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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_ORTH.hpp" 00051 #include "Intrepid_HDIV_TET_In_FEM.hpp" 00052 #include "Intrepid_DefaultCubatureFactory.hpp" 00053 #include "Intrepid_RealSpaceTools.hpp" 00054 #include "Intrepid_ArrayTools.hpp" 00055 #include "Intrepid_FunctionSpaceTools.hpp" 00056 #include "Intrepid_CellTools.hpp" 00057 #include "Teuchos_oblackholestream.hpp" 00058 #include "Teuchos_RCP.hpp" 00059 #include "Teuchos_GlobalMPISession.hpp" 00060 #include "Teuchos_SerialDenseMatrix.hpp" 00061 #include "Teuchos_SerialDenseVector.hpp" 00062 #include "Teuchos_LAPACK.hpp" 00063 00064 using namespace std; 00065 using namespace Intrepid; 00066 00067 void rhsFunc( FieldContainer<double> &, const FieldContainer<double> &, int, int, int ); 00068 void u_exact( FieldContainer<double> &, const FieldContainer<double> &, int, int, int ); 00069 00070 // This is the rhs for (div tau,w) = (f,w), 00071 // which makes f the negative Laplacian of scalar solution 00072 void rhsFunc( FieldContainer<double> &result, 00073 const FieldContainer<double> &points, 00074 int xd, 00075 int yd , 00076 int zd) 00077 { 00078 for (int cell=0;cell<result.dimension(0);cell++) { 00079 for (int pt=0;pt<result.dimension(1);pt++) { 00080 result(cell,pt) = 0.0; 00081 if (xd >=2) { 00082 result(cell,pt) += xd*(xd-1)*pow(points(cell,pt,0),xd-2)*pow(points(cell,pt,1),yd) 00083 *pow(points(cell,pt,2),zd); 00084 } 00085 if (yd >=2) { 00086 result(cell,pt) += yd*(yd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd-2) 00087 *pow(points(cell,pt,2),zd); 00088 } 00089 if (zd>=2) { 00090 result(cell,pt) += zd*(zd-1)*pow(points(cell,pt,0),xd)*pow(points(cell,pt,1),yd) 00091 *pow(points(cell,pt,2),zd-2); 00092 00093 } 00094 } 00095 } 00096 } 00097 00098 void u_exact( FieldContainer<double> &result, 00099 const FieldContainer<double> &points, 00100 int xd, 00101 int yd, 00102 int zd) 00103 { 00104 for (int cell=0;cell<result.dimension(0);cell++){ 00105 for (int pt=0;pt<result.dimension(1);pt++) { 00106 result(cell,pt) = std::pow(points(cell,pt,0),xd)*std::pow(points(cell,pt,1),yd) 00107 *std::pow(points(cell,pt,2),zd); 00108 } 00109 } 00110 return; 00111 } 00112 00113 int main(int argc, char *argv[]) { 00114 Teuchos::GlobalMPISession mpiSession(&argc, &argv); 00115 00116 // This little trick lets us print to std::cout only if 00117 // a (dummy) command-line argument is provided. 00118 int iprint = argc - 1; 00119 Teuchos::RCP<std::ostream> outStream; 00120 Teuchos::oblackholestream bhs; // outputs nothing 00121 if (iprint > 0) 00122 outStream = Teuchos::rcp(&std::cout, false); 00123 else 00124 outStream = Teuchos::rcp(&bhs, false); 00125 00126 // Save the format state of the original std::cout. 00127 Teuchos::oblackholestream oldFormatState; 00128 oldFormatState.copyfmt(std::cout); 00129 00130 *outStream \ 00131 << "===============================================================================\n" \ 00132 << "| |\n" \ 00133 << "| Unit Test (Basis_HGRAD_TET_In_FEM) |\n" \ 00134 << "| |\n" \ 00135 << "| 1) Patch test involving H(div) matrices |\n" \ 00136 << "| for the Dirichlet problem on a tetrahedral patch |\n" \ 00137 << "| Omega with boundary Gamma. |\n" \ 00138 << "| |\n" \ 00139 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00140 << "| Robert Kirby (robert.c.kirby@ttu.edu), |\n" \ 00141 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00142 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00143 << "| |\n" \ 00144 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00145 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00146 << "| |\n" \ 00147 << "===============================================================================\n" \ 00148 << "| TEST 1: Patch test |\n" \ 00149 << "===============================================================================\n"; 00150 00151 00152 int errorFlag = 0; 00153 00154 outStream -> precision(16); 00155 00156 try { 00157 DefaultCubatureFactory<double> cubFactory; // create cubature factory 00158 shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology 00159 shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology 00160 00161 int cellDim = cell.getDimension(); 00162 int sideDim = side.getDimension(); 00163 00164 int min_order = 0; 00165 int max_order = 5; 00166 00167 int numIntervals = max_order; 00168 int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals+3))/6; 00169 FieldContainer<double> interp_points_ref(numInterpPoints, cellDim); 00170 int counter = 0; 00171 for (int j=0; j<=numIntervals; j++) { 00172 for (int i=0; i<=numIntervals-j; i++) { 00173 for (int k=0;k<numIntervals-j-i;k++) { 00174 interp_points_ref(counter,0) = i*(1.0/numIntervals); 00175 interp_points_ref(counter,1) = j*(1.0/numIntervals); 00176 interp_points_ref(counter,2) = k*(1.0/numIntervals); 00177 counter++; 00178 } 00179 } 00180 } 00181 00182 //interp_points_ref.resize(numInterpPoints,cellDim); 00183 00184 for (int basis_order=min_order;basis_order<=max_order;basis_order++) { 00185 // create bases 00186 Teuchos::RCP<Basis<double,FieldContainer<double> > > vectorBasis = 00187 Teuchos::rcp(new Basis_HDIV_TET_In_FEM<double,FieldContainer<double> >(basis_order+1,POINTTYPE_EQUISPACED) ); 00188 Teuchos::RCP<Basis<double,FieldContainer<double> > > scalarBasis = 00189 Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM_ORTH<double,FieldContainer<double> >(basis_order) ); 00190 00191 int numVectorFields = vectorBasis->getCardinality(); 00192 int numScalarFields = scalarBasis->getCardinality(); 00193 int numTotalFields = numVectorFields + numScalarFields; 00194 00195 // create cubatures 00196 Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1)); 00197 Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*(basis_order+1)); 00198 00199 int numCubPointsCell = cellCub->getNumPoints(); 00200 int numCubPointsSide = sideCub->getNumPoints(); 00201 00202 // hold cubature information 00203 FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim); 00204 FieldContainer<double> cub_weights_cell(numCubPointsCell); 00205 FieldContainer<double> cub_points_side( numCubPointsSide, sideDim ); 00206 FieldContainer<double> cub_weights_side( numCubPointsSide ); 00207 FieldContainer<double> cub_points_side_refcell( numCubPointsSide , cellDim ); 00208 00209 // hold basis function information on refcell 00210 FieldContainer<double> value_of_v_basis_at_cub_points_cell(numVectorFields, numCubPointsCell, cellDim ); 00211 FieldContainer<double> w_value_of_v_basis_at_cub_points_cell(1, numVectorFields, numCubPointsCell, cellDim); 00212 FieldContainer<double> div_of_v_basis_at_cub_points_cell( numVectorFields, numCubPointsCell ); 00213 FieldContainer<double> w_div_of_v_basis_at_cub_points_cell( 1, numVectorFields , numCubPointsCell ); 00214 FieldContainer<double> value_of_s_basis_at_cub_points_cell(numScalarFields,numCubPointsCell); 00215 FieldContainer<double> w_value_of_s_basis_at_cub_points_cell(1,numScalarFields,numCubPointsCell); 00216 00217 // containers for side integration: 00218 // I just need the normal component of the vector basis 00219 // and the exact solution at the cub points 00220 FieldContainer<double> value_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide,cellDim); 00221 FieldContainer<double> n_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide); 00222 FieldContainer<double> w_n_of_v_basis_at_cub_points_side(1,numVectorFields,numCubPointsSide); 00223 FieldContainer<double> diri_data_at_cub_points_side(1,numCubPointsSide); 00224 FieldContainer<double> side_normal(cellDim); 00225 00226 // holds rhs data 00227 FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell); 00228 00229 // FEM matrices and vectors 00230 FieldContainer<double> fe_matrix_M(1,numVectorFields,numVectorFields); 00231 FieldContainer<double> fe_matrix_B(1,numVectorFields,numScalarFields); 00232 FieldContainer<double> fe_matrix(1,numTotalFields,numTotalFields); 00233 00234 FieldContainer<double> rhs_vector_vec(1,numVectorFields); 00235 FieldContainer<double> rhs_vector_scal(1,numScalarFields); 00236 