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#include <config.h>
#include <dune/common/bitsetvector.hh>
#include <dune/common/configparser.hh>
#include <dune/grid/uggrid.hh>
#include <dune/grid/onedgrid.hh>
#include <dune/grid/utility/structuredgridfactory.hh>
#include <dune/grid/io/file/amirameshwriter.hh>
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#include <dune/ag-common/functionspacebases/p1nodalbasis.hh>
#include <dune/ag-common/assemblers/operatorassembler.hh>
#include <dune/ag-common/assemblers/localassemblers/laplaceassembler.hh>
#include <dune/ag-common/assemblers/localassemblers/massassembler.hh>
#include <dune/solvers/solvers/iterativesolver.hh>
#include <dune/solvers/norms/h1seminorm.hh>
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#include <dune/gfe/unitvector.hh>
#include <dune/gfe/harmonicenergystiffness.hh>
#include <dune/gfe/geodesicfeassembler.hh>
#include <dune/gfe/riemanniantrsolver.hh>
#include <dune/gfe/geodesicfefunctionadaptor.hh>
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// grid dimension
const int dim = 2;
typedef UnitVector<3> TargetSpace;
typedef std::vector<TargetSpace> SolutionType;
const int blocksize = TargetSpace::TangentVector::size;
using namespace Dune;
using std::string;
template <class GridType>
void solve (const shared_ptr<GridType>& grid,
SolutionType& x,
int numLevels,
ConfigParser& parameters)
{
// read solver setting
const double innerTolerance = parameters.get<double>("innerTolerance");
const double tolerance = parameters.get<double>("tolerance");
const int maxTrustRegionSteps = parameters.get<int>("maxTrustRegionSteps");
const double initialTrustRegionRadius = parameters.get<double>("initialTrustRegionRadius");
const int multigridIterations = parameters.get<int>("numIt");
// /////////////////////////////////////////
// Read Dirichlet values
// /////////////////////////////////////////
BitSetVector<1> allNodes(grid->size(dim));
allNodes.setAll();
LeafBoundaryPatch<GridType> dirichletBoundary(*grid, allNodes);
BitSetVector<blocksize> dirichletNodes(grid->size(dim));
for (int i=0; i<dirichletNodes.size(); i++)
dirichletNodes[i] = dirichletBoundary.containsVertex(i);
// //////////////////////////
// Initial solution
// //////////////////////////
x.resize(grid->size(dim));
FieldVector<double,3> yAxis(0);
yAxis[1] = 1;
typename GridType::LeafGridView::template Codim<dim>::Iterator vIt = grid->template leafbegin<dim>();
typename GridType::LeafGridView::template Codim<dim>::Iterator vEndIt = grid->template leafend<dim>();
for (; vIt!=vEndIt; ++vIt) {
int idx = grid->leafIndexSet().index(*vIt);
FieldVector<double,3> v;
FieldVector<double,2> pos = vIt->geometry().corner(0);
FieldVector<double,3> axis;
axis[0] = pos[0]; axis[1] = pos[1]; axis[2] = 1;
Rotation<3,double> rotation(axis, pos.two_norm()*M_PI*3);
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if (dirichletNodes[idx][0]) {
#if 1
FieldMatrix<double,3,3> rMat;
rotation.matrix(rMat);
v = rMat[2];
#else
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v[0] = std::sin(pos[0]*M_PI);
v[1] = 0;
v[2] = std::cos(pos[0]*M_PI);
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} else {
v[0] = 1;
v[1] = 0;
v[2] = 0;
}
x[idx] = v;
}
// ////////////////////////////////////////////////////////////
// Create an assembler for the Harmonic Energy Functional
// ////////////////////////////////////////////////////////////
HarmonicEnergyLocalStiffness<typename GridType::LeafGridView,TargetSpace> harmonicEnergyLocalStiffness;
GeodesicFEAssembler<typename GridType::LeafGridView,TargetSpace> assembler(grid->leafView(),
&harmonicEnergyLocalStiffness);
// ///////////////////////////////////////////
// Create a solver for the rod problem
// ///////////////////////////////////////////
RiemannianTrustRegionSolver<GridType,TargetSpace> solver;
solver.setup(*grid,
&assembler,
x,
dirichletNodes,
tolerance,
maxTrustRegionSteps,
initialTrustRegionRadius,
multigridIterations,
innerTolerance,
1, 3, 3,
100, // iterations of the base solver
1e-8, // base tolerance
false); // instrumentation
// /////////////////////////////////////////////////////
// Solve!
