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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 00083 // Intrepid includes 00084 #include "Intrepid_FunctionSpaceTools.hpp" 00085 #include "Intrepid_FieldContainer.hpp" 00086 #include "Intrepid_CellTools.hpp" 00087 //#include "Intrepid_ArrayTools.hpp" 00088 #include "Intrepid_HGRAD_HEX_Cn_FEM.hpp" 00089 //#include "Intrepid_RealSpaceTools.hpp" 00090 #include "Intrepid_DefaultCubatureFactory.hpp" 00091 #include "Intrepid_Utils.hpp" 00092 00093 // Epetra includes 00094 #include "Epetra_Time.h" 00095 #include "Epetra_Map.h" 00096 #include "Epetra_FEVector.h" 00097 #include "Epetra_FECrsMatrix.h" 00098 #include "Epetra_SerialComm.h" 00099 00100 // Teuchos includes 00101 #include "Teuchos_oblackholestream.hpp" 00102 #include "Teuchos_RCP.hpp" 00103 //#include "Teuchos_BLAS.hpp" 00104 //#include "Teuchos_BLAS_types.hpp" 00105 00106 // Shards includes 00107 #include "Shards_CellTopology.hpp" 00108 00109 // EpetraExt includes 00110 #include "EpetraExt_MultiVectorOut.h" 00111 00112 using namespace std; 00113 using namespace Intrepid; 00114 00115 int main(int argc, char *argv[]) { 00116 00117 //Check number of arguments 00118 if (argc < 4) { 00119 std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n"; 00120 std::cout <<"Usage:\n\n"; 00121 std::cout <<" ./Intrepid_example_Drivers_Example_10.exe deg NX NY NZ verbose\n\n"; 00122 std::cout <<" where \n"; 00123 std::cout <<" int deg - polynomial degree to be used (assumed >= 1) \n"; 00124 std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n"; 00125 std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n"; 00126 std::cout <<" int NZ - num intervals in y direction (assumed box domain, 0,1) \n"; 00127 std::cout <<" verbose (optional) - any character, indicates verbose output \n\n"; 00128 exit(1); 00129 } 00130 00131 // This little trick lets us print to std::cout only if 00132 // a (dummy) command-line argument is provided. 00133 int iprint = argc - 1; 00134 Teuchos::RCP<std::ostream> outStream; 00135 Teuchos::oblackholestream bhs; // outputs nothing 00136 if (iprint > 2) 00137 outStream = Teuchos::rcp(&std::cout, false); 00138 else 00139 outStream = Teuchos::rcp(&bhs, false); 00140 00141 // Save the format state of the original std::cout. 00142 Teuchos::oblackholestream oldFormatState; 00143 oldFormatState.copyfmt(std::cout); 00144 00145 *outStream \ 00146 << "===============================================================================\n" \ 00147 << "| |\n" \ 00148 << "| Example: Build Stiffness Matrix for |\n" \ 00149 << "| Poisson Equation on Hexahedral Mesh |\n" \ 00150 << "| |\n" \ 00151 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov), |\n" \ 00152 << "| Denis Ridzal (dridzal@sandia.gov), |\n" \ 00153 << "| Kara Peterson (kjpeter@sandia.gov). |\n" \ 00154 << "| |\n" \ 00155 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \ 00156 << "| Trilinos website: http://trilinos.sandia.gov |\n" \ 00157 << "| |\n" \ 00158 << "===============================================================================\n"; 00159 00160 00161 // ************************************ GET INPUTS ************************************** 00162 00163 int deg = atoi(argv[1]); // polynomial degree to use 00164 int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1) 00165 int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1) 00166 int NZ = atoi(argv[4]); // num intervals in y direction (assumed box domain, 0,1) 00167 00168 00169 // *********************************** CELL TOPOLOGY ********************************** 00170 00171 // Get cell topology for base hexahedron 00172 typedef shards::CellTopology