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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_WEDGE_C1_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_WEDGE_C1_FEM) |\n" \ 00214 << "| |\n" \ 00215 << "| 1) Patch test involving mass and stiffness matrices, |\n" \ 00216 << "| for the Neumann problem on a wedge 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 << "| Mauro Perego (mperego@sandia.gov). |\n" \ 00225 << "| |\n" \ 00226 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00227 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00228 << "| |\n" \ 00229 << "===============================================================================\n"\ 00230 << "| TEST 1: Patch test |\n"\ 00231 << "===============================================================================\n"; 00232 00233 00234 int errorFlag = 0; 00235 00236 outStream -> precision(16); 00237 00238 00239 try { 00240 00241 int max_order = 1; // max total order of polynomial solution 00242 DefaultCubatureFactory<double> cubFactory; // create factory 00243 shards::CellTopology cell(shards::getCellTopologyData< shards::Wedge<> >()); // create parent cell topology 00244 shards::CellTopology sideQ(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology 00245 shards::CellTopology sideT(shards::getCellTopologyData< shards::Triangle<> >()); 00246 int cellDim = cell.getDimension(); 00247 int sideQDim = sideQ.getDimension(); 00248 int sideTDim = sideT.getDimension(); 00249 00250 // Define array containing points at which the solution is evaluated, on the reference Wedge. 00251 int numIntervals = 10; 00252 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6; 00253 FieldContainer<double> interp_points_ref(numInterpPoints, 3); 00254 int counter = 0; 00255 for (int k=0; k<=numIntervals; k++) { 00256 for (int j=0; j<=numIntervals; j++) { 00257 for (int i=0; i<=numIntervals; i++) { 00258 if (i+j+k <= numIntervals) { 00259 interp_points_ref(counter,0) = i*(1.0/numIntervals); 00260 interp_points_ref(counter,1) = j*(1.0/numIntervals); 00261 interp_points_ref(counter,2) = k*(1.0/numIntervals); 00262 counter++; 00263 } 00264 } 00265 } 00266 } 00267 00268 /* Definition of parent cell. */ 00269 FieldContainer<double> cell_nodes(1, 6, cellDim); 00270 // funky Wedge (affine mapping) 00271 cell_nodes(0, 0, 0) = -3.0; 00272 cell_nodes(0, 0, 1) = -5.0; 00273 cell_nodes(0, 0, 2) = -5.0; 00274 cell_nodes(0, 1, 0) = -1.0; 00275 cell_nodes(0, 1, 1) = -4.0; 00276 cell_nodes(0, 1, 2) = -4.0; 00277 cell_nodes(0, 2, 0) = 0.0; 00278 cell_nodes(0, 2, 1) = 0.0; 00279 cell_nodes(0, 2, 2) = -5.0; 00280 cell_nodes(0, 3, 0) = 5.0; 00281 cell_nodes(0, 3, 1) = -1.0; 00282 cell_nodes(0, 3, 2) = 1.0; 00283 cell_nodes(0, 4, 0) = 7.0; 00284 cell_nodes(0, 4, 1) = 0.0; 00285 cell_nodes(0, 4, 2) = 2.0; 00286 cell_nodes(0, 5, 0) = 8.0; 00287 cell_nodes(0, 5, 1) = 4.0; 00288 cell_nodes(0, 5, 2) = 1.0; 00289 00290 // perturbed reference Wedge 00291 /*cell_nodes(0, 0, 0) = 0.1; 00292 cell_nodes(0, 0, 1) = 0.1; 00293 cell_nodes(0, 0, 2) = -0.8; 00294 cell_nodes(0, 1, 0) = 1.2; 00295 cell_nodes(0, 1, 1) = 0.1; 00296 cell_nodes(0, 1, 2) = -0.95; 00297 cell_nodes(0, 2, 0) = 0.0; 00298 cell_nodes(0, 2, 1) = 0.9; 00299 cell_nodes(0, 2, 2) = -0.0; 00300 cell_nodes(0, 3, 0) = 0.1; 00301 cell_nodes(0, 3, 1) = 0.0; 00302 cell_nodes(0, 3, 2) = 0.9; 00303 cell_nodes(0, 4, 0) = 0.9; 00304 cell_nodes(0, 4, 1) = 0.1; 00305 cell_nodes(0, 4, 2) = 1.1; 00306 cell_nodes(0, 5, 0) = -0.1; 00307 cell_nodes(0, 5, 1) = 1.0; 00308 cell_nodes(0, 5, 2) = 1.0;*/ 00309 00310 // reference Wedge 00311 /*cell_nodes(0, 0, 0) = 0.0; 00312 cell_nodes(0, 0, 1) = 0.0; 00313 cell_nodes(0, 0, 2) = -1.0; 00314 cell_nodes(0, 1, 0) = 1.0; 00315 cell_nodes(0, 1, 1) = 0.0; 00316 cell_nodes(0, 1, 2) = -1.0; 00317 cell_nodes(0, 2, 0) = 0.0; 00318 cell_nodes(0, 2, 1) = 1.0; 00319 cell_nodes(0, 2, 2) = -1.0; 00320 cell_nodes(0, 3, 0) = 0.0; 00321 cell_nodes(0, 3, 1) = 0.0; 00322 cell_nodes(0, 3, 2) = 1.0; 00323 cell_nodes(0, 4, 0) = 1.0; 00324 cell_nodes(0, 4, 1) = 0.0; 00325 cell_nodes(0, 4, 2) = 1.0; 00326 cell_nodes(0, 5, 0) = 0.0; 