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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_HEX_Cn_FEM.hpp" 00051 #include "Intrepid_HDIV_HEX_In_FEM.hpp" 00052 #include "Intrepid_DefaultCubatureFactory.hpp" 00053 #include "Intrepid_PointTools.hpp" 00054 #include "Intrepid_RealSpaceTools.hpp" 00055 #include "Intrepid_ArrayTools.hpp" 00056 #include "Intrepid_FunctionSpaceTools.hpp" 00057 #include "Intrepid_CellTools.hpp" 00058 #include "Teuchos_oblackholestream.hpp" 00059 #include "Teuchos_RCP.hpp" 00060 #include "Teuchos_GlobalMPISession.hpp" 00061 #include "Teuchos_SerialDenseMatrix.hpp" 00062 #include "Teuchos_SerialDenseVector.hpp" 00063 #include "Teuchos_LAPACK.hpp" 00064 00065 using namespace std; 00066 using namespace Intrepid; 00067 00068 void rhsFunc( FieldContainer<double> &, const FieldContainer<double> &, int, int, int ); 00069 void u_exact( FieldContainer<double> &, const FieldContainer<double> &, int, int, int ); 00070 00071 // This is the rhs for (div tau,w) = (f,w), 00072 // which makes f the negative Laplacian of scalar solution 00073 void rhsFunc( FieldContainer<double> &result, 00074 const FieldContainer<double> &points, 00075 int xd, 00076 int yd , 00077 int zd) 00078 { 00079 for (int cell=0;cell<result.dimension(0);cell++) { 00080 for (int pt=0;pt<result.dimension(1);pt++) { 00081 result(cell,pt) = 0.0; 00082 if (xd >=2) { 00083 result(cell,pt) += xd*(xd-1)*pow(points(cell,pt,0),xd-2)*pow(points(cell,pt,1),yd) 00084 *pow(points(cell,pt,2),zd); 00085 } 00086 if (yd >=2) { 00087 result(cell,pt) += yd*(yd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd-2) 00088 *pow(points(cell,pt,2),zd); 00089 } 00090 if (zd>=2) { 00091 result(cell,pt) += zd*(zd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd) 00092 *pow(points(cell,pt,2),zd-2); 00093 00094 } 00095 } 00096 } 00097 } 00098 00099 void u_exact( FieldContainer<double> &result, 00100 const FieldContainer<double> &points, 00101 int xd, 00102 int yd, 00103 int zd) 00104 { 00105 for (int cell=0;cell<result.dimension(0);cell++){ 00106 for (int pt=0;pt<result.dimension(1);pt++) { 00107 result(cell,pt) = std::pow(points(cell,pt,0),xd)*std::pow(points(cell,pt,1),yd) 00108 *std::pow(points(cell,pt,2),zd); 00109 } 00110 } 00111 return; 00112 } 00113 00114 int main(int argc, char *argv[]) { 00115 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00116 00117 // This little trick lets us print to std::cout only if 00118 // a (dummy) command-line argument is provided. 00119 int iprint = argc - 1; 00120 Teuchos::RCP<std::ostream> outStream; 00121 Teuchos::oblackholestream bhs; // outputs nothing 00122 if (iprint > 0) 00123 outStream = Teuchos::rcp(&std::cout, false); 00124 else 00125 outStream = Teuchos::rcp(&bhs, false); 00126 00127 // Save the format state of the original std::cout. 00128 Teuchos::oblackholestream oldFormatState; 00129 oldFormatState.copyfmt(std::cout); 00130 00131 *outStream \ 00132 << "===============================================================================\n" \ 00133 << "| |\n" \ 00134 << "| Unit Test (Basis_HGRAD_HEX_In_FEM) |\n" \ 00135 << "| |\n" \ 00136 << "| 1) Patch test involving H(div) matrices |\n" \ 00137 << "| for the Dirichlet problem on a hexahedron |\n" \ 00138 << "| Omega with boundary Gamma. |\n" \ 00139 << "| |\n" \ 00140 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00141 << "| Robert Kirby (robert.c.kirby@ttu.edu), |\n" \ 00142 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00143 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00144 << "| |\n" \ 00145 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00146 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00147 << "| |\n" \ 00148 << "===============================================================================\n" \ 00149 << "| TEST 1: Patch test |\n" \ 00150 << "===============================================================================\n"; 00151 00152 00153 int errorFlag = 0; 00154 00155 outStream -> precision(16); 00156 00157 try { 00158 DefaultCubatureFactory<double> cubFactory; // create cubature factory 