CellTopology; 00173 CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() ); 00174 00175 // Get dimensions 00176 int numNodesPerElem = hex_8.getNodeCount(); 00177 int spaceDim = hex_8.getDimension(); 00178 00179 // *********************************** GENERATE MESH ************************************ 00180 00181 *outStream << "Generating mesh ... \n\n"; 00182 00183 *outStream << " NX" << " NY" << " NZ\n"; 00184 *outStream << std::setw(5) << NX << 00185 std::setw(5) << NY << std::setw(5) << NZ << "\n\n"; 00186 00187 // Print mesh information 00188 int numElems = NX*NY*NZ; 00189 int numNodes = (NX+1)*(NY+1)*(NZ+1); 00190 *outStream << " Number of Elements: " << numElems << " \n"; 00191 *outStream << " Number of Nodes: " << numNodes << " \n\n"; 00192 00193 // Cube 00194 double leftX = 0.0, rightX = 1.0; 00195 double leftY = 0.0, rightY = 1.0; 00196 double leftZ = 0.0, rightZ = 1.0; 00197 00198 // Mesh spacing 00199 double hx = (rightX-leftX)/((double)NX); 00200 double hy = (rightY-leftY)/((double)NY); 00201 double hz = (rightZ-leftZ)/((double)NZ); 00202 00203 // Get nodal coordinates 00204 FieldContainer<double> nodeCoord(numNodes, spaceDim); 00205 FieldContainer<int> nodeOnBoundary(numNodes); 00206 int inode = 0; 00207 for (int k=0; k<NZ+1; k++) 00208 { 00209 for (int j=0; j<NY+1; j++) 00210 { 00211 for (int i=0; i<NX+1; i++) 00212 { 00213 nodeCoord(inode,0) = leftX + (double)i*hx; 00214 nodeCoord(inode,1) = leftY + (double)j*hy; 00215 nodeCoord(inode,2) = leftZ + (double)k*hz; 00216 if (k==0 || k==NZ || j==0 || i==0 || j==NY || i==NX) 00217 { 00218 nodeOnBoundary(inode)=1; 00219 } 00220 else 00221 { 00222 nodeOnBoundary(inode)=0; 00223 } 00224 inode++; 00225 } 00226 } 00227 } 00228 #define DUMP_DATA 00229 #ifdef DUMP_DATA 00230 // Print nodal coords 00231 ofstream fcoordout("coords.dat"); 00232 for (int i=0; i<numNodes; i++) { 00233 fcoordout << nodeCoord(i,0) <<" "; 00234 fcoordout << nodeCoord(i,1) <<" "; 00235 fcoordout << nodeCoord(i,2) <<"\n"; 00236 } 00237 fcoordout.close(); 00238 #endif 00239 00240 00241 // Element to Node map 00242 // We'll keep it around, but this is only the DOFMap if you are in the lowest order case. 00243 FieldContainer<int> elemToNode(numElems, numNodesPerElem); 00244 int ielem = 0; 00245 for (int k=0; k<NZ; k++) 00246 { 00247 for (int j=0; j<NY; j++) 00248 { 00249 for (int i=0; i<NX; i++) 00250 { 00251 elemToNode(ielem,0) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i; 00252 elemToNode(ielem,1) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1; 00253 elemToNode(ielem,2) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1; 00254 elemToNode(ielem,3) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i; 00255 elemToNode(ielem,4) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i; 00256 elemToNode(ielem,5) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1; 00257 elemToNode(ielem,6) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1; 00258 elemToNode(ielem,7) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i; 00259 ielem++; 00260 } 00261 } 00262 } 00263 #ifdef DUMP_DATA 00264 // Output connectivity 00265 ofstream fe2nout("elem2node.dat"); 00266 for (int k=0;k<NZ;k++) 00267 { 00268 for (int j=0; j<NY; j++) 00269 { 00270 for (int i=0; i<NX; i++) 00271 { 00272 int ielem = i + j * NX + k * NY * NY; 00273 for (int m=0; m<numNodesPerElem; m++) 00274 { 00275 fe2nout << elemToNode(ielem,m) <<" "; 00276 } 00277 fe2nout <<"\n"; 00278 } 00279 } 00280 } 00281 fe2nout.close(); 00282 #endif 00283 00284 // ************************************ CUBATURE ************************************** 00285 *outStream << "Getting cubature ... \n\n"; 00286 00287 // Get numerical integration points and weights 00288 DefaultCubatureFactory<double> cubFactory; 00289 int cubDegree = 2*deg; 00290 Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(hex_8, cubDegree); 00291 00292 int cubDim = quadCub->getDimension(); 00293 int numCubPoints = quadCub->getNumPoints(); 00294 00295 FieldContainer<double> cubPoints(numCubPoints, cubDim); 00296 FieldContainer<double> cubWeights(numCubPoints); 00297 00298 quadCub->getCubature(cubPoints, cubWeights); 00299 00300 00301 // ************************************** BASIS *************************************** 00302 00303 *outStream << "Getting basis ... \n\n"; 00304 00305 // Define basis 00306 Basis_HGRAD_HEX_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL); 00307 int numFieldsG = quadHGradBasis.getCardinality(); 00308 FieldContainer<double> quadGVals(numFieldsG, numCubPoints); 00309 FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim); 00310 00311 // Evaluate basis values and gradients at cubature points 00312 quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE); 00313 quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD); 00314 00315 // create the local-global mapping 00316 FieldContainer<int> ltgMapping(numElems,numFieldsG); 00317 const int numDOF = (NX*deg+1)*(NY*deg+1)*(NZ*deg+1); 00318 ielem=0; 00319 for (int k=0;k<NZ;k++) 00320 { 00321 for (int j=0;j<NY;j++) 00322 { 00323 for (int i=0;i<NX;i++) 00324 { 00325 const int start = k * ( NY * deg + 1 ) * ( NX * deg + 1 ) + j * ( NX * deg + 1 ) + i * deg; 00326 // loop over local dof on this cell 00327 int local_dof_cur=0; 00328 for (int kloc=0;kloc<=deg;kloc++) 00329 { 00330 for (int jloc=0;jloc<=deg;jloc++) 00331 { 00332 for (int iloc=0;iloc<=deg;iloc++) 00333 { 00334 ltgMapping(ielem,local_dof_cur) = start 00335 + kloc * ( NX * deg + 1 ) * ( NY * deg + 1 ) 00336 + jloc * ( NX * deg + 1 ) 00337 + iloc; 00338 local_dof_cur++; 00339 } 00340 } 00341 } 00342 ielem++; 00343 } 00344 } 00345 } 00346 #ifdef DUMP_DATA 00347 // Output ltg mapping 00348 ielem = 0; 00349 ofstream ltgout("ltg.dat"); 00350 for (int k=0;k<NZ;k++) 00351 { 00352 for (int j=0; j<NY; j++) 00353 { 00354 for (int i=0; i<NX; i++) 00355 { 00356 int ielem = i + j * NX + k * NX * NY; 00357 for (int m=0; m<numFieldsG; m++) 00358 { 00359 ltgout << ltgMapping(ielem,m) <<" "; 00360 } 00361 ltgout <<"\n"; 00362 } 00363 } 00364 } 00365 ltgout.close(); 00366 #endif 00367 00368 // ********** DECLARE GLOBAL OBJECTS ************* 00369 Epetra_SerialComm Comm; 00370 Epetra_Map globalMapG(numDOF, 0, Comm); 00371 Epetra_FEVector u(globalMapG); u.Random(); 00372 Epetra_FEVector Ku(globalMapG); 00373 00374 // Let's preallocate the graph before we instantiate the matrix 00375 Epetra_Time graphTimer(Comm); 00376 Epetra_CrsGraph grph( Copy , globalMapG , 4 * numFieldsG ); 00377 for (int k=0;k<numElems;k++) 00378 { 00379 for (int i=0;i<numFieldsG;i++) 00380 { 00381 grph.InsertGlobalIndices(ltgMapping(k,i),numFieldsG,<gMapping(k,0)); 00382 } 00383 } 00384 grph.FillComplete(); 00385 const double graphTime = graphTimer.ElapsedTime(); 00386 00387 00388 // time the instantiation 00389 Epetra_Time instantiateTimer(Comm); 00390 Epetra_FECrsMatrix StiffMatrix(Copy,grph); 00391 const double instantiateTime = instantiateTimer.ElapsedTime(); 00392 00393 00394 // ********** CONSTRUCT AND INSERT LOCAL STIFFNESS MATRICES *********** 00395 *outStream << "Building local stiffness matrices...