00327 cell_nodes(0, 5, 1) = 1.0; 00328 cell_nodes(0, 5, 2) = 1.0;*/ 00329 00330 00331 FieldContainer<double> interp_points(1, numInterpPoints, cellDim); 00332 CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell); 00333 interp_points.resize(numInterpPoints, cellDim); 00334 00335 for (int x_order=0; x_order <= max_order; x_order++) { 00336 for (int y_order=0; y_order <= max_order-x_order; y_order++) { 00337 for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) { 00338 00339 // evaluate exact solution 00340 FieldContainer<double> exact_solution(1, numInterpPoints); 00341 u_exact(exact_solution, interp_points, x_order, y_order, z_order); 00342 00343 int basis_order = 1; 00344 00345 // set test tolerance; 00346 double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL; 00347 00348 //create basis 00349 Teuchos::RCP<Basis<double,FieldContainer<double> > > basis = 00350 Teuchos::rcp(new Basis_HGRAD_WEDGE_C1_FEM<double,FieldContainer<double> >() ); 00351 int numFields = basis->getCardinality(); 00352 00353 // create cubatures 00354 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order); 00355 Teuchos::RCP<Cubature<double> > sideQCub = cubFactory.create(sideQ, 2*basis_order); 00356 Teuchos::RCP<Cubature<double> > sideTCub = cubFactory.create(sideT, 2*basis_order); 00357 int numCubPointsCell = cellCub->getNumPoints(); 00358 int numCubPointsSideQ = sideQCub->getNumPoints(); 00359 int numCubPointsSideT = sideTCub->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 unsigned numSides = 5; 00384 unsigned numSidesQ = 3; 00385 FieldContainer<double> cub_points_sideQ(numCubPointsSideQ, sideQDim); 00386 FieldContainer<double> cub_points_sideT(numCubPointsSideT, sideTDim); 00387 FieldContainer<double> cub_weights_sideQ(numCubPointsSideQ); 00388 FieldContainer<double> cub_weights_sideT(numCubPointsSideT); 00389 FieldContainer<double> cub_points_sideQ_refcell(numCubPointsSideQ, cellDim); 00390 FieldContainer<double> cub_points_sideT_refcell(numCubPointsSideT, cellDim); 00391 FieldContainer<double> cub_points_sideQ_physical(1, numCubPointsSideQ, cellDim); 00392 FieldContainer<double> cub_points_sideT_physical(1, numCubPointsSideT, cellDim); 00393 FieldContainer<double> jacobian_sideQ_refcell(1, numCubPointsSideQ, cellDim, cellDim); 00394 FieldContainer<double> jacobian_sideT_refcell(1, numCubPointsSideT, cellDim, cellDim); 00395 FieldContainer<double> jacobian_det_sideQ_refcell(1, numCubPointsSideQ); 00396 FieldContainer<double> jacobian_det_sideT_refcell(1, numCubPointsSideT); 00397 FieldContainer<double> weighted_measure_sideQ_refcell(1, numCubPointsSideQ); 00398 FieldContainer<double> weighted_measure_sideT_refcell(1, numCubPointsSideT); 00399 00400 FieldContainer<double> value_of_basis_at_cub_points_sideQ_refcell(numFields, numCubPointsSideQ); 00401 FieldContainer<double> value_of_basis_at_cub_points_sideT_refcell(numFields, numCubPointsSideT); 00402 FieldContainer<double> transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ); 00403 FieldContainer<double> transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT); 00404 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell(1, numFields, numCubPointsSideQ); 00405 FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_sideT_refcell(1, numFields, numCubPointsSideT); 00406 FieldContainer<double> neumann_data_at_cub_points_sideQ_physical(1, numCubPointsSideQ); 00407 FieldContainer<double> neumann_data_at_cub_points_sideT_physical(1, numCubPointsSideT); 00408 FieldContainer<double> neumann_fields_per_side(1, numFields); 00409 00410 /* Section 3: Related to global interpolant. */ 00411 FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints); 00412 FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints); 00413 FieldContainer<double> interpolant(1, numInterpPoints); 00414 00415 FieldContainer<int> ipiv(numFields); 00416 00417 00418 00419 /******************* START COMPUTATION ***********************/ 00420 00421 // get cubature points and weights 00422 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00423 00424 // compute geometric cell information 00425 CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell); 00426 CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell); 00427 CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell); 00428 00429 // compute weighted measure 00430 FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell); 00431 00433 // Computing mass matrices: 00434 // tabulate values of basis functions at (reference) cubature points 00435 basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE); 00436 00437 // transform values of basis functions 00438 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell, 00439 value_of_basis_at_cub_points_cell); 00440 00441 // multiply with weighted measure 00442 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell, 00443 weighted_measure_cell, 00444 transformed_value_of_basis_at_cub_points_cell); 00445 00446 // compute mass matrices 00447 FunctionSpaceTools::integrate<double>(fe_matrix, 00448 transformed_value_of_basis_at_cub_points_cell, 00449 weighted_transformed_value_of_basis_at_cub_points_cell, 00450 COMP_BLAS); 00452 00454 // Computing stiffness matrices: 00455 // tabulate gradients of basis functions at (reference) cubature points 00456 basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD); 00457 00458 // transform gradients of basis functions 00459 FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell, 00460 jacobian_inv_cell, 00461 grad_of_basis_at_cub_points_cell); 00462 00463 // multiply with weighted measure 00464 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell, 00465 weighted_measure_cell, 00466 transformed_grad_of_basis_at_cub_points_cell); 00467 00468 // compute stiffness matrices and sum into fe_matrix 00469 FunctionSpaceTools::integrate<double>(fe_matrix, 00470 transformed_grad_of_basis_at_cub_points_cell, 00471 weighted_transformed_grad_of_basis_at_cub_points_cell, 00472 COMP_BLAS, 00473 true); 00475 00477 // Computing RHS contributions: 00478 // map cell (reference) cubature points to physical space 00479 CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell); 00480 00481 // evaluate rhs function 00482 rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order); 00483 00484 // compute rhs 00485 FunctionSpaceTools::integrate<double>(rhs_and_soln_vector, 00486 rhs_at_cub_points_cell_physical, 00487 weighted_transformed_value_of_basis_at_cub_points_cell, 00488 COMP_BLAS); 00489 00490 // compute neumann b.c. contributions and adjust rhs 00491 sideQCub->getCubature(cub_points_sideQ, cub_weights_sideQ); 00492 sideTCub->getCubature(cub_points_sideT, cub_weights_sideT); 00493 00494 for (unsigned i=0; i<numSidesQ; i++) { 00495 // compute geometric cell information 00496 CellTools<double>::mapToReferenceSubcell(cub_points_sideQ_refcell, cub_points_sideQ, sideQDim, (int)i, cell); 00497 CellTools<double>::setJacobian(jacobian_sideQ_refcell, cub_points_sideQ_refcell, cell_nodes, cell); 00498 CellTools<double>::setJacobianDet(jacobian_det_sideQ_refcell, jacobian_sideQ_refcell); 00499 00500 // compute weighted face measure 00501 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideQ_refcell, 00502 jacobian_sideQ_refcell, 00503 cub_weights_sideQ, 00504 i, 00505 cell); 00506 00507 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00508 basis->getValues(value_of_basis_at_cub_points_sideQ_refcell, cub_points_sideQ_refcell, OPERATOR_VALUE); 00509 // transform 00510 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideQ_refcell, 00511 value_of_basis_at_cub_points_sideQ_refcell); 00512 00513 // multiply with weighted measure 00514 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell, 00515 weighted_measure_sideQ_refcell, 00516 transformed_value_of_basis_at_cub_points_sideQ_refcell); 00517 00518 // compute Neumann data 00519 // map side cubature points in reference parent cell domain to physical space 00520 CellTools<double>::mapToPhysicalFrame(cub_points_sideQ_physical, cub_points_sideQ_refcell, cell_nodes, cell); 00521 // now compute data 00522 neumann(neumann_data_at_cub_points_sideQ_physical, cub_points_sideQ_physical, jacobian_sideQ_refcell, 00523 cell, (int)i, x_order, y_order, z_order); 