From 02f3188e2f3df836d1732d5dbaf0e1f5609e98fe Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 8 Oct 2009 07:52:40 +0000
Subject: [PATCH] new application: a prototype of a Neumann-Dirichlet algorithm
(rod is Neumann this time)
[[Imported from SVN: r4969]]
---
Makefile.am | 7 +-
neudircoupling.cc | 679 ++++++++++++++++++++++++++++++++++++++++++++++
2 files changed, 685 insertions(+), 1 deletion(-)
create mode 100644 neudircoupling.cc
diff --git a/Makefile.am b/Makefile.am
index 684a8ea4..b709735e 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -4,7 +4,7 @@
LDADD = $(IPOPT_LDFLAGS) $(IPOPT_LIBS)
AM_CPPFLAGS += $(IPOPT_CPPFLAGS)
-noinst_PROGRAMS = staticrod staticrod2 rod3d harmonicmaps dirneucoupling rod-eoc
+noinst_PROGRAMS = staticrod staticrod2 rod3d harmonicmaps dirneucoupling neudircoupling rod-eoc
staticrod_SOURCES = staticrod.cc
staticrod2_SOURCES = staticrod2.cc
@@ -22,6 +22,11 @@ dirneucoupling_CXXFLAGS = $(UG_CPPFLAGS) $(AMIRAMESH_CPPFLAGS) $(IPOPT_CPPFLAGS)
dirneucoupling_LDADD = $(UG_LDFLAGS) $(AMIRAMESH_LDFLAGS) $(UG_LIBS) $(AMIRAMESH_LIBS) \
$(IPOPT_LDFLAGS) $(IPOPT_LIBS) $(PSURFACE_LDFLAGS) $(PSURFACE_LIBS)
+neudircoupling_SOURCES = neudircoupling.cc
+neudircoupling_CXXFLAGS = $(UG_CPPFLAGS) $(AMIRAMESH_CPPFLAGS) $(IPOPT_CPPFLAGS) $(PSURFACE_CPPFLAGS)
+neudircoupling_LDADD = $(UG_LDFLAGS) $(AMIRAMESH_LDFLAGS) $(UG_LIBS) $(AMIRAMESH_LIBS) \
+ $(IPOPT_LDFLAGS) $(IPOPT_LIBS) $(PSURFACE_LDFLAGS) $(PSURFACE_LIBS)
+
# don't follow the full GNU-standard
# we need automake 1.5
AUTOMAKE_OPTIONS = foreign 1.5
diff --git a/neudircoupling.cc b/neudircoupling.cc
new file mode 100644
index 00000000..f62610dd
--- /dev/null
+++ b/neudircoupling.cc
@@ -0,0 +1,679 @@
+#include <config.h>
+
+#include <dune/grid/onedgrid.hh>
+#include <dune/grid/uggrid.hh>
+
+#include <dune/istl/io.hh>
+#include <dune/grid/io/file/amirameshreader.hh>
+#include <dune/grid/io/file/amirameshwriter.hh>
+
+#include <dune/common/bitsetvector.hh>
+#include <dune/common/configparser.hh>
+
+#include <dune-solvers/iterationsteps/multigridstep.hh>
+#include <dune-solvers/solvers/loopsolver.hh>
+#include <dune-solvers/iterationsteps/projectedblockgsstep.hh>
+#ifdef HAVE_IPOPT
+#include <dune-solvers/solvers/quadraticipopt.hh>
+#endif
+#include <dune/ag-common/readbitfield.hh>
+#include <dune-solvers/norms/energynorm.hh>
+#include <dune/ag-common/boundarypatch.hh>
+#include <dune/ag-common/prolongboundarypatch.hh>
+#include <dune/ag-common/sampleonbitfield.hh>
+#include <dune/ag-common/neumannassembler.hh>
+#include <dune/ag-common/computestress.hh>
+
+#include <dune/ag-common/functionspacebases/q1nodalbasis.hh>
+#include <dune/ag-common/assemblers/operatorassembler.hh>
+#include <dune/ag-common/assemblers/localassemblers/stvenantkirchhoffassembler.hh>
+
+#include "src/quaternion.hh"
+#include "src/rodassembler.hh"
+#include "src/rigidbodymotion.hh"
+#include "src/averageinterface.hh"
+#include "src/riemanniantrsolver.hh"
+#include "src/geodesicdifference.hh"
+#include "src/rodwriter.hh"
+#include "src/makestraightrod.hh"
+
