|
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_HEX_Cn_FEM.hpp" 00038 #include "Intrepid_PointTools.hpp" 00039 #include "Intrepid_DefaultCubatureFactory.hpp" 00040 #include "Intrepid_RealSpaceTools.hpp" 00041 #include "Intrepid_ArrayTools.hpp" 00042 #include "Intrepid_FunctionSpaceTools.hpp" 00043 #include "Intrepid_CellTools.hpp" 00044 #include "Teuchos_oblackholestream.hpp" 00045 #include "Teuchos_RCP.hpp" 00046 #include "Teuchos_GlobalMPISession.hpp" 00047 #include "Teuchos_SerialDenseMatrix.hpp" 00048 #include "Teuchos_SerialDenseVector.hpp" 00049 #include "Teuchos_LAPACK.hpp" 00050 00051 using namespace std; 00052 using namespace Intrepid; 00053 00054 void rhsFunc(FieldContainer<double> &, const FieldContainer<double> &, int, int, int); 00055 void neumann(FieldContainer<double> & , 00056 const FieldContainer<double> & , 00057 const FieldContainer<double> & , 00058 const shards::CellTopology & , 00059 int, int, int, int); 00060 void u_exact(FieldContainer<double> &, const FieldContainer<double> &, int, int, int); 00061 00063 void rhsFunc(FieldContainer<double> & result, 00064 const FieldContainer<double> & points, 00065 int xd, 00066 int yd, 00067 int zd) { 00068 00069 int x = 0, y = 1, z = 2; 00070 00071 // second x-derivatives of u 00072 if (xd > 1) { 00073 for (int cell=0; cell<result.dimension(0); cell++) { 00074 for (int pt=0; pt<result.dimension(1); pt++) { 00075 result(cell,pt) = - xd*(xd-1)*std::pow(points(cell,pt,x), xd-2) * 00076 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00077 } 00078 } 00079 } 00080 00081 // second y-derivatives of u 00082 if (yd > 1) { 00083 for (int cell=0; cell<result.dimension(0); cell++) { 00084 for (int pt=0; pt<result.dimension(1); pt++) { 00085 result(cell,pt) -= yd*(yd-1)*std::pow(points(cell,pt,y), yd-2) * 00086 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00087 } 00088 } 00089 } 00090 00091 // second z-derivatives of u 00092 if (zd > 1) { 00093 for (int cell=0; cell<result.dimension(0); cell++) { 00094 for (int pt=0; pt<result.dimension(1); pt++) { 00095 result(cell,pt) -= zd*(zd-1)*std::pow(points(cell,pt,z), zd-2) * 00096 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00097 } 00098 } 00099 } 00100 00101 // add u 00102 for (int cell=0; cell<result.dimension(0); cell++) { 00103 for (int pt=0; pt<result.dimension(1); pt++) { 00104 result(cell,pt) += std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00105 } 00106 } 00107 00108 } 00109 00110 00112 void neumann(FieldContainer<double> & result, 00113 const FieldContainer<double> & points, 00114 const FieldContainer<double> & jacs, 00115 const shards::CellTopology & parentCell, 00116 int sideOrdinal, int xd, int yd, int zd) { 00117 00118 int x = 0, y = 1, z = 2; 00119 00120 int numCells = result.dimension(0); 00121 int numPoints = result.dimension(1); 00122 00123 FieldContainer<double> grad_u(numCells, numPoints, 3); 00124 FieldContainer<double> side_normals(numCells, numPoints, 3); 00125 FieldContainer<double> normal_lengths(numCells, numPoints); 00126 00127 // first x-derivatives of u 00128 if (xd > 0) { 00129 for (int cell=0; cell<numCells; cell++) { 00130 for (int pt=0; pt<numPoints; pt++) { 00131 grad_u(cell,pt,x) = xd*std::pow(points(cell,pt,x), xd-1) * 00132 std::pow(points(cell,pt,y), yd) * std::pow(points(cell,pt,z), zd); 00133 } 00134 } 00135 } 00136 00137 // first y-derivatives of u 00138 if (yd > 0) { 00139 for (int cell=0; cell<numCells; cell++) { 00140 for (int pt=0; pt<numPoints; pt++) { 00141 grad_u(cell,pt,y) = yd*std::pow(points(cell,pt,y), yd-1) * 00142 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,z), zd); 00143 } 00144 } 00145 } 00146 00147 // first z-derivatives of u 00148 if (zd > 0) { 00149 for (int cell=0; cell<numCells; cell++) { 00150 for (int pt=0; pt<numPoints; pt++) { 00151 grad_u(cell,pt,z) = zd*std::pow(points(cell,pt,z), zd-1) * 00152 std::pow(points(cell,pt,x), xd) * std::pow(points(cell,pt,y), yd); 00153 } 00154 } 00155 } 00156 00157 CellTools<double>::getPhysicalSideNormals(side_normals, jacs, sideOrdinal, parentCell); 00158 00159 // scale normals 00160 