FieldContainer<double> rhs_and_soln_vec(1,numTotalFields); 00237 00238 FieldContainer<int> ipiv(numTotalFields); 00239 FieldContainer<double> value_of_s_basis_at_interp_points( numScalarFields , numInterpPoints); 00240 FieldContainer<double> interpolant( 1 , numInterpPoints ); 00241 00242 // set test tolerance 00243 double zero = (basis_order+1)*(basis_order+1)*100*INTREPID_TOL; 00244 00245 // build matrices outside the loop, and then just do the rhs 00246 // for each iteration 00247 00248 cellCub->getCubature(cub_points_cell, cub_weights_cell); 00249 sideCub->getCubature(cub_points_side, cub_weights_side); 00250 00251 // need the vector basis & its divergences 00252 vectorBasis->getValues(value_of_v_basis_at_cub_points_cell, 00253 cub_points_cell, 00254 OPERATOR_VALUE); 00255 vectorBasis->getValues(div_of_v_basis_at_cub_points_cell, 00256 cub_points_cell, 00257 OPERATOR_DIV); 00258 00259 // need the scalar basis as well 00260 scalarBasis->getValues(value_of_s_basis_at_cub_points_cell, 00261 cub_points_cell, 00262 OPERATOR_VALUE); 00263 00264 // construct mass matrix 00265 cub_weights_cell.resize(1,numCubPointsCell); 00266 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_v_basis_at_cub_points_cell , 00267 cub_weights_cell , 00268 value_of_v_basis_at_cub_points_cell ); 00269 cub_weights_cell.resize(numCubPointsCell); 00270 00271 00272 value_of_v_basis_at_cub_points_cell.resize( 1 , numVectorFields , numCubPointsCell , cellDim ); 00273 FunctionSpaceTools::integrate<double>(fe_matrix_M, 00274 w_value_of_v_basis_at_cub_points_cell , 00275 value_of_v_basis_at_cub_points_cell , 00276 COMP_BLAS ); 00277 value_of_v_basis_at_cub_points_cell.resize( numVectorFields , numCubPointsCell , cellDim ); 00278 00279 // div matrix 00280 cub_weights_cell.resize(1,numCubPointsCell); 00281 FunctionSpaceTools::multiplyMeasure<double>(w_div_of_v_basis_at_cub_points_cell, 00282 cub_weights_cell, 00283 div_of_v_basis_at_cub_points_cell); 00284 cub_weights_cell.resize(numCubPointsCell); 00285 00286 value_of_s_basis_at_cub_points_cell.resize(1,numScalarFields,numCubPointsCell); 00287 FunctionSpaceTools::integrate<double>(fe_matrix_B, 00288 w_div_of_v_basis_at_cub_points_cell , 00289 value_of_s_basis_at_cub_points_cell , 00290 COMP_BLAS ); 00291 value_of_s_basis_at_cub_points_cell.resize(numScalarFields,numCubPointsCell); 00292 00293 00294 // construct div matrix 00295 00296 for (int x_order=0;x_order<=basis_order;x_order++) { 00297 for (int y_order=0;y_order<=basis_order-x_order;y_order++) { 00298 for (int z_order=0;z_order<=basis_order-x_order-y_order;z_order++) { 00299 00300 00301 // reset global matrix since I destroyed it in LU factorization. 00302 fe_matrix.initialize(); 00303 // insert mass matrix into global matrix 00304 for (int i=0;i<numVectorFields;i++) { 00305 for (int j=0;j<numVectorFields;j++) { 00306 fe_matrix(0,i,j) = fe_matrix_M(0,i,j); 00307 } 00308 } 00309 00310 // insert div matrix into global matrix 00311 for (int i=0;i<numVectorFields;i++) { 00312 for (int j=0;j<numScalarFields;j++) { 00313 fe_matrix(0,i,numVectorFields+j)=-fe_matrix_B(0,i,j); 00314 fe_matrix(0,j+numVectorFields,i)=fe_matrix_B(0,i,j); 00315 } 00316 } 00317 00318 // clear old vector data 00319 rhs_vector_vec.initialize(); 00320 rhs_vector_scal.initialize(); 00321 rhs_and_soln_vec.initialize(); 00322 00323 // now get rhs vector 00324 // rhs_vector_scal is just (rhs,w) for w in the scalar basis 00325 // I already have the scalar basis tabulated. 