+// Space dimension
+const int dim = 3;
+
+using namespace Dune;
+using std::string;
+using std::vector;
+
+// Some types that I need
+typedef vector<RigidBodyMotion<dim> > RodSolutionType;
+typedef BlockVector<FieldVector<double, 6> > RodDifferenceType;
+
+
+int main (int argc, char *argv[]) try
+{
+ // Some types that I need
+ typedef BCRSMatrix<FieldMatrix<double, dim, dim> > MatrixType;
+ typedef BlockVector<FieldVector<double, dim> > VectorType;
+
+ // parse data file
+ ConfigParser parameterSet;
+ if (argc==2)
+ parameterSet.parseFile(argv[1]);
+ else
+ parameterSet.parseFile("neudircoupling.parset");
+
+ // read solver settings
+ const int numLevels = parameterSet.get<int>("numLevels");
+ const double ddTolerance = parameterSet.get<double>("ddTolerance");
+ const int maxDirichletNeumannSteps = parameterSet.get<int>("maxDirichletNeumannSteps");
+ const double trTolerance = parameterSet.get<double>("trTolerance");
+ const int maxTrustRegionSteps = parameterSet.get<int>("maxTrustRegionSteps");
+ const int trVerbosity = parameterSet.get<int>("trVerbosity");
+ const int multigridIterations = parameterSet.get<int>("numIt");
+ const int nu1 = parameterSet.get<int>("nu1");
+ const int nu2 = parameterSet.get<int>("nu2");
+ const int mu = parameterSet.get<int>("mu");
+ const int baseIterations = parameterSet.get<int>("baseIt");
+ const double mgTolerance = parameterSet.get<double>("mgTolerance");
+ const double baseTolerance = parameterSet.get<double>("baseTolerance");
+ const double initialTrustRegionRadius = parameterSet.get<double>("initialTrustRegionRadius");
+ const double damping = parameterSet.get<double>("damping");
+ string resultPath = parameterSet.get("resultPath", "");
+
+ // Problem settings
+ string path = parameterSet.get<string>("path");
+ string objectName = parameterSet.get<string>("gridFile");
+ string dirichletNodesFile = parameterSet.get<string>("dirichletNodes");
+ string dirichletValuesFile = parameterSet.get<string>("dirichletValues");
+ string interfaceNodesFile = parameterSet.get<string>("interfaceNodes");
+ const int numRodBaseElements = parameterSet.get<int>("numRodBaseElements");
+
+ double E = parameterSet.get<double>("E");
+ double nu = parameterSet.get<double>("nu");
+
+ // rod material parameters
+ double rodA = parameterSet.get<double>("rodA");
+ double rodJ1 = parameterSet.get<double>("rodJ1");
+ double rodJ2 = parameterSet.get<double>("rodJ2");
+ double rodE = parameterSet.get<double>("rodE");
+ double rodNu = parameterSet.get<double>("rodNu");
+
+ std::tr1::array<FieldVector<double,3>,2> rodRestEndPoint;
+ rodRestEndPoint[0][0] = parameterSet.get<double>("rodRestEndPoint0X");
+ rodRestEndPoint[0][1] = parameterSet.get<double>("rodRestEndPoint0Y");
+ rodRestEndPoint[0][2] = parameterSet.get<double>("rodRestEndPoint0Z");
+ rodRestEndPoint[1][0] = parameterSet.get<double>("rodRestEndPoint1X");
+ rodRestEndPoint[1][1] = parameterSet.get<double>("rodRestEndPoint1Y");
+ rodRestEndPoint[1][2] = parameterSet.get<double>("rodRestEndPoint1Z");
+
+ // ///////////////////////////////////////
