Intrepid
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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
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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 
00082 // Intrepid includes
00083 #include "Intrepid_FunctionSpaceTools.hpp"
00084 #include "Intrepid_FieldContainer.hpp"
00085 #include "Intrepid_CellTools.hpp"
00086 //#include "Intrepid_ArrayTools.hpp"
00087 #include "Intrepid_HGRAD_HEX_Cn_FEM.hpp"
00088 //#include "Intrepid_RealSpaceTools.hpp"
00089 #include "Intrepid_DefaultCubatureFactory.hpp"
00090 #include "Intrepid_Utils.hpp"
00091 
00092 // Epetra includes
00093 #include "Epetra_Time.h"
00094 #include "Epetra_Map.h"
00095 #include "Epetra_FEVector.h"
00096 #include "Epetra_SerialComm.h"
00097 
00098 // Teuchos includes
00099 #include "Teuchos_oblackholestream.hpp"
00100 #include "Teuchos_RCP.hpp"
00101 //#include "Teuchos_BLAS.hpp"
00102 //#include "Teuchos_BLAS_types.hpp"
00103 
00104 // Shards includes
00105 #include "Shards_CellTopology.hpp"
00106 
00107 // EpetraExt includes
00108 #include "EpetraExt_MultiVectorOut.h"
00109 
00110 using namespace std;
00111 using namespace Intrepid;
00112 
00113 int main(int argc, char *argv[]) {
00114 
00115   //Check number of arguments
00116   if (argc < 4) {
00117     std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
00118     std::cout <<"Usage:\n\n";
00119     std::cout <<"  ./Intrepid_example_Drivers_Example_10.exe deg NX NY NZ verbose\n\n";
00120     std::cout <<" where \n";
00121     std::cout <<"   int deg             - polynomial degree to be used (assumed >= 1) \n";
00122     std::cout <<"   int NX              - num intervals in x direction (assumed box domain, 0,1) \n";
00123     std::cout <<"   int NY              - num intervals in y direction (assumed box domain, 0,1) \n";
00124     std::cout <<"   int NZ              - num intervals in y direction (assumed box domain, 0,1) \n";
00125     std::cout <<"   verbose (optional)  - any character, indicates verbose output \n\n";
00126     exit(1);
00127   }
00128   
00129   // This little trick lets us print to std::cout only if
00130   // a (dummy) command-line argument is provided.
00131   int iprint     = argc - 1;
00132   Teuchos::RCP<std::ostream> outStream;
00133   Teuchos::oblackholestream bhs; // outputs nothing
00134   if (iprint > 2)
00135     outStream = Teuchos::rcp(&std::cout, false);
00136   else
00137     outStream = Teuchos::rcp(&bhs, false);
00138   
00139   // Save the format state of the original std::cout.
00140   Teuchos::oblackholestream oldFormatState;
00141   oldFormatState.copyfmt(std::cout);
00142   
00143   *outStream                                                            \
00144     << "===============================================================================\n" \
00145     << "|                                                                             |\n" \
00146     << "|  Example: Build Stiffness Matrix for                                        |\n" \
00147     << "|                   Poisson Equation on Hexahedral Mesh                       |\n" \
00148     << "|                                                                             |\n" \
00149     << "|  Questions? Contact  Pavel Bochev  (pbboche@sandia.gov),                    |\n" \
00150     << "|                      Denis Ridzal  (dridzal@sandia.gov),                    |\n" \
00151     << "|                      Kara Peterson (kjpeter@sandia.gov).                    |\n" \
00152     << "|                                                                             |\n" \
00153     << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
00154     << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
00155     << "|                                                                             |\n" \
00156     << "===============================================================================\n";
00157 
00158   
00159   // ************************************ GET INPUTS **************************************
00160   
00161   int deg          = atoi(argv[1]);  // polynomial degree to use
00162   int NX           = atoi(argv[2]);  // num intervals in x direction (assumed box domain, 0,1)
00163   int NY           = atoi(argv[3]);  // num intervals in y direction (assumed box domain, 0,1)