00159 shards::CellTopology cell(shards::getCellTopologyData< shards::Hexahedron<> >()); // create parent cell topology 00160 shards::CellTopology side(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology 00161 shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >() ); // for getting points to construct the basis 00162 00163 int cellDim = cell.getDimension(); 00164 int sideDim = side.getDimension(); 00165 00166 int min_order = 0; 00167 int max_order = 3; 00168 00169 int numIntervals = 2; 00170 int numInterpPoints = (numIntervals + 1)*(numIntervals + 1)*(numIntervals+1); 00171 FieldContainer<double> interp_points_ref(numInterpPoints, cellDim); 00172 int counter = 0; 00173 for (int k=0;k<numIntervals;k++) { 00174 for (int j=0; j<=numIntervals; j++) { 00175 for (int i=0; i<=numIntervals; i++) { 00176 interp_points_ref(counter,0) = i*(1.0/numIntervals); 00177 interp_points_ref(counter,1) = j*(1.0/numIntervals); 00178 interp_points_ref(counter,2) = k*(1.0/numIntervals); 00179 counter++; 00180 } 00181 } 00182 } 00183 00184 for (int basis_order=min_order;basis_order<=max_order;basis_order++) { 00185 // create bases 00186 // get the points for the vector basis 00187 Teuchos::RCP<Basis<double,FieldContainer<double> > > vectorBasis = 00188 Teuchos::rcp(new Basis_HDIV_HEX_In_FEM<double,FieldContainer<double> >(basis_order+1,POINTTYPE_SPECTRAL) ); 00189 00190 Teuchos::RCP<Basis<double,FieldContainer<double> > > scalarBasis = 00191 Teuchos::rcp(new Basis_HGRAD_HEX_Cn_FEM<double,FieldContainer<double> >(basis_order,POINTTYPE_SPECTRAL) ); 00192 00193 int numVectorFields = vectorBasis->getCardinality(); 00194 int numScalarFields = scalarBasis->getCardinality(); 00195 int numTotalFields = numVectorFields + numScalarFields; 00196 00197 // create cubatures 00198 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1)); 00199 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*(basis_order+1)); 00200 00201 int numCubPointsCell = cellCub->getNumPoints(); 00202 int numCubPointsSide = sideCub->getNumPoints(); 00203 00204 // hold cubature information 00205 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00206 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00207 FieldContainer<double> cub_points_side( numCubPointsSide, sideDim ); 00208 FieldContainer<double> cub_weights_side( numCubPointsSide ); 00209 FieldContainer<double> cub_points_side_refcell( numCubPointsSide , cellDim ); 00210 00211 // hold basis function information on refcell 00212 FieldContainer<double> value_of_v_basis_at_cub_points_cell(numVectorFields, numCubPointsCell, cellDim ); 00213 FieldContainer<double> w_value_of_v_basis_at_cub_points_cell(1, numVectorFields, numCubPointsCell, cellDim); 00214 FieldContainer<double> div_of_v_basis_at_cub_points_cell( numVectorFields, numCubPointsCell ); 00215 FieldContainer<double> w_div_of_v_basis_at_cub_points_cell( 1, numVectorFields , numCubPointsCell ); 00216 FieldContainer<double> value_of_s_basis_at_cub_points_cell(numScalarFields,numCubPointsCell); 00217 FieldContainer<double> w_value_of_s_basis_at_cub_points_cell(1,numScalarFields,numCubPointsCell); 00218 00219 // containers for side integration: 00220 // I just need the normal component of the vector basis 00221 // and the exact solution at the cub points 00222 FieldContainer<double> value_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide,cellDim); 00223 FieldContainer<double> n_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide); 00224 FieldContainer<double> w_n_of_v_basis_at_cub_points_side(1,numVectorFields,numCubPointsSide); 00225 FieldContainer<double> diri_data_at_cub_points_side(1,numCubPointsSide); 00226 FieldContainer<double> side_normal(cellDim); 00227 00228 // holds rhs data 00229 FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell); 00230 00231 // FEM matrices and vectors 00232 FieldContainer<double> fe_matrix_M(1,numVectorFields,numVectorFields); 00233 FieldContainer<double> fe_matrix_B(1,numVectorFields,numScalarFields); 00234 FieldContainer<double> fe_matrix(1,numTotalFields,numTotalFields); 00235 00236 