+ // Create the rod grid
+ // ///////////////////////////////////////
+ typedef OneDGrid RodGridType;
+ RodGridType rodGrid(numRodBaseElements, 0, (rodRestEndPoint[1]-rodRestEndPoint[0]).two_norm());
+
+ // ///////////////////////////////////////
+ // Create the grid for the 3d object
+ // ///////////////////////////////////////
+ typedef UGGrid<dim> GridType;
+ GridType grid;
+ grid.setRefinementType(GridType::COPY);
+
+ AmiraMeshReader<GridType>::read(grid, path + objectName);
+
+ // //////////////////////////////////////
+ // Globally refine grids
+ // //////////////////////////////////////
+
+ rodGrid.globalRefine(numLevels-1);
+ grid.globalRefine(numLevels-1);
+
+ std::vector<BitSetVector<dim> > dirichletNodes(1);
+
+ RodSolutionType rodX(rodGrid.size(1));
+
+ // //////////////////////////
+ // Initial solution
+ // //////////////////////////
+
+ makeStraightRod(rodX, rodGrid.size(1), rodRestEndPoint[0], rodRestEndPoint[1]);
+
+ // /////////////////////////////////////////
+ // Read Dirichlet values
+ // /////////////////////////////////////////
+ rodX.back().r[0] = parameterSet.get("dirichletValueX", rodRestEndPoint[1][0]);
+ rodX.back().r[1] = parameterSet.get("dirichletValueY", rodRestEndPoint[1][1]);
+ rodX.back().r[2] = parameterSet.get("dirichletValueZ", rodRestEndPoint[1][2]);
+
+ FieldVector<double,3> axis;
+ axis[0] = parameterSet.get("dirichletAxisX", double(0));
+ axis[1] = parameterSet.get("dirichletAxisY", double(0));
+ axis[2] = parameterSet.get("dirichletAxisZ", double(0));
+ double angle = parameterSet.get("dirichletAngle", double(0));
+
+ rodX.back().q = Rotation<3,double>(axis, M_PI*angle/180);
+
+ // Backup initial rod iterate for later reference
+ RodSolutionType initialIterateRod = rodX;
+
+ int toplevel = rodGrid.maxLevel();
+
+ // /////////////////////////////////////////////////////
+ // Determine the Dirichlet nodes
+ // /////////////////////////////////////////////////////
+ std::vector<VectorType> dirichletValues;
+ dirichletValues.resize(toplevel+1);
+ dirichletValues[0].resize(grid.size(0, dim));
+ AmiraMeshReader<int>::readFunction(dirichletValues[0], path + dirichletValuesFile);
+
+ std::vector<LevelBoundaryPatch<GridType> > dirichletBoundary;
+ dirichletBoundary.resize(numLevels);
+ dirichletBoundary[0].setup(grid, 0);
+ readBoundaryPatch(dirichletBoundary[0], path + dirichletNodesFile);
+ PatchProlongator<GridType>::prolong(dirichletBoundary);
+
+ dirichletNodes.resize(toplevel+1);
+ for (int i=0; i<=toplevel; i++) {
+
+ dirichletNodes[i].resize( grid.size(i,dim));
+
+ for (int j=0; j<grid.size(i,dim); j++)
+ dirichletNodes[i][j] = dirichletBoundary[i].containsVertex(j);
+
+ }
+
+ sampleOnBitField(grid, dirichletValues, dirichletNodes);
+
+ // /////////////////////////////////////////////////////
+ // Determine the interface boundary
+ // /////////////////////////////////////////////////////
+ std::vector<LevelBoundaryPatch<GridType> > interfaceBoundary;
+ interfaceBoundary.resize(numLevels);
+ interfaceBoundary[0].setup(grid, 0);
+ readBoundaryPatch(interfaceBoundary[0], path + interfaceNodesFile);