00164   int NZ           = atoi(argv[4]);  // num intervals in y direction (assumed box domain, 0,1)
00165   
00166 
00167   // *********************************** CELL TOPOLOGY **********************************
00168   
00169   // Get cell topology for base hexahedron
00170   typedef shards::CellTopology    CellTopology;
00171   CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() );
00172   
00173   // Get dimensions 
00174   int numNodesPerElem = hex_8.getNodeCount();
00175   int spaceDim = hex_8.getDimension();
00176   
00177   // *********************************** GENERATE MESH ************************************
00178   
00179   *outStream << "Generating mesh ... \n\n";
00180   
00181   *outStream << "   NX" << "   NY" << "   NZ\n";
00182   *outStream << std::setw(5) << NX <<
00183     std::setw(5) << NY << std::setw(5) << NZ << "\n\n";
00184   
00185   // Print mesh information
00186   int numElems = NX*NY*NZ;
00187   int numNodes = (NX+1)*(NY+1)*(NZ+1);
00188   *outStream << " Number of Elements: " << numElems << " \n";
00189   *outStream << "    Number of Nodes: " << numNodes << " \n\n";
00190   
00191   // Cube
00192   double leftX = 0.0, rightX = 1.0;
00193   double leftY = 0.0, rightY = 1.0;
00194   double leftZ = 0.0, rightZ = 1.0;
00195 
00196   // Mesh spacing
00197   double hx = (rightX-leftX)/((double)NX);
00198   double hy = (rightY-leftY)/((double)NY);
00199   double hz = (rightZ-leftZ)/((double)NZ);
00200 
00201   // Get nodal coordinates
00202   FieldContainer<double> nodeCoord(numNodes, spaceDim);
00203   FieldContainer<int> nodeOnBoundary(numNodes);
00204   int inode = 0;
00205   for (int k=0; k<NZ+1; k++) 
00206     {
00207       for (int j=0; j<NY+1; j++) 
00208         {
00209           for (int i=0; i<NX+1; i++) 
00210             {
00211               nodeCoord(inode,0) = leftX + (double)i*hx;
00212               nodeCoord(inode,1) = leftY + (double)j*hy;
00213               nodeCoord(inode,2) = leftZ + (double)k*hz;
00214               if (k==0 || k==NZ || j==0 || i==0 || j==NY || i==NX)
00215                 {
00216                   nodeOnBoundary(inode)=1;
00217                 }
00218               else 
00219                 {
00220                   nodeOnBoundary(inode)=0;
00221                 }
00222               inode++;
00223             }
00224         }
00225     }
00226 #define DUMP_DATA
00227 #ifdef DUMP_DATA
00228   // Print nodal coords
00229   ofstream fcoordout("coords.dat");
00230   for (int i=0; i<numNodes; i++) {
00231     fcoordout << nodeCoord(i,0) <<" ";
00232     fcoordout << nodeCoord(i,1) <<" ";
00233     fcoordout << nodeCoord(i,2) <<"\n";
00234   }
00235   fcoordout.close();
00236 #endif
00237   
00238   
00239   // Element to Node map
00240   // We'll keep it around, but this is only the DOFMap if you are in the lowest order case.
00241   FieldContainer<int> elemToNode(numElems, numNodesPerElem);
00242   int ielem = 0;
00243   for (int k=0; k<NZ; k++) 
00244     {
00245       for (int j=0; j<NY; j++) 
00246         {
00247           for (int i=0; i<NX; i++) 
00248             {
00249               elemToNode(ielem,0) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
00250               elemToNode(ielem,1) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
00251               elemToNode(ielem,2) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
00252               elemToNode(ielem,3) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
00253               elemToNode(ielem,4) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
00254               elemToNode(ielem,5) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
00255               elemToNode(ielem,6) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
00256               elemToNode(ielem,7) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
00257               ielem++;
00258             }
00259         }
00260     }
00261 #ifdef DUMP_DATA
00262   // Output connectivity
00263   ofstream fe2nout("elem2node.dat");
00264   for (int k=0;k<NZ;k++)
00265     {
00266       for (int j=0; j<NY; j++) 
00267         {
00268           for (int i=0; i<NX; i++) 
00269             {
00270               int ielem = i + j * NX + k * NY * NY;
00271               for (int m=0; m<numNodesPerElem; m++)
00272                 {
00273                   fe2nout << elemToNode(ielem,m) <<"  ";