FieldContainer<double> rhs_vector_vec(1,numVectorFields); 00237 FieldContainer<double> rhs_vector_scal(1,numScalarFields); 00238 FieldContainer<double> rhs_and_soln_vec(1,numTotalFields); 00239 00240 FieldContainer<int> ipiv(numTotalFields); 00241 FieldContainer<double> value_of_s_basis_at_interp_points( numScalarFields , numInterpPoints); 00242 FieldContainer<double> interpolant( 1 , numInterpPoints ); 00243 00244 // set test tolerance 00245 double zero = (basis_order+1)*(basis_order+1)*1000.0*INTREPID_TOL; 00246 00247 // build matrices outside the loop, and then just do the rhs 00248 // for each iteration 00249 00250 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00251 sideCub->getCubature(cub_points_side, cub_weights_side); 00252 00253 // need the vector basis & its divergences 00254 vectorBasis->getValues(value_of_v_basis_at_cub_points_cell, 00255 cub_points_cell, 00256 OPERATOR_VALUE); 00257 vectorBasis->getValues(div_of_v_basis_at_cub_points_cell, 00258 cub_points_cell, 00259 OPERATOR_DIV); 00260 00261 // need the scalar basis as well 00262 scalarBasis->getValues(value_of_s_basis_at_cub_points_cell, 00263 cub_points_cell, 00264 OPERATOR_VALUE); 00265 00266 // construct mass matrix 00267 cub_weights_cell.resize(1,numCubPointsCell); 00268 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_v_basis_at_cub_points_cell , 00269 cub_weights_cell , 00270 value_of_v_basis_at_cub_points_cell ); 00271 cub_weights_cell.resize(numCubPointsCell); 00272 00273 00274 value_of_v_basis_at_cub_points_cell.resize( 1 , numVectorFields , numCubPointsCell , cellDim ); 00275 FunctionSpaceTools::integrate<double>(fe_matrix_M, 00276 w_value_of_v_basis_at_cub_points_cell , 00277 value_of_v_basis_at_cub_points_cell , 00278 COMP_BLAS ); 00279 value_of_v_basis_at_cub_points_cell.resize( numVectorFields , numCubPointsCell , cellDim ); 00280 00281 // div matrix 00282 cub_weights_cell.resize(1,numCubPointsCell); 00283 FunctionSpaceTools::multiplyMeasure<double>(w_div_of_v_basis_at_cub_points_cell, 00284 cub_weights_cell, 00285 div_of_v_basis_at_cub_points_cell); 00286 cub_weights_cell.resize(numCubPointsCell); 00287 00288 value_of_s_basis_at_cub_points_cell.resize(1,numScalarFields,numCubPointsCell); 00289 FunctionSpaceTools::integrate<double>(fe_matrix_B, 00290 w_div_of_v_basis_at_cub_points_cell , 00291 value_of_s_basis_at_cub_points_cell , 00292 COMP_BLAS ); 00293 value_of_s_basis_at_cub_points_cell.resize(numScalarFields,numCubPointsCell); 00294 00295 for (int x_order=0;x_order<=basis_order;x_order++) { 00296 for (int y_order=0;y_order<=basis_order;y_order++) { 00297 for (int z_order=0;z_order<=basis_order;z_order++) { 00298 00299 00300 // reset global matrix since I destroyed it in LU factorization. 00301 fe_matrix.initialize(); 00302 // insert mass matrix into global matrix 00303 for (int i=0;i<numVectorFields;i++) { 00304 for (int j=0;j<numVectorFields;j++) { 00305 fe_matrix(0,i,j) = fe_matrix_M(0,i,j); 00306 } 00307 } 00308 00309 // insert div matrix into global matrix 00310 for (int i=0;i<numVectorFields;i++) { 00311 for (int j=0;j<numScalarFields;j++) { 00312 fe_matrix(0,i,numVectorFields+j)=-fe_matrix_B(0,i,j); 00313 fe_matrix(0,j+numVectorFields,i)=fe_matrix_B(0,i,j); 00314 } 00315 } 00316 00317 // clear old vector data 00318 rhs_vector_vec.initialize(); 00319 rhs_vector_scal.initialize(); 00320 rhs_and_soln_vec.initialize(); 00321 00322 // now get rhs vector 00323 // rhs_vector_scal is just (rhs,w) for w in the scalar basis 00324 // I already have the scalar basis tabulated. 