00326 cub_points_cell.resize(1,numCubPointsCell,cellDim); 00327 rhsFunc(rhs_at_cub_points_cell, 00328 cub_points_cell, 00329 x_order, 00330 y_order, 00331 z_order); 00332 00333 cub_points_cell.resize(numCubPointsCell,cellDim); 00334 00335 cub_weights_cell.resize(1,numCubPointsCell); 00336 FunctionSpaceTools::multiplyMeasure<double>(w_value_of_s_basis_at_cub_points_cell, 00337 cub_weights_cell, 00338 value_of_s_basis_at_cub_points_cell); 00339 cub_weights_cell.resize(numCubPointsCell); 00340 FunctionSpaceTools::integrate<double>(rhs_vector_scal, 00341 rhs_at_cub_points_cell, 00342 w_value_of_s_basis_at_cub_points_cell, 00343 COMP_BLAS); 00344 00345 for (int i=0;i<numScalarFields;i++) { 00346 rhs_and_soln_vec(0,numVectorFields+i) = rhs_vector_scal(0,i); 00347 } 00348 00349 00350 // now get <u,v.n> on boundary 00351 for (unsigned side_cur=0;side_cur<4;side_cur++) { 00352 // map side cubature to current side 00353 CellTools<double>::mapToReferenceSubcell( cub_points_side_refcell , 00354 cub_points_side , 00355 sideDim , 00356 (int)side_cur , 00357 cell ); 00358 00359 // Evaluate dirichlet data 00360 cub_points_side_refcell.resize(1,numCubPointsSide,cellDim); 00361 u_exact(diri_data_at_cub_points_side, 00362 cub_points_side_refcell,x_order,y_order,z_order); 00363 cub_points_side_refcell.resize(numCubPointsSide,cellDim); 00364 00365 // get normal direction, this has the edge weight factored into it already 00366 CellTools<double>::getReferenceSideNormal(side_normal , 00367 (int)side_cur,cell ); 00368 00369 // v.n at cub points on side 00370 vectorBasis->getValues(value_of_v_basis_at_cub_points_side , 00371 cub_points_side_refcell , 00372 OPERATOR_VALUE ); 00373 00374 00375 for (int i=0;i<numVectorFields;i++) { 00376 for (int j=0;j<numCubPointsSide;j++) { 00377 n_of_v_basis_at_cub_points_side(i,j) = 0.0; 00378 for (int k=0;k<cellDim;k++) { 00379 n_of_v_basis_at_cub_points_side(i,j) += side_normal(k) * 00380 value_of_v_basis_at_cub_points_side(i,j,k); 00381 } 00382 } 00383 } 00384 00385 cub_weights_side.resize(1,numCubPointsSide); 00386 FunctionSpaceTools::multiplyMeasure<double>(w_n_of_v_basis_at_cub_points_side, 00387 cub_weights_side, 00388 n_of_v_basis_at_cub_points_side); 00389 cub_weights_side.resize(numCubPointsSide); 00390 00391 FunctionSpaceTools::integrate<double>(rhs_vector_vec, 00392 diri_data_at_cub_points_side, 00393 w_n_of_v_basis_at_cub_points_side, 00394 COMP_BLAS, 00395 false); 00396 for (int i=0;i<numVectorFields;i++) { 00397 rhs_and_soln_vec(0,i) -= rhs_vector_vec(0,i); 00398 } 00399 00400 } 00401 00402 // solve linear system 00403 int info = 0; 00404 Teuchos::LAPACK<int, double> solver; 00405 solver.GESV(numTotalFields, 1, &fe_matrix[0], numTotalFields, &ipiv(0), &rhs_and_soln_vec[0], 00406 numTotalFields, &info); 00407 00408 // compute interpolant; the scalar entries are last 00409 scalarBasis->getValues(value_of_s_basis_at_interp_points, 00410 interp_points_ref, 00411 OPERATOR_VALUE); 00412 for (int pt=0;pt<numInterpPoints;pt++) { 00413 interpolant(0,pt)=0.0; 00414 for (int i=0;i<numScalarFields;i++) { 00415 interpolant(0,pt) += rhs_and_soln_vec(0,numVectorFields+i) 00416 * value_of_s_basis_at_interp_points(i,pt); 00417 } 00418 } 00419 00420 interp_points_ref.resize(1,numInterpPoints,cellDim); 00421 // get exact solution for comparison 00422 FieldContainer<double> exact_solution(1,numInterpPoints); 00423 u_exact( exact_solution , interp_points_ref , x_order, y_order, z_order); 00424 interp_points_ref.resize(numInterpPoints,cellDim); 00425 00426 RealSpaceTools<double>::add(interpolant,exact_solution); 00427 00428 double nrm= RealSpaceTools<double>::vectorNorm(&interpolant[0],interpolant.dimension(1), NORM_TWO); 00429 00430 *outStream << "\nNorm-2 error between scalar components of exact solution of order (" 00431 << x_order << ", " << y_order << ", " << z_order 00432 << ") and finite element interpolant of order " << basis_order << ": " 00433 << nrm << "\n"; 00434 00435 if (nrm > zero) { 00436 *outStream << "\n\nPatch test failed for solution polynomial order (" 00437 << x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) (" 00438 << basis_order << ", " << basis_order+1 << ")\n\n"; 00439 errorFlag++; 00440 } 00441 00442 } 00443 } 00444 } 00445 } 00446 00447 } 00448 00449 catch (std::logic_error err) { 00450 *outStream << err.what() << "\n\n"; 00451 errorFlag = -1000; 00452 }; 00453 00454 if (errorFlag != 0) 00455 std::cout << "End Result: TEST FAILED\n"; 00456 else 00457 std::cout << "End Result: TEST PASSED\n"; 00458 00459 // reset format state of std::cout 00460 std::cout.copyfmt(oldFormatState); 00461 00462 return errorFlag; 00463 }
1.7.6.1