00274                 }
00275               fe2nout <<"\n";
00276             }
00277         }
00278     }
00279   fe2nout.close();
00280 #endif
00281   
00282   // ************************************ CUBATURE ************************************** 
00283   *outStream << "Getting cubature ... \n\n";
00284   
00285   // Get numerical integration points and weights
00286   DefaultCubatureFactory<double>  cubFactory;                                   
00287   int cubDegree = 2*deg;
00288   Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(hex_8, cubDegree); 
00289   
00290   int cubDim       = quadCub->getDimension();
00291   int numCubPoints = quadCub->getNumPoints();
00292   
00293   FieldContainer<double> cubPoints(numCubPoints, cubDim);
00294   FieldContainer<double> cubWeights(numCubPoints);
00295   
00296   quadCub->getCubature(cubPoints, cubWeights);
00297 
00298   // ************************************** BASIS ***************************************
00299   
00300   *outStream << "Getting basis ... \n\n";
00301   
00302   // Define basis 
00303   Basis_HGRAD_HEX_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL);
00304   int numFieldsG = quadHGradBasis.getCardinality();
00305   FieldContainer<double> quadGVals(numFieldsG, numCubPoints); 
00306   FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim); 
00307   
00308   // Evaluate basis values and gradients at cubature points
00309   quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE);
00310   quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD);
00311 
00312   // create the local-global mapping
00313   FieldContainer<int> ltgMapping(numElems,numFieldsG);
00314   const int numDOF = (NX*deg+1)*(NY*deg+1)*(NZ*deg+1);
00315   ielem=0;
00316   for (int k=0;k<NZ;k++) 
00317     {
00318       for (int j=0;j<NY;j++) 
00319         {
00320           for (int i=0;i<NX;i++) 
00321             {
00322               const int start = k * ( NY * deg + 1 ) * ( NX * deg + 1 ) + j * ( NX * deg + 1 ) + i * deg;
00323               // loop over local dof on this cell
00324               int local_dof_cur=0;
00325               for (int kloc=0;kloc<=deg;kloc++) 
00326                 {
00327                   for (int jloc=0;jloc<=deg;jloc++) 
00328                     {
00329                       for (int iloc=0;iloc<=deg;iloc++)
00330                         {
00331                           ltgMapping(ielem,local_dof_cur) = start 
00332                             + kloc * ( NX * deg + 1 ) * ( NY * deg + 1 )
00333                             + jloc * ( NX * deg + 1 )
00334                             + iloc;
00335                           local_dof_cur++;
00336                         }
00337                     }
00338                 }
00339               ielem++;
00340             }
00341         }
00342     }
00343 #ifdef DUMP_DATA
00344   // Output ltg mapping 
00345   ielem = 0;
00346   ofstream ltgout("ltg.dat");
00347   for (int k=0;k<NZ;k++)  
00348     {
00349       for (int j=0; j<NY; j++) 
00350         {
00351           for (int i=0; i<NX; i++) 
00352             {
00353               int ielem = i + j * NX + k * NX * NY;
00354               for (int m=0; m<numFieldsG; m++)
00355                 {
00356                   ltgout << ltgMapping(ielem,m) <<"  ";
00357                 }
00358               ltgout <<"\n";
00359             }
00360         }
00361     }
00362   ltgout.close();
00363 #endif
00364 
00365   // ********** DECLARE GLOBAL OBJECTS *************
00366   Epetra_SerialComm Comm;
00367   Epetra_Map globalMapG(numDOF, 0, Comm);
00368   Epetra_FEVector u(globalMapG);  u.Random();
00369   Epetra_FEVector Ku(globalMapG);
00370 
00371 
00372 
00373   // ********** CONSTRUCT AND INSERT LOCAL STIFFNESS MATRICES ***********
00374   *outStream << "Building reference stiffness matrix...\n\n";
00375   typedef CellTools<double>  CellTools;
00376   typedef FunctionSpaceTools fst;
00377 
00378   // jacobian information
00379   FieldContainer<double> refCellNodes(1,numNodesPerElem,spaceDim);
00380   FieldContainer<double> cellJacobian(1,numCubPoints,spaceDim,spaceDim);
00381   FieldContainer<double> cellJacobInv(1,numCubPoints,spaceDim,spaceDim);
00382   FieldContainer<double> cellJacobDet(1,numCubPoints);
00383 
00384   // element stiffness matrices and supporting storage space
00385   FieldContainer<double> localStiffMatrix(1, numFieldsG, numFieldsG);
