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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 // This library is free software; you can redistribute it and/or modify 00011 // it under the terms of the GNU Lesser General Public License as 00012 // published by the Free Software Foundation; either version 2.1 of the 00013 // License, or (at your option) any later version. 00014 // 00015 // This library is distributed in the hope that it will be useful, but 00016 // WITHOUT ANY WARRANTY; without even the implied warranty of 00017 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00018 // Lesser General Public License for more details. 00019 // 00020 // You should have received a copy of the GNU Lesser General Public 00021 // License along with this library; if not, write to the Free Software 00022 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 00023 // USA 00024 // Questions? Contact Pavel Bochev (pbboche@sandia.gov), 00025 // Denis Ridzal (dridzal@sandia.gov), 00026 // Kara Peterson (kjpeter@sandia.gov). 00027 // 00028 // ************************************************************************ 00029 // @HEADER 00030 00070 // Intrepid includes 00071 #include "Intrepid_FunctionSpaceTools.hpp" 00072 #include "Intrepid_FieldContainer.hpp" 00073 #include "Intrepid_CellTools.hpp" 00074 //#include "Intrepid_ArrayTools.hpp" 00075 #include "Intrepid_HGRAD_HEX_Cn_FEM.hpp" 00076 //#include "Intrepid_RealSpaceTools.hpp" 00077 #include "Intrepid_DefaultCubatureFactory.hpp" 00078 #include "Intrepid_Utils.hpp" 00079 00080 // Epetra includes 00081 #include "Epetra_Time.h" 00082 #include "Epetra_Map.h" 00083 #include "Epetra_FEVector.h" 00084 #include "Epetra_FECrsMatrix.h" 00085 #include "Epetra_SerialComm.h" 00086 00087 // Teuchos includes 00088 #include "Teuchos_oblackholestream.hpp" 00089 #include "Teuchos_RCP.hpp" 00090 //#include "Teuchos_BLAS.hpp" 00091 //#include "Teuchos_BLAS_types.hpp" 00092 00093 // Shards includes 00094 #include "Shards_CellTopology.hpp" 00095 00096 // EpetraExt includes 00097 #include "EpetraExt_MultiVectorOut.h" 00098 00099 using namespace std; 00100 using namespace Intrepid; 00101 00102 int main(int argc, char *argv[]) { 00103 00104 //Check number of arguments 00105 if (argc < 4) { 00106 std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n"; 00107 std::cout <<"Usage:\n\n"; 00108 std::cout <<" ./Intrepid_example_Drivers_Example_10.exe deg NX NY NZ verbose\n\n"; 00109 std::cout <<" where \n"; 00110 std::cout <<" int deg - polynomial degree to be used (assumed >= 1) \n"; 00111 std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n"; 00112 std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n"; 00113 std::cout <<" int NZ - num intervals in y direction (assumed box domain, 0,1) \n"; 00114 std::cout <<" verbose (optional) - any character, indicates verbose output \n\n"; 00115 exit(1); 00116 } 00117 00118 // This little trick lets us print to std::cout only if 00119 // a (dummy) command-line argument is provided. 00120 int iprint = argc - 1; 00121 Teuchos::RCP<std::ostream> outStream; 00122 Teuchos::oblackholestream bhs; // outputs nothing 00123 if (iprint > 2) 00124 outStream = Teuchos::rcp(&std::cout, false); 00125 else 00126 outStream = Teuchos::rcp(&bhs, false); 00127 00128 // Save the format state of the original std::cout. 00129 Teuchos::oblackholestream oldFormatState; 00130 oldFormatState.copyfmt(std::cout); 00131 00132 *outStream \ 00133 << "===============================================================================\n" \ 00134 << "| |\n" \ 00135 << "| Example: Build Stiffness Matrix for |\n" \ 00136 << "| Poisson Equation on Hexahedral Mesh |\n" \ 00137 << "| |\n" \ 00138 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00139 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00140 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00141 << "| |\n" \ 00142 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00143 