RealSpaceTools<double>::vectorNorm(normal_lengths, side_normals, NORM_TWO); 00161 FunctionSpaceTools::scalarMultiplyDataData<double>(side_normals, normal_lengths, side_normals, true); 00162 00163 FunctionSpaceTools::dotMultiplyDataData<double>(result, grad_u, side_normals); 00164 00165 } 00166 00168 void u_exact(FieldContainer<double> & result, const FieldContainer<double> & points, int xd, int yd, int zd) { 00169 int x = 0, y = 1, z = 2; 00170 for (int cell=0; cell<result.dimension(0); cell++) { 00171 for (int pt=0; pt<result.dimension(1); pt++) { 00172 result(cell,pt) = std::pow(points(pt,x), xd)*std::pow(points(pt,y), yd)*std::pow(points(pt,z), zd); 00173 } 00174 } 00175 } 00176 00177 00178 00179 00180 int main(int argc, char *argv[]) { 00181 00182 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00183 00184 // This little trick lets us print to std::cout only if 00185 // a (dummy) command-line argument is provided. 00186 int iprint = argc - 1; 00187 Teuchos::RCP<std::ostream> outStream; 00188 Teuchos::oblackholestream bhs; // outputs nothing 00189 if (iprint > 0) 00190 outStream = Teuchos::rcp(&std::cout, false); 00191 else 00192 outStream = Teuchos::rcp(&bhs, false); 00193 00194 // Save the format state of the original std::cout. 00195 Teuchos::oblackholestream oldFormatState; 00196 oldFormatState.copyfmt(std::cout); 00197 00198 *outStream \ 00199 << "===============================================================================\n" \ 00200 << "| |\n" \ 00201 << "| Unit Test (Basis_HGRAD_HEX_Cn_FEM) |\n" \ 00202 << "| |\n" \ 00203 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00204 << "| for the Neumann problem on a physical parallelepiped |\n" \ 00205 << "| AND a reference hex Omega with boundary Gamma. |\n" \ 00206 << "| |\n" \ 00207 << "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \ 00208 << "| |\n" \ 00209 << "| For a generic parallelepiped, the basis recovers a complete |\n" \ 00210 << "| polynomial space of order 2. On a (scaled and/or translated) |\n" \ 00211 << "| reference hex, the basis recovers a complete tensor product |\n" \ 00212 << "| space of order 1 (i.e. incl. cross terms, e.g. x^2*y^2*z^2). |\n" \ 00213 << "| |\n" \ 00214 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00215 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00216 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00217 << "| |\n" \ 00218 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00219 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00220 << "| |\n" \ 00221 << "===============================================================================\n"\ 00222 << "| TEST 1: Patch test |\n"\ 00223 << "===============================================================================\n"; 00224 00225 00226 int errorFlag = 0; 00227 00228 outStream -> precision(16); 00229 00230 00231 try { 00232 00233 int max_order = 3; // max total order of polynomial solution 00234 DefaultCubatureFactory<double> cubFactory; // create factory 00235 shards::CellTopology cell(shards::getCellTopologyData< shards::Hexahedron<> >()); // create parent cell topology 00236 shards::CellTopology side(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology 00237 shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >()); // create relevant subcell (side) topology 00238 int cellDim = cell.getDimension(); 00239 int sideDim = side.getDimension(); 00240 unsigned numSides = 6; 00241 00242 // Define array containing points at which the solution is evaluated, on the reference tet. 00243 int numIntervals = 10; 00244 int numInterpPoints = (numIntervals + 1)*(numIntervals + 1)*(numIntervals + 1); 00245 FieldContainer<double> interp_points_ref(numInterpPoints, 3); 00246 int counter = 0; 00247 for (int k=0; k<=numIntervals; k++) { 00248 for (int j=0; j<=numIntervals; j++) { 00249 for (int i=0; i<=numIntervals; i++) { 00250 interp_points_ref(counter,0) = i*(1.0/numIntervals)-1.0; 00251 interp_points_ref(counter,1) = j*(1.0/numIntervals)-1.0; 00252 interp_points_ref(counter,2) = k*(1.0/numIntervals)-1.0; 00253 counter++; 00254 } 00255 } 00256 } 00257 00258 /* Parent cell definition. */ 00259 FieldContainer<double> cell_nodes[2]; 00260 cell_nodes[0].resize(1, 8, cellDim); 00261 cell_nodes[1].resize(1, 8, cellDim); 00262 00263 // Generic parallelepiped. 