00386   FieldContainer<double> transformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim);
00387   FieldContainer<double> weightedTransformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim);
00388   FieldContainer<double> weightedMeasure(1, numCubPoints);
00389 
00390   Epetra_Time localConstructTimer( Comm );
00391   refCellNodes(0,0,0) = 0.0;  refCellNodes(0,0,1) = 0.0;  refCellNodes(0,0,2) = 0.0;
00392   refCellNodes(0,1,0) = hx;   refCellNodes(0,1,1) = 0.0;  refCellNodes(0,1,2) = 0.0;
00393   refCellNodes(0,2,0) = hx;   refCellNodes(0,2,1) = hy;   refCellNodes(0,2,2) = 0.0;
00394   refCellNodes(0,3,0) = 0.0;  refCellNodes(0,3,1) = hy;   refCellNodes(0,3,2) = 0.0;
00395   refCellNodes(0,4,0) = 0.0;  refCellNodes(0,4,1) = 0.0;  refCellNodes(0,4,2) = hz;
00396   refCellNodes(0,5,0) = hx;   refCellNodes(0,5,1) = 0.0;  refCellNodes(0,5,2) = hz;
00397   refCellNodes(0,6,0) = hx;   refCellNodes(0,6,1) = hy;   refCellNodes(0,6,2) = hz;
00398   refCellNodes(0,7,0) = 0.0;  refCellNodes(0,7,1) = hy;   refCellNodes(0,7,2) = hz;
00399 
00400      // jacobian evaluation 
00401   CellTools::setJacobian(cellJacobian,cubPoints,refCellNodes,hex_8);
00402   CellTools::setJacobianInv(cellJacobInv, cellJacobian );
00403   CellTools::setJacobianDet(cellJacobDet, cellJacobian );
00404 
00405   // transform reference element gradients to each cell
00406   fst::HGRADtransformGRAD<double>(transformedBasisGradients, cellJacobInv, quadGrads);
00407       
00408   // compute weighted measure
00409   fst::computeCellMeasure<double>(weightedMeasure, cellJacobDet, cubWeights);
00410 
00411   // multiply values with weighted measure
00412   fst::multiplyMeasure<double>(weightedTransformedBasisGradients,
00413                                weightedMeasure, transformedBasisGradients);
00414 
00415   // integrate to compute element stiffness matrix
00416   fst::integrate<double>(localStiffMatrix,
00417                          transformedBasisGradients, weightedTransformedBasisGradients , COMP_BLAS);
00418 
00419   const double localConstructTime = localConstructTimer.ElapsedTime();
00420 
00421   // ************* MATRIX-FREE APPLICATION 
00422   FieldContainer<double> uScattered(numElems,numFieldsG);
00423   FieldContainer<double> KuScattered(numElems,numFieldsG);
00424 
00425   u.GlobalAssemble();
00426 
00427   Epetra_Time multTimer(Comm);
00428   Teuchos::BLAS<int,double> blas;
00429   Ku.PutScalar(0.0);
00430   Ku.GlobalAssemble();
00431 
00432   double *uVals = u[0];
00433   double *KuVals = Ku[0];
00434 
00435   Epetra_Time scatterTimer(Comm);
00436   std::cout << "Scattering\n";
00437   // Scatter
00438   for (int k=0; k<numElems; k++) 
00439     {
00440       for (int i=0;i<numFieldsG;i++) 
00441         {
00442           uScattered(k,i) = uVals[ltgMapping(k,i)];
00443         }
00444     }
00445   const double scatterTime = scatterTimer.ElapsedTime();
00446 
00447   Epetra_Time blasTimer(Comm);
00448   blas.GEMM(Teuchos::NO_TRANS , Teuchos::NO_TRANS , 
00449             numFieldsG , numElems, numFieldsG  , 
00450             1.0 , 
00451             &localStiffMatrix(0,0,0) , 
00452             numFieldsG ,
00453             &uScattered(0,0) , 
00454             numFieldsG , 
00455             0.0 , 
00456             &KuScattered(0,0) , 
00457             numFieldsG );
00458   const double blasTime = blasTimer.ElapsedTime();
00459 
00460   Epetra_Time gatherTimer(Comm);
00461   // Gather
00462   for (int k=0;k<numElems;k++)
00463     {
00464       for (int i=0;i<numFieldsG;i++)
00465         {
00466           KuVals[ltgMapping(k,i)] += KuScattered(k,i);
00467         }
00468     }
00469   
00470   const double gatherTime = gatherTimer.ElapsedTime();
00471   
00472 
00473   *outStream << "Time to build local matrix (including Jacobian computation): "<< localConstructTime << "\n";
00474   *outStream << "Time to scatter " << scatterTime << "\n";
00475   *outStream << "Time for local application " << blasTime << "\n";
00476   *outStream << "Time to gather " << gatherTime << "\n";
00477   *outStream << "Total matrix-free time " << scatterTime + blasTime + gatherTime << "\n";
00478  
00479 
00480   *outStream << "End Result: TEST PASSED\n";
00481   
00482   // reset format state of std::cout
00483   std::cout.copyfmt(oldFormatState);
00484   
00485   return 0;
00486 }
00487