\n\n"; 00396 typedef CellTools<double> CellTools; 00397 typedef FunctionSpaceTools fst; 00398 int numCells = numElems; 00399 00400 00401 // jacobian information 00402 FieldContainer<double> refCellNodes(1,numNodesPerElem,spaceDim); 00403 FieldContainer<double> cellJacobian(1,numCubPoints,spaceDim,spaceDim); 00404 FieldContainer<double> cellJacobInv(1,numCubPoints,spaceDim,spaceDim); 00405 FieldContainer<double> cellJacobDet(1,numCubPoints); 00406 00407 // element stiffness matrices and supporting storage space 00408 FieldContainer<double> localStiffMatrix(1, numFieldsG, numFieldsG); 00409 FieldContainer<double> transformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim); 00410 FieldContainer<double> weightedTransformedBasisGradients(1,numFieldsG,numCubPoints,spaceDim); 00411 FieldContainer<double> weightedMeasure(1, numCubPoints); 00412 00413 00414 Epetra_Time localConstructTimer( Comm ); 00415 refCellNodes(0,0,0) = 0.0; refCellNodes(0,0,1) = 0.0; refCellNodes(0,0,2) = 0.0; 00416 refCellNodes(0,1,0) = hx; refCellNodes(0,1,1) = 0.0; refCellNodes(0,1,2) = 0.0; 00417 refCellNodes(0,2,0) = hx; refCellNodes(0,2,1) = hy; refCellNodes(0,2,2) = 0.0; 00418 refCellNodes(0,3,0) = 0.0; refCellNodes(0,3,1) = hy; refCellNodes(0,3,2) = 0.0; 00419 refCellNodes(0,4,0) = 0.0; refCellNodes(0,4,1) = 0.0; refCellNodes(0,4,2) = hz; 00420 refCellNodes(0,5,0) = hx; refCellNodes(0,5,1) = 0.0; refCellNodes(0,5,2) = hz; 00421 refCellNodes(0,6,0) = hx; refCellNodes(0,6,1) = hy; refCellNodes(0,6,2) = hz; 00422 refCellNodes(0,7,0) = 0.0; refCellNodes(0,7,1) = hy; refCellNodes(0,7,2) = hz; 00423 00424 00425 // jacobian evaluation 00426 CellTools::setJacobian(cellJacobian,cubPoints,refCellNodes,hex_8); 00427 CellTools::setJacobianInv(cellJacobInv, cellJacobian ); 00428 CellTools::setJacobianDet(cellJacobDet, cellJacobian ); 00429 00430 // transform reference element gradients to each cell 00431 fst::HGRADtransformGRAD<double>(transformedBasisGradients, cellJacobInv, quadGrads); 00432 00433 // compute weighted measure 00434 fst::computeCellMeasure<double>(weightedMeasure, cellJacobDet, cubWeights); 00435 00436 // multiply values with weighted measure 00437 fst::multiplyMeasure<double>(weightedTransformedBasisGradients, 00438 weightedMeasure, transformedBasisGradients); 00439 00440 // integrate to compute element stiffness matrix 00441 fst::integrate<double>(localStiffMatrix, 00442 transformedBasisGradients, weightedTransformedBasisGradients , COMP_BLAS); 00443 00444 const double localConstructTime = localConstructTimer.ElapsedTime(); 00445 00446 00447 Epetra_Time insertionTimer(Comm); 00448 00449 // *** Element loop *** 00450 for (int k=0; k<numElems; k++) 00451 { 00452 // assemble into global matrix 00453 StiffMatrix.InsertGlobalValues(numFieldsG,<gMapping(k,0),numFieldsG,<gMapping(k,0),&localStiffMatrix(0,0,0)); 00454 00455 } 00456 StiffMatrix.GlobalAssemble(); StiffMatrix.FillComplete(); 00457 const double insertionTime = insertionTimer.ElapsedTime( ); 00458 00459 *outStream << "Time to construct matrix graph: " << graphTime << "\n"; 00460 *outStream << "Time to instantiate global stiffness matrix: " << instantiateTime << "\n"; 00461 *outStream << "Time to build local matrices (including Jacobian computation): "<< localConstructTime << "\n"; 00462 *outStream << "Time to assemble global matrix from local matrices: " << insertionTime << "\n"; 00463 *outStream << "Total construction time: " << graphTime + instantiateTime + localConstructTime + insertionTime << "\n"; 00464 00465 Epetra_Time applyTimer(Comm); 00466 StiffMatrix.Apply(u,Ku); 00467 const double multTime = applyTimer.ElapsedTime(); 00468 *outStream << "Time to multiply onto a vector: " << multTime << "\n"; 00469 00470 *outStream << "End Result: TEST PASSED\n"; 00471 00472 // reset format state of std::cout 00473 std::cout.copyfmt(oldFormatState); 00474 00475 return 0; 00476 } 00477
1.7.6.1