00264 cell_nodes[0](0, 0, 0) = -5.0; 00265 cell_nodes[0](0, 0, 1) = -1.0; 00266 cell_nodes[0](0, 0, 2) = 0.0; 00267 cell_nodes[0](0, 1, 0) = 4.0; 00268 cell_nodes[0](0, 1, 1) = 1.0; 00269 cell_nodes[0](0, 1, 2) = 1.0; 00270 cell_nodes[0](0, 2, 0) = 8.0; 00271 cell_nodes[0](0, 2, 1) = 3.0; 00272 cell_nodes[0](0, 2, 2) = 1.0; 00273 cell_nodes[0](0, 3, 0) = -1.0; 00274 cell_nodes[0](0, 3, 1) = 1.0; 00275 cell_nodes[0](0, 3, 2) = 0.0; 00276 cell_nodes[0](0, 4, 0) = 5.0; 00277 cell_nodes[0](0, 4, 1) = 9.0; 00278 cell_nodes[0](0, 4, 2) = 1.0; 00279 cell_nodes[0](0, 5, 0) = 14.0; 00280 cell_nodes[0](0, 5, 1) = 11.0; 00281 cell_nodes[0](0, 5, 2) = 2.0; 00282 cell_nodes[0](0, 6, 0) = 18.0; 00283 cell_nodes[0](0, 6, 1) = 13.0; 00284 cell_nodes[0](0, 6, 2) = 2.0; 00285 cell_nodes[0](0, 7, 0) = 9.0; 00286 cell_nodes[0](0, 7, 1) = 11.0; 00287 cell_nodes[0](0, 7, 2) = 1.0; 00288 // Reference hex. 00289 cell_nodes[1](0, 0, 0) = -1.0; 00290 cell_nodes[1](0, 0, 1) = -1.0; 00291 cell_nodes[1](0, 0, 2) = -1.0; 00292 cell_nodes[1](0, 1, 0) = 1.0; 00293 cell_nodes[1](0, 1, 1) = -1.0; 00294 cell_nodes[1](0, 1, 2) = -1.0; 00295 cell_nodes[1](0, 2, 0) = 1.0; 00296 cell_nodes[1](0, 2, 1) = 1.0; 00297 cell_nodes[1](0, 2, 2) = -1.0; 00298 cell_nodes[1](0, 3, 0) = -1.0; 00299 cell_nodes[1](0, 3, 1) = 1.0; 00300 cell_nodes[1](0, 3, 2) = -1.0; 00301 cell_nodes[1](0, 4, 0) = -1.0; 00302 cell_nodes[1](0, 4, 1) = -1.0; 00303 cell_nodes[1](0, 4, 2) = 1.0; 00304 cell_nodes[1](0, 5, 0) = 1.0; 00305 cell_nodes[1](0, 5, 1) = -1.0; 00306 cell_nodes[1](0, 5, 2) = 1.0; 00307 cell_nodes[1](0, 6, 0) = 1.0; 00308 cell_nodes[1](0, 6, 1) = 1.0; 00309 cell_nodes[1](0, 6, 2) = 1.0; 00310 cell_nodes[1](0, 7, 0) = -1.0; 00311 cell_nodes[1](0, 7, 1) = 1.0; 00312 cell_nodes[1](0, 7, 2) = 1.0; 00313 00314 std::stringstream mystream[2]; 00315 mystream[0].str("\n>> Now testing basis on a generic parallelepiped ...\n"); 00316 mystream[1].str("\n>> Now testing basis on the reference hex ...\n"); 00317 00318 00319 for (int pcell = 0; pcell < 2; pcell++) { 00320 *outStream << mystream[pcell].str(); 00321 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00322 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes[pcell], cell); 00323 interp_points.resize(numInterpPoints, cellDim); 00324 00325 for (int x_order=0; x_order <= max_order; x_order++) { 00326 int max_y_order = max_order; 00327 if (pcell == 0) { 00328 max_y_order -= x_order; 00329 } 00330 for (int y_order=0; y_order <= max_y_order; y_order++) { 00331 int max_z_order = max_order; 00332 if (pcell == 0) { 00333 max_z_order -= x_order; 00334 max_z_order -= y_order; 00335 } 00336 for (int z_order=0; z_order <= max_z_order; z_order++) { 00337 00338 // evaluate exact solution 00339 FieldContainer<double> exact_solution(1, numInterpPoints); 00340 u_exact(exact_solution, interp_points, x_order, y_order, z_order); 00341 00342 int basis_order = max_order; 00343 00344 // set test tolerance; 00345 double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL; 00346 00347 //create basis 00348 FieldContainer<double> pts(PointTools::getLatticeSize(line,basis_order),1); 00349 PointTools::getLattice<double,FieldContainer<double> >(pts,line,basis_order); 00350 00351 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00352 Teuchos::rcp(new Basis_HGRAD_HEX_Cn_FEM<double,FieldContainer<double> >( basis_order, POINTTYPE_SPECTRAL ) ); 00353 int numFields = basis->getCardinality(); 00354 00355 // create cubatures 00356 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00357 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order); 00358 int numCubPointsCell = cellCub->getNumPoints(); 00359 int numCubPointsSide = sideCub->getNumPoints(); 00360 00361 /* Computational arrays. */ 00362 /* Section 1: Related to parent cell integration. */ 00363 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00364 FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim); 