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00144 << "| |\n" \ 00145 << "===============================================================================\n"; 00146 00147 00148 // ************************************ GET INPUTS ************************************** 00149 00150 int deg = atoi(argv[1]); // polynomial degree to use 00151 int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1) 00152 int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1) 00153 int NZ = atoi(argv[4]); // num intervals in y direction (assumed box domain, 0,1) 00154 00155 00156 // *********************************** CELL TOPOLOGY ********************************** 00157 00158 // Get cell topology for base hexahedron 00159 typedef shards::CellTopology CellTopology; 00160 CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() ); 00161 00162 // Get dimensions 00163 int numNodesPerElem = hex_8.getNodeCount(); 00164 int spaceDim = hex_8.getDimension(); 00165 00166 // *********************************** GENERATE MESH ************************************ 00167 00168 *outStream << "Generating mesh ... \n\n"; 00169 00170 *outStream << " NX" << " NY" << " NZ\n"; 00171 *outStream << std::setw(5) << NX << 00172 std::setw(5) << NY << std::setw(5) << NZ << "\n\n"; 00173 00174 // Print mesh information 00175 int numElems = NX*NY*NZ; 00176 int numNodes = (NX+1)*(NY+1)*(NZ+1); 00177 *outStream << " Number of Elements: " << numElems << " \n"; 00178 *outStream << " Number of Nodes: " << numNodes << " \n\n"; 00179 00180 // Cube 00181 double leftX = 0.0, rightX = 1.0; 00182 double leftY = 0.0, rightY = 1.0; 00183 double leftZ = 0.0, rightZ = 1.0; 00184 00185 // Mesh spacing 00186 double hx = (rightX-leftX)/((double)NX); 00187 double hy = (rightY-leftY)/((double)NY); 00188 double hz = (rightZ-leftZ)/((double)NZ); 00189 00190 // Get nodal coordinates 00191 FieldContainer<double> nodeCoord(numNodes, spaceDim); 00192 FieldContainer<int> nodeOnBoundary(numNodes); 00193 int inode = 0; 00194 for (int k=0; k<NZ+1; k++) 00195 { 00196 for (int j=0; j<NY+1; j++) 00197 { 00198 for (int i=0; i<NX+1; i++) 00199 { 00200 nodeCoord(inode,0) = leftX + (double)i*hx; 00201 nodeCoord(inode,1) = leftY + (double)j*hy; 00202 nodeCoord(inode,2) = leftZ + (double)k*hz; 00203 if (k==0 || k==NZ || j==0 || i==0 || j==NY || i==NX) 00204 { 00205 nodeOnBoundary(inode)=1; 00206 } 00207 else 00208 { 00209 nodeOnBoundary(inode)=0; 00210 } 00211 inode++; 00212 } 00213 } 00214 } 00215 #define DUMP_DATA 00216 #ifdef DUMP_DATA 00217 // Print nodal coords 00218 ofstream fcoordout("coords.dat"); 00219 for (int i=0; i<numNodes; i++) { 00220 fcoordout << nodeCoord(i,0) <<" "; 00221 fcoordout << nodeCoord(i,1) <<" "; 00222 fcoordout << nodeCoord(i,2) <<"\n"; 00223 } 00224 fcoordout.close(); 00225 #endif 00226 00227 00228 // Element to Node map 00229 // We'll keep it around, but this is only the DOFMap if you are in the lowest order case. 00230 FieldContainer<int> elemToNode(numElems, numNodesPerElem); 00231 int ielem = 0; 00232 for (int k=0; k<NZ; k++) 00233 { 00234 for (int j=0; j<NY; j++) 00235 { 00236 for (int i=0; i<NX; i++) 00237 { 00238 elemToNode(ielem,0) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i; 00239 elemToNode(ielem,1) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1; 00240 elemToNode(ielem,2) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1; 00241 elemToNode(ielem,3) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i; 00242 elemToNode(ielem,4) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i; 00243 elemToNode(ielem,5) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1; 00244 elemToNode(ielem,6) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1; 00245 elemToNode(ielem,7) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i; 00246 ielem++; 00247 } 00248 } 00249 } 00250 #ifdef DUMP_DATA 00251 // Output connectivity 00252 ofstream fe2nout("elem2node.dat"); 