+ PatchProlongator<GridType>::prolong(interfaceBoundary);
+
+ // //////////////////////////////////////////
+ // Assemble 3d linear elasticity problem
+ // //////////////////////////////////////////
+
+ typedef Q1NodalBasis<GridType::LeafGridView,double> FEBasis;
+ FEBasis basis(grid.leafView());
+ OperatorAssembler<FEBasis,FEBasis> assembler(basis, basis);
+
+ StVenantKirchhoffAssembler<GridType, FEBasis::LocalFiniteElement, FEBasis::LocalFiniteElement> localAssembler(E, nu);
+ MatrixType stiffnessMatrix3d;
+
+ assembler.assemble(localAssembler, stiffnessMatrix3d);
+
+ // ////////////////////////////////////////////////////////////
+ // Create solution and rhs vectors
+ // ////////////////////////////////////////////////////////////
+
+ VectorType x3d(grid.size(toplevel,dim));
+ VectorType rhs3d(grid.size(toplevel,dim));
+
+ // No external forces
+ rhs3d = 0;
+
+ // Set initial solution
+ x3d = 0;
+ for (int i=0; i<x3d.size(); i++)
+ for (int j=0; j<dim; j++)
+ if (dirichletNodes[toplevel][i][j])
+ x3d[i][j] = dirichletValues[toplevel][i][j];
+
+ // ///////////////////////////////////////////
+ // Dirichlet nodes for the rod problem
+ // ///////////////////////////////////////////
+
+ BitSetVector<6> rodDirichletNodes(rodGrid.size(1));
+ rodDirichletNodes.unsetAll();
+
+ //rodDirichletNodes[0] = true;
+ rodDirichletNodes.back() = true;
+
+ // ///////////////////////////////////////////
+ // Create a solver for the rod problem
+ // ///////////////////////////////////////////
+
+ RodLocalStiffness<RodGridType::LeafGridView,double> rodLocalStiffness(rodGrid.leafView(),
+ rodA, rodJ1, rodJ2, rodE, rodNu);
+
+ RodAssembler<RodGridType> rodAssembler(rodGrid, &rodLocalStiffness);
+
+ RiemannianTrustRegionSolver<RodGridType,RigidBodyMotion<3> > rodSolver;
+ rodSolver.setup(rodGrid,
+ &rodAssembler,
+ rodX,
+ rodDirichletNodes,
+ trTolerance,
+ maxTrustRegionSteps,
+ initialTrustRegionRadius,
+ multigridIterations,
+ mgTolerance,
+ mu, nu1, nu2,
+ baseIterations,
+ baseTolerance,
+ false);
+
+ switch (trVerbosity) {
+ case 0:
+ rodSolver.verbosity_ = Solver::QUIET; break;
+ case 1:
+ rodSolver.verbosity_ = Solver::REDUCED; break;
+ default:
+ rodSolver.verbosity_ = Solver::FULL; break;
+ }
+
+
+ // ////////////////////////////////
+ // Create a multigrid solver
+ // ////////////////////////////////
+
+ // First create a gauss-seidel base solver
+#ifdef HAVE_IPOPT
+ QuadraticIPOptSolver<MatrixType,VectorType> baseSolver;
+#endif
+ baseSolver.verbosity_ = NumProc::QUIET;
+ baseSolver.tolerance_ = baseTolerance;
+
+ // Make pre and postsmoothers
+ BlockGSStep<MatrixType, VectorType> presmoother, postsmoother;
+
+ MultigridStep<MatrixType, VectorType> multigridStep(stiffnessMatrix3d, x3d, rhs3d, 1);
+
+ multigridStep.setMGType(mu, nu1, nu2);
+ multigridStep.ignoreNodes_ = &dirichletNodes.back();
+ multigridStep.basesolver_ = &baseSolver;
+ multigridStep.presmoother_ = &presmoother;
+ multigridStep.postsmoother_ = &postsmoother;
+ multigridStep.verbosity_ = Solver::QUIET;
+
+
+
