,pt,y) = yd*std::pow(points(cell,pt,y), yd-1) * 00154 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00155 } 00156 } 00157 } 00158 00159 // first z-derivatives of u 00160 if (zd > 0) { 00161 for (int cell=0; cell<numCells; cell++) { 00162 for (int pt=0; pt<numPoints; pt++) { 00163 grad_u(cell,pt,z) = zd*std::pow(points(cell,pt,z), zd-1) * 00164 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00165 } 00166 } 00167 } 00168 00169 CellTools<double>::getPhysicalSideNormals(side_normals, jacs, sideOrdinal, parentCell); 00170 00171 // scale normals 00172 RealSpaceTools<double>::vectorNorm(normal_lengths, side_normals, NORM_TWO); 00173 FunctionSpaceTools::scalarMultiplyDataData<double>(side_normals, normal_lengths, side_normals, true); 00174 00175 FunctionSpaceTools::dotMultiplyDataData<double>(result, grad_u, side_normals); 00176 00177 } 00178 00180 void u_exact(FieldContainer<double> & result, const FieldContainer<double> & points, int xd, int yd, int zd) { 00181 int x = 0, y = 1, z = 2; 00182 for (int cell=0; cell<result.dimension(0); cell++) { 00183 for (int pt=0; pt<result.dimension(1); pt++) { 00184 result(cell,pt) = std::pow(points(pt,x), xd)*std::pow(points(pt,y), yd)*std::pow(points(pt,z), zd); 00185 } 00186 } 00187 } 00188 00189 00190 00191 00192 int main(int argc, char *argv[]) { 00193 00194 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00195 00196 // This little trick lets us print to std::cout only if 00197 // a (dummy) command-line argument is provided. 00198 int iprint = argc - 1; 00199 Teuchos::RCP<std::ostream> outStream; 00200 Teuchos::oblackholestream bhs; // outputs nothing 00201 if (iprint > 0) 00202 outStream = Teuchos::rcp(&std::cout, false); 00203 else 00204 outStream = Teuchos::rcp(&bhs, false); 00205 00206 // Save the format state of the original std::cout. 00207 Teuchos::oblackholestream oldFormatState; 00208 oldFormatState.copyfmt(std::cout); 00209 00210 *outStream \ 00211 << "===============================================================================\n" \ 00212 << "| |\n" \ 00213 << "| Unit Test (Basis_HGRAD_TET_Cn_FEM) |\n" \ 00214 << "| |\n" \ 00215 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00216 << "| for the Neumann problem on a tetrahedral patch |\n" \ 00217 << "| Omega with boundary Gamma. |\n" \ 00218 << "| |\n" \ 00219 << "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \ 00220 << "| |\n" \ 00221 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00222 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00223 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00224 << "| |\n" \ 00225 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00226 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00227 << "| |\n" \ 00228 << "===============================================================================\n"\ 00229 << "| TEST 1: Patch test |\n"\ 00230 << "===============================================================================\n"; 00231 00232 00233 int errorFlag = 0; 00234 00235 outStream -> precision(16); 00236 00237 00238 try { 00239 00240 int max_order = 5; // max total order of polynomial solution 00241 DefaultCubatureFactory<double> cubFactory; // create factory 00242 shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology 00243 shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology 00244 int cellDim = cell.getDimension(); 00245 int sideDim = side.getDimension(); 00246 00247 // Define array containing points at which the solution is evaluated, on the reference tet. 00248 int numIntervals = 10; 00249 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6; 00250 FieldContainer<double> interp_points_ref(numInterpPoints, 3); 00251 int counter = 0; 00252 for (int k=0; k<=numIntervals; k++) { 00253 for (int j=0; j<=numIntervals; j++) { 00254 for (int i=0; i<=numIntervals; i++) { 00255 if (i+j+k <= numIntervals) { 00256 interp_points_ref(counter,0) = i*(1.0/numIntervals); 00257 interp_points_ref(counter,1) = j*(1.0/numIntervals); 00258 interp_points_ref(counter,2) = k*(1.0/numIntervals); 00259 counter++; 00260 } 00261 } 00262 } 00263 } 00264 00265 /* Definition of parent cell. */ 00266 FieldContainer<double> cell_nodes(1, 4, cellDim); 00267 // funky tet 00268 cell_nodes(0, 0, 0) = -1.0; 00269 cell_nodes(0, 0, 1) = -2.0; 00270 cell_nodes(0, 0, 2) = 0.0; 00271 cell_nodes(0, 1, 0) = 6.0; 00272 cell_nodes(0, 1, 1) = 2.0; 00273 cell_nodes(0, 1, 2) = 0.0; 00274 cell_nodes(0, 2, 0) = -5.0; 00275 cell_nodes(0, 2, 1) = 1.0; 00276 cell_nodes(0, 2, 2) = 0.0; 00277 cell_nodes(0, 3, 0) = -4.0; 00278 cell_nodes(0, 3, 1) = -1.0; 00279 cell_nodes(0, 3, 2) = 3.0; 00280 // perturbed reference tet 00281 /*cell_nodes(0, 0, 0) = 0.1; 00282 cell_nodes(0, 0, 1) = -0.1; 00283 cell_nodes(0, 0, 2) = 0.2; 00284 cell_nodes(0, 1, 0) = 1.2; 00285 cell_nodes(0, 1, 1) = -0.1; 00286 cell_nodes(0, 1, 2) = 0.05; 00287 cell_nodes(0, 2, 0) = 0.0; 00288 cell_nodes(0, 2, 1) = 0.9; 00289 cell_nodes(0, 2, 2) = 0.1; 00290 cell_nodes(0, 3, 0) = 0.1; 00291 cell_nodes(0, 3, 1) = -0.1; 00292 cell_nodes(0, 3, 2) = 1.1;*/ 00293 // reference tet 00294 /*cell_nodes(0, 0, 0) = 0.0; 00295 cell_nodes(0, 0, 1) = 0.0; 00296 