00524 00525 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00526 neumann_data_at_cub_points_sideQ_physical, 00527 weighted_transformed_value_of_basis_at_cub_points_sideQ_refcell, 00528 COMP_BLAS); 00529 00530 // adjust RHS 00531 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00532 } 00533 00534 for (unsigned i=numSidesQ; i<numSides; i++) { 00535 // compute geometric cell information 00536 CellTools<double>::mapToReferenceSubcell(cub_points_sideT_refcell, cub_points_sideT, sideTDim, (int)i, cell); 00537 CellTools<double>::setJacobian(jacobian_sideT_refcell, cub_points_sideT_refcell, cell_nodes, cell); 00538 CellTools<double>::setJacobianDet(jacobian_det_sideT_refcell, jacobian_sideT_refcell); 00539 00540 // compute weighted face measure 00541 FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_sideT_refcell, 00542 jacobian_sideT_refcell, 00543 cub_weights_sideT, 00544 i, 00545 cell); 00546 00547 // tabulate values of basis functions at side cubature points, in the reference parent cell domain 00548 basis->getValues(value_of_basis_at_cub_points_sideT_refcell, cub_points_sideT_refcell, OPERATOR_VALUE); 00549 // transform 00550 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_sideT_refcell, 00551 value_of_basis_at_cub_points_sideT_refcell); 00552 00553 // multiply with weighted measure 00554 FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_sideT_refcell, 00555 weighted_measure_sideT_refcell, 00556 transformed_value_of_basis_at_cub_points_sideT_refcell); 00557 00558 // compute Neumann data 00559 // map side cubature points in reference parent cell domain to physical space 00560 CellTools<double>::mapToPhysicalFrame(cub_points_sideT_physical, cub_points_sideT_refcell, cell_nodes, cell); 00561 // now compute data 00562 neumann(neumann_data_at_cub_points_sideT_physical, cub_points_sideT_physical, jacobian_sideT_refcell, 00563 cell, (int)i, x_order, y_order, z_order); 00564 00565 FunctionSpaceTools::integrate<double>(neumann_fields_per_side, 00566 neumann_data_at_cub_points_sideT_physical, 00567 weighted_transformed_value_of_basis_at_cub_points_sideT_refcell, 00568 COMP_BLAS); 00569 00570 // adjust RHS 00571 RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);; 00572 } 00574 00576 // Solution of linear system: 00577 int info = 0; 00578 Teuchos::LAPACK<int, double> solver; 00579 solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info); 00581 00583 // Building interpolant: 00584 // evaluate basis at interpolation points 00585 basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE); 00586 // transform values of basis functions 00587 FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref, 00588 value_of_basis_at_interp_points_ref); 00589 FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref); 00591 00592 /******************* END COMPUTATION ***********************/ 00593 00594 RealSpaceTools<double>::subtract(interpolant, exact_solution); 00595 00596 *outStream << "\nRelative norm-2 error between exact solution polynomial of order (" 00597 << x_order << ", " << y_order << ", " << z_order 00598 << ") and finite element interpolant of order " << basis_order << ": " 00599 << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00600 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n"; 00601 00602 if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) / 00603 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) { 00604 *outStream << "\n\nPatch test failed for solution polynomial order (" 00605 << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n"; 00606 errorFlag++; 00607 } 00608 } // end for z_order 00609 } // end for y_order 00610 } // end for x_order 00611 00612 } 00613 // Catch unexpected errors 00614 catch (std::logic_error err) { 00615 *outStream << err.what() << "\n\n"; 00616 errorFlag = -1000; 00617 }; 00618 00619 if (errorFlag != 0) 00620 std::cout << "End Result: TEST FAILED\n"; 00621 else 00622 std::cout << "End Result: TEST PASSED\n"; 00623 00624 // reset format state of std::cout 00625 std::cout.copyfmt(oldFormatState); 00626 00627 return errorFlag; 00628 }
1.7.6.1