00253 for (int k=0;k<NZ;k++) 00254 { 00255 for (int j=0; j<NY; j++) 00256 { 00257 for (int i=0; i<NX; i++) 00258 { 00259 int ielem = i + j * NX + k * NY * NY; 00260 for (int m=0; m<numNodesPerElem; m++) 00261 { 00262 fe2nout << elemToNode(ielem,m) <<" "; 00263 } 00264 fe2nout <<"\n"; 00265 } 00266 } 00267 } 00268 fe2nout.close(); 00269 #endif 00270 00271 // ************************************ CUBATURE ************************************** 00272 *outStream << "Getting cubature ... \n\n"; 00273 00274 // Get numerical integration points and weights 00275 DefaultCubatureFactory<double> cubFactory; 00276 int cubDegree = 2*deg; 00277 Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(hex_8, cubDegree); 00278 00279 int cubDim = quadCub->getDimension(); 00280 int numCubPoints = quadCub->getNumPoints(); 00281 00282 FieldContainer<double> cubPoints(numCubPoints, cubDim); 00283 FieldContainer<double> cubWeights(numCubPoints); 00284 00285 quadCub->getCubature(cubPoints, cubWeights); 00286 00287 00288 // ************************************** BASIS *************************************** 00289 00290 *outStream << "Getting basis ... \n\n"; 00291 00292 // Define basis 00293 Basis_HGRAD_HEX_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL); 00294 int numFieldsG = quadHGradBasis.getCardinality(); 00295 FieldContainer<double> quadGVals(numFieldsG, numCubPoints); 00296 FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim); 00297 00298 // Evaluate basis values and gradients at cubature points 00299 quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE); 00300 quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD); 00301 00302 // create the local-global mapping 00303 FieldContainer<int> ltgMapping(numElems,numFieldsG); 00304 const int numDOF = (NX*deg+1)*(NY*deg+1)*(NZ*deg+1); 00305 ielem=0; 00306 for (int k=0;k<NZ;k++) 00307 { 00308 for (int j=0;j<NY;j++) 00309 { 00310 for (int i=0;i<NX;i++) 00311 { 00312 const int start = k * ( NY * deg + 1 ) * ( NX * deg + 1 ) + j * ( NX * deg + 1 ) + i * deg; 00313 // loop over local dof on this cell 00314 int local_dof_cur=0; 00315 for (int kloc=0;kloc<=deg;kloc++) 00316 { 00317 for (int jloc=0;jloc<=deg;jloc++) 00318 { 00319 for (int iloc=0;iloc<=deg;iloc++) 00320 { 00321 ltgMapping(ielem,local_dof_cur) = start 00322 + kloc * ( NX * deg + 1 ) * ( NY * deg + 1 ) 00323 + jloc * ( NX * deg + 1 ) 00324 + iloc; 00325 local_dof_cur++; 00326 } 00327 } 00328 } 00329 ielem++; 00330 } 00331 } 00332 } 00333 #ifdef DUMP_DATA 00334 // Output ltg mapping 00335 ielem = 0; 00336 ofstream ltgout("ltg.dat"); 00337 for (int k=0;k<NZ;k++) 00338 { 00339 for (int j=0; j<NY; j++) 00340 { 00341 for (int i=0; i<NX; i++) 00342 { 00343 int ielem = i + j * NX + k * NX * NY; 00344 for (int m=0; m<numFieldsG; m++) 00345 { 00346 ltgout << ltgMapping(ielem,m) <<" "; 00347 } 00348 ltgout <<"\n"; 00349 } 00350 } 00351 } 00352 ltgout.close(); 00353 #endif 00354 00355 // ********** DECLARE GLOBAL OBJECTS ************* 00356 Epetra_SerialComm Comm; 00357 Epetra_Map globalMapG(numDOF, 0, Comm); 00358 Epetra_FEVector u(globalMapG); u.Random(); 00359 Epetra_FEVector Ku(globalMapG); 00360 00361 // Let's preallocate the graph before we instantiate the matrix 00362 Epetra_Time graphTimer(Comm); 00363 Epetra_CrsGraph grph( Copy , globalMapG , 4 * numFieldsG ); 00364 for (int k=0;k<numElems;k++) 00365 { 00366 for (int i=0;i<numFieldsG;i++) 00367 { 00368 grph.InsertGlobalIndices(ltgMapping(k,i),numFieldsG,<gMapping(k,0)); 00369 } 00370 } 00371 grph.FillComplete(); 00372 const double graphTime = graphTimer.ElapsedTime(); 00373 00374 00375 // time the instantiation 00376 Epetra_Time instantiateTimer(Comm); 00377 Epetra_FECrsMatrix StiffMatrix(Copy,grph); 00378 const double instantiateTime = instantiateTimer.ElapsedTime(); 00379 00380 00381 // ********** CONSTRUCT AND INSERT LOCAL STIFFNESS MATRICES *********** 00382 *outStream << "Building local stiffness matrices...