cell_nodes(0, 0, 2) = 0.0; 00297 cell_nodes(0, 1, 0) = 1.0; 00298 cell_nodes(0, 1, 1) = 0.0; 00299 cell_nodes(0, 1, 2) = 0.0; 00300 cell_nodes(0, 2, 0) = 0.0; 00301 cell_nodes(0, 2, 1) = 1.0; 00302 cell_nodes(0, 2, 2) = 0.0; 00303 cell_nodes(0, 3, 0) = 0.0; 00304 cell_nodes(0, 3, 1) = 0.0; 00305 cell_nodes(0, 3, 2) = 1.0;*/ 00306 00307 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00308 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell); 00309 interp_points.resize(numInterpPoints, cellDim); 00310 00311 // we test two types of bases 00312 EPointType pointtype[] = {POINTTYPE_EQUISPACED, POINTTYPE_WARPBLEND}; 00313 for (int ptype=0; ptype < 2; ptype++) { 00314 00315 *outStream << "\nTesting bases with " << EPointTypeToString(pointtype[ptype]) << ":\n"; 00316 00317 for (int x_order=0; x_order <= max_order; x_order++) { 00318 for (int y_order=0; y_order <= max_order-x_order; y_order++) { 00319 for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) { 00320 00321 // evaluate exact solution 00322 FieldContainer<double> exact_solution(1, numInterpPoints); 00323 u_exact(exact_solution, interp_points, x_order, y_order, z_order); 00324 00325 int total_order = std::max(x_order + y_order + z_order, 1); 00326 00327 for (int basis_order=total_order; basis_order <= max_order; basis_order++) { 00328 00329 // set test tolerance; 00330 double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL; 00331 00332 //create basis 00333 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00334 Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM<double,FieldContainer<double> >(basis_order, pointtype[ptype]) ); 00335 int numFields = basis->getCardinality(); 00336 00337 // create cubatures 00338 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00339 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order); 00340 int numCubPointsCell = cellCub->getNumPoints(); 00341 int numCubPointsSide = sideCub->getNumPoints(); 00342 00343 /* Computational arrays. */ 00344 /* Section 1: Related to parent cell integration. */ 00345 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00346 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim); 00347 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00348 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim); 00349 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim); 00350 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell); 00351 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell); 00352 00353 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell); 00354 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00355 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00356 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim); 00357 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00358 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00359 FieldContainer<double> fe_matrix(1, numFields, numFields); 00360 00361 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell); 00362 FieldContainer<double> rhs_and_soln_vector(1, numFields); 00363 00364 /* Section 2: Related to subcell (side) integration. */ 00365 unsigned numSides = 4; 00366 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim); 00367 FieldContainer<double> cub_weights_side(numCubPointsSide); 00368 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim); 00369 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim); 00370 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim); 00371 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide); 00372 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide); 00373 00374 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide); 00375 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00376 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00377 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide); 00378 FieldContainer<double> neumann_fields_per_side(1, numFields); 00379 00380 /* Section 3: Related to global interpolant. */ 00381 FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints); 00382 FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints); 00383 FieldContainer<double> interpolant(1, numInterpPoints); 00384 00385 FieldContainer<int> ipiv(numFields); 00386 00387 00388 00389 /******************* START COMPUTATION ***********************/ 00390 00391 // get cubature points and weights 00392 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00393 00394 // compute geometric cell information 00395 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell); 00396 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00397 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00398 00399 // compute weighted measure 00400 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00401 00403 // Computing mass matrices: 00404 // tabulate values of basis functions at (reference) cubature points 00405 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00406 00407 // transform values of basis functions 00408 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00409 value_of_basis_at_cub_points_cell); 00410 00411 // multiply with weighted measure 00412 