Intrepid
http://trilinos.sandia.gov/packages/docs/r10.10/packages/intrepid/test/Discretization/Basis/HGRAD_TET_Cn_FEM_ORTH/test_02.cpp
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00004 //                           Intrepid Package
00005 //                 Copyright (2007) Sandia Corporation
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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
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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_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_ORTH)                     |\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 = 7;                                                                  // 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     for (int x_order=0; x_order <= max_order; x_order++) {
00312       for (int y_order=0; y_order <= max_order-x_order; y_order++) {
00313         for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
00314 
00315           // evaluate exact solution
00316           FieldContainer<double> exact_solution(1, numInterpPoints);
00317           u_exact(exact_solution, interp_points, x_order, y_order, z_order);
00318 
00319           int total_order = std::max(x_order + y_order + z_order, 1);
00320 
00321           for (int basis_order=total_order; basis_order <= max_order; basis_order++) {
00322 
00323             // set test tolerance;
00324             double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
00325 
00326             //create basis
00327             Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
00328               Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM_ORTH<double,FieldContainer<double> >(basis_order) );
00329             int numFields = basis->getCardinality();
00330 
00331             // create cubatures
00332             Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
00333             Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order);
00334             int numCubPointsCell = cellCub->getNumPoints();
00335             int numCubPointsSide = sideCub->getNumPoints();
00336 
00337             /* Computational arrays. */
00338             /* Section 1: Related to parent cell integration. */
00339             FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
00340             FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
00341             FieldContainer<double> cub_weights_cell(numCubPointsCell);
00342             FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
00343             FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
00344             FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
00345             FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
00346 
00347             FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
00348             FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
00349             FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
00350             FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
00351             FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
00352             FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
00353             FieldContainer<double> fe_matrix(1, numFields, numFields);
00354 
00355             FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
00356             FieldContainer<double> rhs_and_soln_vector(1, numFields);
00357 
00358             /* Section 2: Related to subcell (side) integration. */
00359             unsigned numSides = 4;
00360             FieldContainer<double> cub_points_side(numCubPointsSide, sideDim);
00361             FieldContainer<double> cub_weights_side(numCubPointsSide);
00362             FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim);
00363             FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim);
00364             FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim);
00365             FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide);
00366             FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide);
00367 
00368             FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide);
00369             FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
00370             FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
00371             FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide);
00372             FieldContainer<double> neumann_fields_per_side(1, numFields);
00373 
00374             /* Section 3: Related to global interpolant. */
00375             FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
00376             FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
00377             FieldContainer<double> interpolant(1, numInterpPoints);
00378 
00379             FieldContainer<int> ipiv(numFields);
00380 
00381 
00382 
00383             /******************* START COMPUTATION ***********************/
00384 
00385             // get cubature points and weights
00386             cellCub->getCubature(cub_points_cell, cub_weights_cell);
00387 
00388             // compute geometric cell information
00389             CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
00390             CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
00391             CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
00392 
00393             // compute weighted measure
00394             FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
00395 
00397             // Computing mass matrices:
00398             // tabulate values of basis functions at (reference) cubature points
00399             basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
00400 
00401             // transform values of basis functions 
00402             FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
00403                                                             value_of_basis_at_cub_points_cell);
00404 
00405             // multiply with weighted measure
00406             FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
00407                                                         weighted_measure_cell,
00408                                                         transformed_value_of_basis_at_cub_points_cell);
00409 
00410             // compute mass matrices
00411             FunctionSpaceTools::integrate<double>(fe_matrix,
00412                                                   transformed_value_of_basis_at_cub_points_cell,
00413                                                   weighted_transformed_value_of_basis_at_cub_points_cell,
00414                                                   COMP_BLAS);
00416 
00418             // Computing stiffness matrices:
00419             // tabulate gradients of basis functions at (reference) cubature points
00420             basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