00325 cub_points_cell.resize(1,numCubPointsCell,cellDim); 00326 rhsFunc(rhs_at_cub_points_cell, 00327 cub_points_cell, 00328 x_order, 00329 y_order, 00330 z_order); 00331 00332 cub_points_cell.resize(numCubPointsCell,cellDim); 00333 00334 cub_weights_cell.resize(1,numCubPointsCell); 00335 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_s_basis_at_cub_points_cell, 00336 cub_weights_cell, 00337 value_of_s_basis_at_cub_points_cell); 00338 cub_weights_cell.resize(numCubPointsCell); 00339 FunctionSpaceTools::integrate<double>(rhs_vector_scal, 00340 rhs_at_cub_points_cell, 00341 w_value_of_s_basis_at_cub_points_cell, 00342 COMP_BLAS); 00343 00344 for (int i=0;i<numScalarFields;i++) { 00345 rhs_and_soln_vec(0,numVectorFields+i) = rhs_vector_scal(0,i); 00346 } 00347 00348 00349 // now get <u,v.n> on boundary 00350 for (unsigned side_cur=0;side_cur<6;side_cur++) { 00351 // map side cubature to current side 00352 CellTools<double>::mapToReferenceSubcell( cub_points_side_refcell , 00353 cub_points_side , 00354 sideDim , 00355 (int)side_cur , 00356 cell ); 00357 // Evaluate dirichlet data 00358 cub_points_side_refcell.resize(1,numCubPointsSide,cellDim); 00359 u_exact(diri_data_at_cub_points_side, 00360 cub_points_side_refcell,x_order,y_order,z_order); 00361 00362 cub_points_side_refcell.resize(numCubPointsSide,cellDim); 00363 00364 // get normal direction, this has the edge weight factored into it already 00365 CellTools<double>::getReferenceSideNormal(side_normal , 00366 (int)side_cur,cell ); 00367 00368 // v.n at cub points on side 00369 vectorBasis->getValues(value_of_v_basis_at_cub_points_side , 00370 cub_points_side_refcell , 00371 OPERATOR_VALUE ); 00372 00373 for (int i=0;i<numVectorFields;i++) { 00374 for (int j=0;j<numCubPointsSide;j++) { 00375 n_of_v_basis_at_cub_points_side(i,j) = 0.0; 00376 for (int k=0;k<cellDim;k++) { 00377 n_of_v_basis_at_cub_points_side(i,j) += side_normal(k) * 00378 value_of_v_basis_at_cub_points_side(i,j,k); 00379 } 00380 } 00381 } 00382 00383 cub_weights_side.resize(1,numCubPointsSide); 00384 FunctionSpaceTools::multiplyMeasure<double>(w_n_of_v_basis_at_cub_points_side, 00385 cub_weights_side, 00386 n_of_v_basis_at_cub_points_side); 00387 cub_weights_side.resize(numCubPointsSide); 00388 00389 FunctionSpaceTools::integrate<double>(rhs_vector_vec, 00390 diri_data_at_cub_points_side, 00391 w_n_of_v_basis_at_cub_points_side, 00392 COMP_BLAS, 00393 false); 00394 00395 for (int i=0;i<numVectorFields;i++) { 00396 rhs_and_soln_vec(0,i) -= rhs_vector_vec(0,i); 00397 } 00398 00399 } 00400 00401 // solve linear system 00402 int info = 0; 00403 Teuchos::LAPACK<int, double> solver; 00404 solver.GESV(numTotalFields, 1, &fe_matrix[0], numTotalFields, &ipiv(0), &rhs_and_soln_vec[0], 00405 numTotalFields, &info); 00406 00407 // compute interpolant; the scalar entries are last 00408 scalarBasis->getValues(value_of_s_basis_at_interp_points, 00409 interp_points_ref, 00410 OPERATOR_VALUE); 00411 for (int pt=0;pt<numInterpPoints;pt++) { 00412 interpolant(0,pt)=0.0; 00413 for (int i=0;i<numScalarFields;i++) { 00414 interpolant(0,pt) += rhs_and_soln_vec(0,numVectorFields+i) 00415 * value_of_s_basis_at_interp_points(i,pt); 00416 } 00417 } 00418 00419 interp_points_ref.resize(1,numInterpPoints,cellDim); 00420 // get exact solution for comparison 00421 FieldContainer<double> exact_solution(1,numInterpPoints); 00422 u_exact( exact_solution , interp_points_ref , x_order, y_order, z_order); 00423 interp_points_ref.resize(numInterpPoints,cellDim); 00424 00425 RealSpaceTools<double>::add(interpolant,exact_solution); 00426 00427 double nrm= RealSpaceTools<double>::vectorNorm(&interpolant[0],interpolant.dimension(1), NORM_TWO); 00428 00429 *outStream << "\nNorm-2 error between scalar components of exact solution of order (" 00430 << x_order << ", " << y_order << ", " << z_order 00431 << ") and finite element interpolant of order " << basis_order << ": " 00432 << nrm << "\n"; 00433 00434 if (nrm > zero) { 00435 *outStream << "\n\nPatch test failed for solution polynomial order (" 00436 << x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) (" 00437 << basis_order << ", " << basis_order+1 << ")\n\n"; 00438 errorFlag++; 00439 } 00440 00441 } 00442 } 00443 } 00444 } 00445 00446 } 00447 00448 catch (std::logic_error err) { 00449 *outStream << err.what() << "\n\n"; 00450 errorFlag = -1000; 00451 }; 00452 00453 if (errorFlag != 0) 00454 std::cout << "End Result: TEST FAILED\n"; 00455 else 00456 std::cout << "End Result: TEST PASSED\n"; 00457 00458 // reset format state of std::cout 00459 std::cout.copyfmt(oldFormatState); 00460 00461 return errorFlag; 00462 }
1.7.6.1