\n\n"; 00383 typedef CellTools<double> CellTools; 00384 typedef FunctionSpaceTools fst; 00385 int numCells = numElems; 00386 00387 00388 // jacobian information 00389 FieldContainer<double> refCellNodes(1,numNodesPerElem,spaceDim); 00390 FieldContainer<double> cellJacobian(1,numCubPoints,spaceDim,spaceDim); 00391 FieldContainer<double> cellJacobInv(1,numCubPoints,spaceDim,spaceDim); 00392 FieldContainer<double> cellJacobDet(1,numCubPoints); 00393 00394 // element stiffness matrices and supporting storage space 00395 FieldContainer<double> localStiffMatrix(1, numFieldsG, numFieldsG); 00396 FieldContainer<double> transformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim); 00397 FieldContainer<double> weightedTransformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim); 00398 FieldContainer<double> weightedMeasure(1, numCubPoints); 00399 00400 00401 Epetra_Time localConstructTimer( Comm ); 00402 refCellNodes(0,0,0) = 0.0; refCellNodes(0,0,1) = 0.0; refCellNodes(0,0,2) = 0.0; 00403 refCellNodes(0,1,0) = hx; refCellNodes(0,1,1) = 0.0; refCellNodes(0,1,2) = 0.0; 00404 refCellNodes(0,2,0) = hx; refCellNodes(0,2,1) = hy; refCellNodes(0,2,2) = 0.0; 00405 refCellNodes(0,3,0) = 0.0; refCellNodes(0,3,1) = hy; refCellNodes(0,3,2) = 0.0; 00406 refCellNodes(0,4,0) = 0.0; refCellNodes(0,4,1) = 0.0; refCellNodes(0,4,2) = hz; 00407 refCellNodes(0,5,0) = hx; refCellNodes(0,5,1) = 0.0; refCellNodes(0,5,2) = hz; 00408 refCellNodes(0,6,0) = hx; refCellNodes(0,6,1) = hy; refCellNodes(0,6,2) = hz; 00409 refCellNodes(0,7,0) = 0.0; refCellNodes(0,7,1) = hy; refCellNodes(0,7,2) = hz; 00410 00411 00412 // jacobian evaluation 00413 CellTools::setJacobian(cellJacobian,cubPoints,refCellNodes,hex_8); 00414 CellTools::setJacobianInv(cellJacobInv, cellJacobian ); 00415 CellTools::setJacobianDet(cellJacobDet, cellJacobian ); 00416 00417 // transform reference element gradients to each cell 00418 fst::HGRADtransformGRAD<double>(transformedBasisGradients, cellJacobInv, quadGrads); 00419 00420 // compute weighted measure 00421 fst::computeCellMeasure<double>(weightedMeasure, cellJacobDet, cubWeights); 00422 00423 // multiply values with weighted measure 00424 fst::multiplyMeasure<double>(weightedTransformedBasisGradients, 00425 weightedMeasure, transformedBasisGradients); 00426 00427 // integrate to compute element stiffness matrix 00428 fst::integrate<double>(localStiffMatrix, 00429 transformedBasisGradients, weightedTransformedBasisGradients , COMP_BLAS); 00430 00431 const double localConstructTime = localConstructTimer.ElapsedTime(); 00432 00433 00434 Epetra_Time insertionTimer(Comm); 00435 00436 // *** Element loop *** 00437 for (int k=0; k<numElems; k++) 00438 { 00439 // assemble into global matrix 00440 StiffMatrix.InsertGlobalValues(numFieldsG,<gMapping(k,0),numFieldsG,<gMapping(k,0),&localStiffMatrix(0,0,0)); 00441 00442 } 00443 StiffMatrix.GlobalAssemble(); StiffMatrix.FillComplete(); 00444 const double insertionTime = insertionTimer.ElapsedTime( ); 00445 00446 *outStream << "Time to construct matrix graph: " << graphTime << "\n"; 00447 *outStream << "Time to instantiate global stiffness matrix: " << instantiateTime << "\n"; 00448 *outStream << "Time to build local matrices (including Jacobian computation): "<< localConstructTime << "\n"; 00449 *outStream << "Time to assemble global matrix from local matrices: " << insertionTime << "\n"; 00450 *outStream << "Total construction time: " << graphTime + instantiateTime + localConstructTime + insertionTime << "\n"; 00451 00452 Epetra_Time applyTimer(Comm); 00453 StiffMatrix.Apply(u,Ku); 00454 const double multTime = applyTimer.ElapsedTime(); 00455 *outStream << "Time to multiply onto a vector: " << multTime << "\n"; 00456 00457 *outStream << "End Result: TEST PASSED\n"; 00458 00459 // reset format state of std::cout 00460 std::cout.copyfmt(oldFormatState); 00461 00462 return 0; 00463 } 00464
1.7.4