00421 
00422             // transform gradients of basis functions 
00423             FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
00424                                                            jacobian_inv_cell,
00425                                                            grad_of_basis_at_cub_points_cell);
00426 
00427             // multiply with weighted measure
00428             FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
00429                                                         weighted_measure_cell,
00430                                                         transformed_grad_of_basis_at_cub_points_cell);
00431 
00432             // compute stiffness matrices and sum into fe_matrix
00433             FunctionSpaceTools::integrate<double>(fe_matrix,
00434                                                   transformed_grad_of_basis_at_cub_points_cell,
00435                                                   weighted_transformed_grad_of_basis_at_cub_points_cell,
00436                                                   COMP_BLAS,
00437                                                   true);
00439 
00441             // Computing RHS contributions:
00442             // map cell (reference) cubature points to physical space
00443             CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
00444 
00445             // evaluate rhs function
00446             rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
00447 
00448             // compute rhs
00449             FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
00450                                                   rhs_at_cub_points_cell_physical,
00451                                                   weighted_transformed_value_of_basis_at_cub_points_cell,
00452                                                   COMP_BLAS);
00453 
00454             // compute neumann b.c. contributions and adjust rhs
00455             sideCub->getCubature(cub_points_side, cub_weights_side);
00456             for (unsigned i=0; i<numSides; i++) {
00457               // compute geometric cell information
00458               CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell);
00459               CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell);
00460               CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell);
00461 
00462               // compute weighted face measure
00463               FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell,
00464                                                              jacobian_side_refcell,
00465                                                              cub_weights_side,
00466                                                              i,
00467                                                              cell);
00468 
00469               // tabulate values of basis functions at side cubature points, in the reference parent cell domain
00470               basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE);
00471               // transform 
00472               FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell,
00473                                                               value_of_basis_at_cub_points_side_refcell);
00474 
00475               // multiply with weighted measure
00476               FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell,
00477                                                           weighted_measure_side_refcell,
00478                                                           transformed_value_of_basis_at_cub_points_side_refcell);
00479 
00480               // compute Neumann data
00481               // map side cubature points in reference parent cell domain to physical space
00482               CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell);
00483               // now compute data
00484               neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell,
00485                       cell, (int)i, x_order, y_order, z_order);
00486 
00487               FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
00488                                                     neumann_data_at_cub_points_side_physical,
00489                                                     weighted_transformed_value_of_basis_at_cub_points_side_refcell,
00490                                                     COMP_BLAS);
00491 
00492               // adjust RHS
00493               RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
00494             }
00496 
00498             // Solution of linear system:
00499             int info = 0;
00500             Teuchos::LAPACK<int, double> solver;
00501             solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
00503 
00505             // Building interpolant:
00506             // evaluate basis at interpolation points
00507             basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
00508             // transform values of basis functions 
00509             FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
00510                                                             value_of_basis_at_interp_points_ref);
00511             FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
00513 
00514             /******************* END COMPUTATION ***********************/
00515         
00516             RealSpaceTools<double>::subtract(interpolant, exact_solution);
00517 
00518             *outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
00519                        << x_order << ", " << y_order << ", " << z_order
00520                        << ") and finite element interpolant of order " << basis_order << ": "
00521                        << RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
00522                           RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
00523 
00524             if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
00525                 RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
00526               *outStream << "\n\nPatch test failed for solution polynomial order ("
00527                          << x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
00528               errorFlag++;
00529             }
00530           } // end for basis_order
00531         } // end for z_order
00532       } // end for y_order
00533     } // end for x_order
00534 
00535   }
00536   // Catch unexpected errors
00537   catch (std::logic_error err) {
00538     *outStream << err.what() << "\n\n";
00539     errorFlag = -1000;
00540   };
00541 
00542   if (errorFlag != 0)
00543     std::cout << "End Result: TEST FAILED\n";
00544   else
00545     std::cout << "End Result: TEST PASSED\n";
00546 
00547   // reset format state of std::cout
00548   std::cout.copyfmt(oldFormatState);
00549 
00550   return errorFlag;
00551 }