+ EnergyNorm<MatrixType, VectorType> energyNorm(multigridStep);
+
+ LoopSolver<VectorType> solver(&multigridStep,
+ // IPOpt doesn't like to be started in the solution
+ (numLevels!=1) ? multigridIterations : 1,
+ mgTolerance,
+ &energyNorm,
+ Solver::QUIET);
+
+ // ////////////////////////////////////
+ // Create the transfer operators
+ // ////////////////////////////////////
+ for (int k=0; k<multigridStep.mgTransfer_.size(); k++)
+ delete(multigridStep.mgTransfer_[k]);
+
+ multigridStep.mgTransfer_.resize(toplevel);
+
+ for (int i=0; i<multigridStep.mgTransfer_.size(); i++){
+ CompressedMultigridTransfer<VectorType>* newTransferOp = new CompressedMultigridTransfer<VectorType>;
+ newTransferOp->setup(grid,i,i+1);
+ multigridStep.mgTransfer_[i] = newTransferOp;
+ }
+
+ // /////////////////////////////////////////////////////
+ // Dirichlet-Neumann Solver
+ // /////////////////////////////////////////////////////
+
+ // Init interface value
+ RigidBodyMotion<3> referenceInterface = rodX[0];
+ RigidBodyMotion<3> lambda = referenceInterface;
+ FieldVector<double,3> lambdaForce(0);
+ FieldVector<double,3> lambdaTorque(0);
+
+ //
+ double normOfOldCorrection = 0;
+ int dnStepsActuallyTaken = 0;
+ for (int i=0; i<maxDirichletNeumannSteps; i++) {
+
+ std::cout << "----------------------------------------------------" << std::endl;
+ std::cout << " Dirichlet-Neumann Step Number: " << i << std::endl;
+ std::cout << "----------------------------------------------------" << std::endl;
+
+ // Backup of the current solution for the error computation later on
+ VectorType oldSolution3d = x3d;
+ RodSolutionType oldSolutionRod = rodX;
+
+ // //////////////////////////////////////////////////
+ // Dirichlet step for the rod
+ // //////////////////////////////////////////////////
+
+ rodX[0] = lambda;
+ rodSolver.setInitialSolution(rodX);
+ rodSolver.solve();
+
+ rodX = rodSolver.getSol();
+
+// for (int j=0; j<rodX.size(); j++)
+// std::cout << rodX[j] << std::endl;
+
+ // ///////////////////////////////////////////////////////////
+ // Extract Neumann values and transfer it to the 3d object
+ // ///////////////////////////////////////////////////////////
+
+ BitSetVector<1> couplingBitfield(rodX.size(),false);
+ // Using that index 0 is always the left boundary for a uniformly refined OneDGrid
+ couplingBitfield[0] = true;
+ LevelBoundaryPatch<RodGridType> couplingBoundary(rodGrid, rodGrid.maxLevel(), couplingBitfield);
+
+ FieldVector<double,dim> resultantForce, resultantTorque;
+ resultantForce = rodAssembler.getResultantForce(couplingBoundary, rodX, resultantTorque);
+
+ std::cout << "resultant force: " << resultantForce << std::endl;
+ std::cout << "resultant torque: " << resultantTorque << std::endl;
+
+ VectorType neumannValues(rhs3d.size());
+
+ // Using that index 0 is always the left boundary for a uniformly refined OneDGrid
+ computeAveragePressure<GridType>(resultantForce, resultantTorque,
+ interfaceBoundary[grid.maxLevel()],
+ rodX[0],
+ neumannValues);
+
+ rhs3d = 0;