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00413 weighted_measure_cell, 00414 transformed_value_of_basis_at_cub_points_cell); 00415 00416 // compute mass matrices 00417 FunctionSpaceTools::integrate<double>(fe_matrix, 00418 transformed_value_of_basis_at_cub_points_cell, 00419 weighted_transformed_value_of_basis_at_cub_points_cell, 00420 COMP_BLAS); 00422 00424 // Computing stiffness matrices: 00425 // tabulate gradients of basis functions at (reference) cubature points 00426 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00427 00428 // transform gradients of basis functions 00429 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00430 jacobian_inv_cell, 00431 grad_of_basis_at_cub_points_cell); 00432 00433 // multiply with weighted measure 00434 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00435 weighted_measure_cell, 00436 transformed_grad_of_basis_at_cub_points_cell); 00437 00438 // compute stiffness matrices and sum into fe_matrix 00439 FunctionSpaceTools::integrate<double>(fe_matrix, 00440 transformed_grad_of_basis_at_cub_points_cell, 00441 weighted_transformed_grad_of_basis_at_cub_points_cell, 00442 COMP_BLAS, 00443 true); 00445 00447 // Computing RHS contributions: 00448 // map cell (reference) cubature points to physical space 00449 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell); 00450 00451 // evaluate rhs function 00452 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order); 00453 00454 // compute rhs 00455 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00456 rhs_at_cub_points_cell_physical, 00457 weighted_transformed_value_of_basis_at_cub_points_cell, 00458 COMP_BLAS); 00459 00460 // compute neumann b.c. contributions and adjust rhs 00461 sideCub->getCubature(cub_points_side, cub_weights_side); 00462 for (unsigned i=0; i<numSides; i++) { 00463 // compute geometric cell information 00464 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell); 00465 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell); 00466 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell); 00467 00468 // compute weighted face measure 00469 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell, 00470 jacobian_side_refcell, 00471 cub_weights_side, 00472 i, 00473 cell); 00474 00475 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00476 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE); 00477 // transform 00478 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell, 00479 value_of_basis_at_cub_points_side_refcell); 00480 00481 // multiply with weighted measure 00482 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00483 weighted_measure_side_refcell, 00484 transformed_value_of_basis_at_cub_points_side_refcell); 00485 00486 // compute Neumann data 00487 // map side cubature points in reference parent cell domain to physical space 00488 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell); 00489 // now compute data 00490 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell, 00491 cell, (int)i, x_order, y_order, z_order); 00492 00493 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00494 neumann_data_at_cub_points_side_physical, 00495 weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00496 COMP_BLAS); 00497 00498 // adjust RHS 00499 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00500 } 00502 00504 // Solution of linear system: 00505 int info = 0; 00506 Teuchos::LAPACK<int, double> solver; 00507 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00509 00511 // Building interpolant: 00512 // evaluate basis at interpolation points 00513 basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE); 00514 // transform values of basis functions 00515 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref, 00516 value_of_basis_at_interp_points_ref); 00517 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref); 00519 00520 /******************* END COMPUTATION ***********************/ 00521 00522 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00523 00524 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00525 << x_order << ", " << y_order << ", " << z_order 00526 << ") and finite element interpolant of order " << basis_order << ": " 00527 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00528 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00529 00530 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00531 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00532 *outStream << "\n\nPatch test failed for solution polynomial order (" 00533 << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n"; 00534 errorFlag++; 00535 } 00536 } // end for basis_order 00537 } // end for z_order 00538 } // end for y_order 00539 } // end for x_order 00540 } // end for ptype 00541 00542 } 00543 // Catch unexpected errors 00544 catch (std::logic_error err) { 00545 *outStream << err.what() << "\n\n"; 00546 errorFlag = -1000; 00547 }; 00548 00549 if (errorFlag != 0) 00550 std::cout << "End Result: TEST FAILED\n"; 00551 else 00552 std::cout << "End Result: TEST PASSED\n"; 00553 00554 // reset format state of std::cout 00555 std::cout.copyfmt(oldFormatState); 00556 00557 return errorFlag; 00558 }
1.7.6.1