// /////////////////////////////////////////////////////
solver.setInitialSolution(x);
solver.solve();
x = solver.getSol();
}
int main (int argc, char *argv[]) try
{
// parse data file
ConfigParser parameterSet;
if (argc==2)
parameterSet.parseFile(argv[1]);
else
parameterSet.parseFile("harmonicmaps-eoc.parset");
// read solver settings
const int numLevels = parameterSet.get<int>("numLevels");
const int baseIterations = parameterSet.get<int>("baseIt");
const double baseTolerance = parameterSet.get<double>("baseTolerance");
const int numBaseElements = parameterSet.get<int>("numBaseElements");
// /////////////////////////////////////////
// Read Dirichlet values
// /////////////////////////////////////////
// ///////////////////////////////////////////////////////////
// First compute the 'exact' solution on a very fine grid
// ///////////////////////////////////////////////////////////
typedef std::conditional<dim==1,OneDGrid,UGGrid<dim> >::type GridType;
// Create the reference grid
array<unsigned int,dim> elements;
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shared_ptr<GridType> referenceGrid = StructuredGridFactory<GridType>::createSimplexGrid(FieldVector<double,dim>(0),
FieldVector<double,dim>(1),
elements);
referenceGrid->globalRefine(numLevels-1);
// Solve the rod Dirichlet problem
SolutionType referenceSolution;
solve(referenceGrid, referenceSolution, numLevels, parameterSet);
// //////////////////////////////////////////////////////////////////////
// Compute mass matrix and laplace matrix to emulate L2 and H1 norms
// //////////////////////////////////////////////////////////////////////
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typedef P1NodalBasis<GridType::LeafGridView,double> FEBasis;
FEBasis basis(referenceGrid->leafView());
OperatorAssembler<FEBasis,FEBasis> operatorAssembler(basis, basis);
LaplaceAssembler<GridType, FEBasis::LocalFiniteElement, FEBasis::LocalFiniteElement> laplaceLocalAssembler;
MassAssembler<GridType, FEBasis::LocalFiniteElement, FEBasis::LocalFiniteElement> massMatrixLocalAssembler;
typedef Dune::BCRSMatrix<Dune::FieldMatrix<double,1,1> > ScalarMatrixType;
ScalarMatrixType laplace, massMatrix;
operatorAssembler.assemble(laplaceLocalAssembler, laplace);
operatorAssembler.assemble(massMatrixLocalAssembler, massMatrix);
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// ///////////////////////////////////////////////////////////
// Compute on all coarser levels, and compare
// ///////////////////////////////////////////////////////////
for (int i=1; i<=numLevels; i++) {
array<unsigned int,dim> elements;
elements.fill(numBaseElements);
shared_ptr<GridType> grid = StructuredGridFactory<GridType>::createSimplexGrid(FieldVector<double,dim>(0),
FieldVector<double,dim>(1),
elements);
grid->globalRefine(i-1);
// compute again
SolutionType solution;
solve(grid, solution, i, parameterSet);
// write solution
std::stringstream numberAsAscii;
numberAsAscii << i;
BlockVector<FieldVector<double,3> > xEmbedded(solution.size());
for (int j=0; j<solution.size(); j++)
xEmbedded[j] = solution[j].globalCoordinates();
LeafAmiraMeshWriter<GridType> amiramesh;
amiramesh.addGrid(grid->leafView());
amiramesh.addVertexData(xEmbedded, grid->leafView());
amiramesh.write("harmonic_result_" + numberAsAscii.str() + ".am");
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// Prolong solution to the very finest grid
for (int j=i; j<numLevels; j++)
geodesicFEFunctionAdaptor(*grid, solution);
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//assert(referenceSolution.size() == solution.size());
xEmbedded.resize(solution.size());
for (int j=0; j<solution.size(); j++)
xEmbedded[j] = solution[j].globalCoordinates();
LeafAmiraMeshWriter<GridType> amirameshRefined;
amirameshRefined.addGrid(grid->leafView());
amirameshRefined.addVertexData(xEmbedded, grid->leafView());
amirameshRefined.write("harmonic_result_" + numberAsAscii.str() + "_refined.am");
// Interpret TargetSpace as isometrically embedded into an R^m, because this is
// how the corresponding Sobolev spaces are defined.
BlockVector<TargetSpace::TangentVector> difference(referenceSolution.size());
for (int j=0; j<referenceSolution.size(); j++)
difference[j] = solution[j].globalCoordinates() - referenceSolution[j].globalCoordinates();
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H1SemiNorm< BlockVector<TargetSpace::TangentVector> > h1Norm(laplace);
H1SemiNorm< BlockVector<TargetSpace::TangentVector> > l2Norm(massMatrix);
// Compute max-norm difference
std::cout << "Level: " << i-1
<< ", max-norm error: " << difference.infinity_norm()
<< std::endl;
std::cout << "Level: " << i-1
<< ", L2 error: " << l2Norm(difference)
<< std::endl;
std::cout << "Level: " << i-1
<< ", H1 error: " << h1Norm(difference)
<< std::endl;
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}
} catch (Exception e) {
std::cout << e << std::endl;
}