+ assembleAndAddNeumannTerm<GridType::LevelGridView, VectorType>(interfaceBoundary[grid.maxLevel()],
+ neumannValues,
+ rhs3d);
+
+ // ///////////////////////////////////////////////////////////
+ // Solve the Neumann problem for the 3d body
+ // ///////////////////////////////////////////////////////////
+ multigridStep.setProblem(stiffnessMatrix3d, x3d, rhs3d, grid.maxLevel()+1);
+
+ solver.preprocess();
+ multigridStep.preprocess();
+
+ solver.solve();
+
+ x3d = multigridStep.getSol();
+
+ // ///////////////////////////////////////////////////////////
+ // Extract new interface position and orientation
+ // ///////////////////////////////////////////////////////////
+
+ RigidBodyMotion<3> averageInterface;
+ computeAverageInterface(interfaceBoundary[toplevel], x3d, averageInterface);
+
+ //averageInterface.r[0] = averageInterface.r[1] = 0;
+ //averageInterface.q = Quaternion<double>::identity();
+ std::cout << "average interface: " << averageInterface << std::endl;
+
+ std::cout << "director 0: " << averageInterface.q.director(0) << std::endl;
+ std::cout << "director 1: " << averageInterface.q.director(1) << std::endl;
+ std::cout << "director 2: " << averageInterface.q.director(2) << std::endl;
+ std::cout << std::endl;
+
+ // ///////////////////////////////////////////////////////////
+ // Compute new damped interface value
+ // ///////////////////////////////////////////////////////////
+ for (int j=0; j<dim; j++)
+ lambda.r[j] = (1-damping) * lambda.r[j]
+ + damping * (referenceInterface.r[j] + averageInterface.r[j]);
+
+ lambda.q = Rotation<3,double>::interpolate(lambda.q,
+ referenceInterface.q.mult(averageInterface.q),
+ damping);
+
+ std::cout << "Lambda: " << lambda << std::endl;
+
+ // ////////////////////////////////////////////////////////////////////////
+ // Write the two iterates to disk for later convergence rate measurement
+ // ////////////////////////////////////////////////////////////////////////
+
+ // First the 3d body
+ std::stringstream iAsAscii;
+ iAsAscii << i;
+ std::string iSolFilename = resultPath + "tmp/intermediate3dSolution_" + iAsAscii.str();
+
+ LeafAmiraMeshWriter<GridType> amiraMeshWriter;
+ amiraMeshWriter.addVertexData(x3d, grid.leafView());
+ amiraMeshWriter.write(iSolFilename);
+
+ // Then the rod
+ iSolFilename = resultPath + "tmp/intermediateRodSolution_" + iAsAscii.str();
+
+ FILE* fpRod = fopen(iSolFilename.c_str(), "wb");
+ if (!fpRod)
+ DUNE_THROW(SolverError, "Couldn't open file " << iSolFilename << " for writing");
+
+ for (int j=0; j<rodX.size(); j++) {
+
+ for (int k=0; k<dim; k++)
+ fwrite(&rodX[j].r[k], sizeof(double), 1, fpRod);
+
+ for (int k=0; k<4; k++) // 3d hardwired here!
+ fwrite(&rodX[j].q[k], sizeof(double), 1, fpRod);
+
+ }
+
+ fclose(fpRod);
+
+ // ////////////////////////////////////////////
+ // Compute error in the energy norm
+ // ////////////////////////////////////////////
+
+ // the 3d body
+ double oldNorm = EnergyNorm<MatrixType,VectorType>::normSquared(oldSolution3d, stiffnessMatrix3d);
+ oldSolution3d -= x3d;
+ double normOfCorrection = EnergyNorm<MatrixType,VectorType>::normSquared(oldSolution3d, stiffnessMatrix3d);