00365 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00366 FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim); 00367 FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim); 00368 FieldContainer<double> jacobian_det_cell(1, numCubPointsCell); 00369 FieldContainer<double> weighted_measure_cell(1, numCubPointsCell); 00370 00371 FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell); 00372 FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00373 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell); 00374 FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim); 00375 FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00376 FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim); 00377 FieldContainer<double> fe_matrix(1, numFields, numFields); 00378 00379 FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell); 00380 FieldContainer<double> rhs_and_soln_vector(1, numFields); 00381 00382 /* Section 2: Related to subcell (side) integration. */ 00383 FieldContainer<double> cub_points_side(numCubPointsSide, sideDim); 00384 FieldContainer<double> cub_weights_side(numCubPointsSide); 00385 FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim); 00386 FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim); 00387 FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim); 00388 FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide); 00389 FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide); 00390 00391 FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide); 00392 FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00393 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide); 00394 FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide); 00395 FieldContainer<double> neumann_fields_per_side(1, numFields); 00396 00397 /* Section 3: Related to global interpolant. */ 00398 FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints); 00399 FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints); 00400 FieldContainer<double> interpolant(1, numInterpPoints); 00401 00402 FieldContainer<int> ipiv(numFields); 00403 00404 00405 00406 /******************* START COMPUTATION ***********************/ 00407 00408 // get cubature points and weights 00409 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00410 00411 // compute geometric cell information 00412 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes[pcell], cell); 00413 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00414 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00415 00416 // compute weighted measure 00417 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00418 00420 // Computing mass matrices: 00421 // tabulate values of basis functions at (reference) cubature points 00422 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00423 00424 // transform values of basis functions 00425 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00426 value_of_basis_at_cub_points_cell); 00427 00428 // multiply with weighted measure 00429 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00430 weighted_measure_cell, 00431 transformed_value_of_basis_at_cub_points_cell); 00432 00433 // compute mass matrices 00434 FunctionSpaceTools::integrate<double>(fe_matrix, 00435 transformed_value_of_basis_at_cub_points_cell, 00436 weighted_transformed_value_of_basis_at_cub_points_cell, 00437 COMP_BLAS); 00439 00441 // Computing stiffness matrices: 00442 // tabulate gradients of basis functions at (reference) cubature points 00443 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00444 00445 // transform gradients of basis functions 00446 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00447 jacobian_inv_cell, 00448 grad_of_basis_at_cub_points_cell); 00449 00450 // multiply with weighted measure 00451 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00452 weighted_measure_cell, 00453 transformed_grad_of_basis_at_cub_points_cell); 00454 00455 // compute stiffness matrices and sum into fe_matrix 00456 FunctionSpaceTools::integrate<double>(fe_matrix, 00457 transformed_grad_of_basis_at_cub_points_cell, 00458 