+
+ double max3dRelCorrection = 0;
+ for (size_t j=0; j<x3d.size(); j++)
+ for (int k=0; k<dim; k++)
+ max3dRelCorrection = std::max(max3dRelCorrection,
+ std::fabs(oldSolution3d[j][k])/ std::fabs(x3d[j][k]));
+
+ // the rod
+ RodDifferenceType rodDiff = computeGeodesicDifference(oldSolutionRod, rodX);
+ double maxRodRelCorrection = 0;
+ for (size_t j=0; j<rodX.size(); j++)
+ for (int k=0; k<dim; k++)
+ maxRodRelCorrection = std::max(maxRodRelCorrection,
+ std::fabs(rodDiff[j][k])/ std::fabs(rodX[j].r[k]));
+
+ // Absolute corrections
+ double maxRodCorrection = computeGeodesicDifference(oldSolutionRod, rodX).infinity_norm();
+ double max3dCorrection = oldSolution3d.infinity_norm();
+
+
+ std::cout << "rod correction: " << maxRodCorrection
+ << " rod rel correction: " << maxRodRelCorrection
+ << " 3d correction: " << max3dCorrection
+ << " 3d rel correction: " << max3dRelCorrection << std::endl;
+
+
+ oldNorm = std::sqrt(oldNorm);
+
+ normOfCorrection = std::sqrt(normOfCorrection);
+
+ double relativeError = normOfCorrection / oldNorm;
+
+ double convRate = normOfCorrection / normOfOldCorrection;
+
+ normOfOldCorrection = normOfCorrection;
+
+ // Output
+ std::cout << "DD iteration: " << i << " -- ||u^{n+1} - u^n|| / ||u^n||: " << relativeError << ", "
+ << "convrate " << convRate << "\n";
+
+ dnStepsActuallyTaken = i;
+
+ //if (relativeError < ddTolerance)
+ if (std::max(max3dRelCorrection,maxRodRelCorrection) < ddTolerance)
+ break;
+
+ }
+
+
+
+ // //////////////////////////////////////////////////////////
+ // Recompute and compare against exact solution
+ // //////////////////////////////////////////////////////////
+ VectorType exactSol3d = x3d;
+ RodSolutionType exactSolRod = rodX;
+
+ // //////////////////////////////////////////////////////////
+ // Compute hessian of the rod functional at the exact solution
+ // for use of the energy norm it creates.
+ // //////////////////////////////////////////////////////////
+
+ BCRSMatrix<FieldMatrix<double, 6, 6> > hessianRod;
+ MatrixIndexSet indices(exactSolRod.size(), exactSolRod.size());
+ rodAssembler.getNeighborsPerVertex(indices);
+ indices.exportIdx(hessianRod);
+ rodAssembler.assembleMatrix(exactSolRod, hessianRod);
+
+
+ double error = std::numeric_limits<double>::max();
+ double oldError = 0;
+
+ VectorType intermediateSol3d(x3d.size());
+ RodSolutionType intermediateSolRod(rodX.size());
+
+ // Compute error of the initial 3d solution
+
+ // This should really be exactSol-initialSol, but we're starting
+ // from zero anyways
+ oldError += EnergyNorm<MatrixType,VectorType>::normSquared(exactSol3d, stiffnessMatrix3d);
+
+ // Error of the initial rod iterate
+ RodDifferenceType rodDifference = computeGeodesicDifference(initialIterateRod, exactSolRod);
+ oldError += EnergyNorm<BCRSMatrix<FieldMatrix<double,6,6> >,RodDifferenceType>::normSquared(rodDifference, hessianRod);
+
+ oldError = std::sqrt(oldError);
+
+ // Store the history of total conv rates so we can filter out numerical
+ // dirt in the end.