weighted_transformed_grad_of_basis_at_cub_points_cell, 00459 COMP_BLAS, 00460 true); 00462 00464 // Computing RHS contributions: 00465 // map cell (reference) cubature points to physical space 00466 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes[pcell], cell); 00467 00468 // evaluate rhs function 00469 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order); 00470 00471 // compute rhs 00472 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00473 rhs_at_cub_points_cell_physical, 00474 weighted_transformed_value_of_basis_at_cub_points_cell, 00475 COMP_BLAS); 00476 00477 // compute neumann b.c. contributions and adjust rhs 00478 sideCub->getCubature(cub_points_side, cub_weights_side); 00479 for (unsigned i=0; i<numSides; i++) { 00480 // compute geometric cell information 00481 CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell); 00482 CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes[pcell], cell); 00483 CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell); 00484 00485 // compute weighted face measure 00486 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell, 00487 jacobian_side_refcell, 00488 cub_weights_side, 00489 i, 00490 cell); 00491 00492 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00493 basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE); 00494 // transform 00495 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell, 00496 value_of_basis_at_cub_points_side_refcell); 00497 00498 // multiply with weighted measure 00499 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00500 weighted_measure_side_refcell, 00501 transformed_value_of_basis_at_cub_points_side_refcell); 00502 00503 // compute Neumann data 00504 // map side cubature points in reference parent cell domain to physical space 00505 CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes[pcell], cell); 00506 // now compute data 00507 neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell, 00508 cell, (int)i, x_order, y_order, z_order); 00509 00510 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00511 neumann_data_at_cub_points_side_physical, 00512 weighted_transformed_value_of_basis_at_cub_points_side_refcell, 00513 COMP_BLAS); 00514 00515 // adjust RHS 00516 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00517 } 00519 00521 // Solution of linear system: 00522 int info = 0; 00523 Teuchos::LAPACK<int, double> solver; 00524 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00526 00528 // Building interpolant: 00529 // evaluate basis at interpolation points 00530 basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE); 00531 // transform values of basis functions 00532 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref, 00533 value_of_basis_at_interp_points_ref); 00534 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref); 00536 00537 /******************* END COMPUTATION ***********************/ 00538 00539 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00540 00541 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00542 << x_order << ", " << y_order << ", " << z_order 00543 << ") and finite element interpolant of order " << basis_order << ": " 00544 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00545 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00546 00547 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00548 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00549 *outStream << "\n\nPatch test failed for solution polynomial order (" 00550 << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n"; 00551 errorFlag++; 00552 } 00553 } // end for z_order 00554 } // end for y_order 00555 } // end for x_order 00556 } // end for pcell 00557 00558 } 00559 // Catch unexpected errors 00560 catch (std::logic_error err) { 00561 *outStream << err.what() << "\n\n"; 00562 errorFlag = -1000; 00563 }; 00564 00565 if (errorFlag != 0) 00566 std::cout << "End Result: TEST FAILED\n"; 00567 else 00568 std::cout << "End Result: TEST PASSED\n"; 00569 00570 // reset format state of std::cout 00571 std::cout.copyfmt(oldFormatState); 00572 00573 return errorFlag; 00574 }
1.7.4