+ std::vector<double> totalConvRate(maxDirichletNeumannSteps+1);
+ totalConvRate[0] = 1;
+
+
+ double oldConvRate = 100;
+ bool firstTime = true;
+ std::stringstream levelAsAscii, dampingAsAscii;
+ levelAsAscii << numLevels;
+ dampingAsAscii << damping;
+ std::string filename = resultPath + "convrate_" + levelAsAscii.str() + "_" + dampingAsAscii.str();
+
+ int i;
+ for (i=0; i<dnStepsActuallyTaken; i++) {
+
+ // /////////////////////////////////////////////////////
+ // Read iteration from file
+ // /////////////////////////////////////////////////////
+
+ // Read 3d solution from file
+ std::stringstream iAsAscii;
+ iAsAscii << i;
+ std::string iSolFilename = resultPath + "tmp/intermediate3dSolution_" + iAsAscii.str();
+
+ AmiraMeshReader<int>::readFunction(intermediateSol3d, iSolFilename);
+
+ // Read rod solution from file
+ iSolFilename = resultPath + "tmp/intermediateRodSolution_" + iAsAscii.str();
+
+ FILE* fpInt = fopen(iSolFilename.c_str(), "rb");
+ if (!fpInt)
+ DUNE_THROW(IOError, "Couldn't open intermediate solution '" << iSolFilename << "'");
+ for (int j=0; j<intermediateSolRod.size(); j++) {
+ fread(&intermediateSolRod[j].r, sizeof(double), dim, fpInt);
+ fread(&intermediateSolRod[j].q, sizeof(double), 4, fpInt);
+ }
+
+ fclose(fpInt);
+
+
+
+ // /////////////////////////////////////////////////////
+ // Compute error
+ // /////////////////////////////////////////////////////
+
+ VectorType solBackup0 = intermediateSol3d;
+ solBackup0 -= exactSol3d;
+
+ RodDifferenceType rodDifference = computeGeodesicDifference(exactSolRod, intermediateSolRod);
+
+ error = std::sqrt(EnergyNorm<MatrixType,VectorType>::normSquared(solBackup0, stiffnessMatrix3d)
+ +
+ EnergyNorm<BCRSMatrix<FieldMatrix<double,6,6> >,RodDifferenceType>::normSquared(rodDifference, hessianRod));
+
+
+ double convRate = error / oldError;
+ totalConvRate[i+1] = totalConvRate[i] * convRate;
+
+ // Output
+ std::cout << "DD iteration: " << i << " error : " << error << ", "
+ << "convrate " << convRate
+ << " total conv rate " << std::pow(totalConvRate[i+1], 1/((double)i+1)) << std::endl;
+
+ // Convergence rates tend to stay fairly constant after a few initial iterates.
+ // Only when we hit numerical dirt are they starting to wiggle around wildly.
+ // We use this to detect 'the' convergence rate as the last averaged rate before
+ // we hit the dirt.
+ if (convRate > oldConvRate + 0.1 && i > 5 && firstTime) {
+
+ std::cout << "Damping: " << damping
+ << " convRate: " << std::pow(totalConvRate[i], 1/((double)i))
+ << std::endl;
+
+ std::ofstream convRateFile(filename.c_str());
+ convRateFile << damping << " "
+ << std::pow(totalConvRate[i], 1/((double)i))
+ << std::endl;
+
+ firstTime = false;
+ }
+
+ if (error < 1e-12)
+ break;
+
+ oldError = error;
+ oldConvRate = convRate;
+
+ }
+
+ // Convergence without dirt: write the overall convergence rate now
+ if (firstTime) {
+ int backTrace = std::min(size_t(4),totalConvRate.size());
+ std::cout << "Damping: " << damping
+ << " convRate: " << std::pow(totalConvRate[i+1-backTrace], 1/((double)i+1-backTrace))
+ << std::endl;
+
+ std::ofstream convRateFile(filename.c_str());
+ convRateFile << damping << " "
+ << std::pow(totalConvRate[i+1-backTrace], 1/((double)i+1-backTrace))
+ << std::endl;
+ }
+
+
+ // //////////////////////////////
+ // Delete temporary memory
+ // //////////////////////////////
+ std::string removeTmpCommand = "rm -rf " + resultPath + "tmp/intermediate*";
+ system(removeTmpCommand.c_str());
+
+ // //////////////////////////////
+ // Output result
+ // //////////////////////////////
+ LeafAmiraMeshWriter<GridType> amiraMeshWriter(grid);
+ amiraMeshWriter.addVertexData(x3d, grid.leafView());
+
+ BlockVector<FieldVector<double,1> > stress;
+ Stress<GridType>::getStress(grid, x3d, stress, E, nu);
+ amiraMeshWriter.addCellData(stress, grid.leafView());
+
+ amiraMeshWriter.write(resultPath + "grid.result");
+
+
+
+ writeRod(rodX, resultPath + "rod3d.result");
+
+ } catch (Exception e) {
+
+ std::cout << e << std::endl;
+
+ }
--
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