cosserat-continuum.cc

#include <config.h>

#define SECOND_ORDER

#include <fenv.h>

// Includes for the ADOL-C automatic differentiation library
// Need to come before (almost) all others.
#include <adolc/adouble.h>
#include <adolc/drivers/drivers.h>    // use of "Easy to Use" drivers
#include <adolc/taping.h>
#undef overwrite  // stupid: ADOL-C sets this to 1, so the name cannot be used

#include <dune/gfe/adolcnamespaceinjections.hh>
#include <dune/common/bitsetvector.hh>
#include <dune/common/parametertree.hh>
#include <dune/common/parametertreeparser.hh>

#include <dune/grid/uggrid.hh>
#include <dune/grid/onedgrid.hh>
#include <dune/grid/geometrygrid.hh>
#include <dune/grid/utility/structuredgridfactory.hh>

#include <dune/grid/io/file/gmshreader.hh>

#include <dune/fufem/boundarypatch.hh>
#include <dune/fufem/functiontools/boundarydofs.hh>
#include <dune/fufem/functiontools/basisinterpolator.hh>
#include <dune/fufem/functionspacebases/p1nodalbasis.hh>
#include <dune/fufem/functionspacebases/p2nodalbasis.hh>
#include <dune/fufem/dunepython.hh>

#include <dune/solvers/solvers/iterativesolver.hh>
#include <dune/solvers/norms/energynorm.hh>

#include <dune/gfe/rigidbodymotion.hh>
#include <dune/gfe/localgeodesicfeadolcstiffness.hh>
#include <dune/gfe/cosseratenergystiffness.hh>
#include <dune/gfe/cosseratvtkwriter.hh>
#include <dune/gfe/geodesicfeassembler.hh>
#include <dune/gfe/riemanniantrsolver.hh>

// grid dimension
const int dim = 2;

// Image space of the geodesic fe functions
typedef RigidBodyMotion<double,3> TargetSpace;

// Tangent vector of the image space
const int blocksize = TargetSpace::TangentVector::dimension;

using namespace Dune;

class Identity
: public Dune::VirtualFunction<FieldVector<double,dim>, FieldVector<double,3>>
{
public:
  void evaluate(const FieldVector<double,dim>& x, FieldVector<double,3>& y) const
  {
    y = 0;
    for (int i=0; i<dim; i++)
      y[i] = x[i];

    //y[2] = 0.002*std::cos(1e4*x[0]);
  }
};


// Dirichlet boundary data for the shear/wrinkling example
class WrinklingDirichletValues
: public Dune::VirtualFunction<FieldVector<double,dim>, FieldVector<double,3> >
{
  FieldVector<double,2> upper_;
  double homotopy_;
public:
  WrinklingDirichletValues(FieldVector<double,2> upper, double homotopy)
  : upper_(upper), homotopy_(homotopy)
  {}

  void evaluate(const FieldVector<double,dim>& in, FieldVector<double,3>& out) const
  {
    out = 0;
    for (int i=0; i<dim; i++)
      out[i] = in[i];

    //     if (out[1] > 1-1e-3)
    if (out[1] > upper_[1]-1e-4)
      out[0] += 0.003*homotopy_;
  }
};


// Dirichlet boundary data for the 'twisted-strip' example
class TwistedStripDeformationDirichletValues
: public Dune::VirtualFunction<FieldVector<double,dim>, FieldVector<double,3> >
{
  FieldVector<double,2> upper_;
  double homotopy_;
public:

  TwistedStripDeformationDirichletValues(FieldVector<double,2> upper, double homotopy)
  : upper_(upper), homotopy_(homotopy)
  {}

  void evaluate(const FieldVector<double,dim>& in, FieldVector<double,3>& out) const
  {
    double angle = 6*M_PI * in[0]/upper_[0];
    angle *= homotopy_;

    // center of rotation
    FieldVector<double,3> center(0);
    center[1] = upper_[1]/2.0;

    FieldMatrix<double,3,3> rotation(0);
    rotation[0][0] = 1;
    rotation[1][1] =  std::cos(angle);
    rotation[1][2] = -std::sin(angle);
    rotation[2][1] =  std::sin(angle);
    rotation[2][2] =  std::cos(angle);

    FieldVector<double,3> inEmbedded(0);
    for (int i=0; i<dim; i++)
        inEmbedded[i] = in[i];
    inEmbedded -= center;

    rotation.mv(inEmbedded, out);

    out += center;
  }
};

// Dirichlet boundary data for the 'twisted-strip' example
class TwistedStripOrientationDirichletValues
: public Dune::VirtualFunction<FieldVector<double,dim>, FieldMatrix<double,3,3> >
{
  FieldVector<double,2> upper_;
  double homotopy_;
public:

  TwistedStripOrientationDirichletValues(FieldVector<double,2> upper, double homotopy)
  : upper_(upper), homotopy_(homotopy)
  {}

  void evaluate(const FieldVector<double,dim>& in, FieldMatrix<double,3,3>& out) const
  {
    double angle = 6*M_PI * in[0]/upper_[0];
    angle *= homotopy_;

    // center of rotation
    FieldMatrix<double,3,3> rotation(0);
    rotation[0][0] = 1;
    rotation[1][1] =  std::cos(angle);
    rotation[1][2] = -std::sin(angle);
    rotation[2][1] =  std::sin(angle);
    rotation[2][2] =  std::cos(angle);

    out = rotation;
  }
};


/** \brief A constant vector-valued function, for simple Neumann boundary values */
struct NeumannFunction
    : public Dune::VirtualFunction<FieldVector<double,dim>, FieldVector<double,3> >
{
    NeumannFunction(const FieldVector<double,3> values,
                    double homotopyParameter)
    : values_(values),
      homotopyParameter_(homotopyParameter)
    {}

    void evaluate(const FieldVector<double, dim>& x, FieldVector<double,3>& out) const {
        out = 0;
        out.axpy(homotopyParameter_, values_);
    }

    FieldVector<double,3> values_;
    double homotopyParameter_;
};


int main (int argc, char *argv[]) try
{
    // initialize MPI, finalize is done automatically on exit
    Dune::MPIHelper& mpiHelper = MPIHelper::instance(argc, argv);

    // Start Python interpreter
    Python::start();
    Python::Reference main = Python::import("__main__");

    //feenableexcept(FE_INVALID);

    typedef std::vector<TargetSpace> SolutionType;

    // parse data file
    ParameterTree parameterSet;
    if (argc != 2)
      DUNE_THROW(Exception, "Usage: ./cosserat-continuum <parameter file>");

    ParameterTreeParser::readINITree(argv[1], parameterSet);

    ParameterTreeParser::readOptions(argc, argv, parameterSet);

    // read solver settings
    const int numLevels                   = parameterSet.get<int>("numLevels");
    int numHomotopySteps                  = parameterSet.get<int>("numHomotopySteps");
    const double tolerance                = parameterSet.get<double>("tolerance");
    const int maxTrustRegionSteps         = parameterSet.get<int>("maxTrustRegionSteps");
    const double initialTrustRegionRadius = parameterSet.get<double>("initialTrustRegionRadius");
    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 bool instrumented               = parameterSet.get<bool>("instrumented");
    std::string resultPath                = parameterSet.get("resultPath", "");

    // ///////////////////////////////////////
    //    Create the grid
    // ///////////////////////////////////////
    typedef std::conditional<dim==1,OneDGrid,UGGrid<dim> >::type GridType;

    shared_ptr<GridType> grid;

    FieldVector<double,dim> lower, upper;

    if (parameterSet.get<bool>("structuredGrid")) {

        lower = parameterSet.get<FieldVector<double,dim> >("lower");
        upper = parameterSet.get<FieldVector<double,dim> >("upper");

        array<unsigned int,dim> elements = parameterSet.get<array<unsigned int,dim> >("elements");
        grid = StructuredGridFactory<GridType>::createCubeGrid(lower, upper, elements);

    } else {
        std::string path                = parameterSet.get<std::string>("path");
        std::string gridFile            = parameterSet.get<std::string>("gridFile");
        grid = shared_ptr<GridType>(GmshReader<GridType>::read(path + "/" + gridFile));
    }

    grid->globalRefine(numLevels-1);

    grid->loadBalance();

    if (mpiHelper.rank()==0)
      std::cout << "There are " << grid->leafGridView().comm().size() << " processes" << std::endl;

    typedef GridType::LeafGridView GridView;
    GridView gridView = grid->leafGridView();

#ifdef SECOND_ORDER
    typedef P2NodalBasis<GridView,double> FEBasis;
#else
    typedef P1NodalBasis<GridView,double> FEBasis;
#endif
    FEBasis feBasis(gridView);

    // /////////////////////////////////////////
    //   Read Dirichlet values
    // /////////////////////////////////////////

    BitSetVector<1> dirichletVertices(feBasis.size(), false);
    BitSetVector<1> neumannNodes(feBasis.size(), false);

    GridType::Codim<dim>::LeafIterator vIt    = gridView.begin<dim>();
    GridType::Codim<dim>::LeafIterator vEndIt = gridView.end<dim>();

    const GridView::IndexSet& indexSet = gridView.indexSet();

    // Make Python function that computes which vertices are on the Dirichlet boundary,
    // based on the vertex positions.
    std::string lambda = std::string("lambda x: (") + parameterSet.get<std::string>("dirichletVerticesPredicate") + std::string(")");
    PythonFunction<FieldVector<double,dim>, int> pythonDirichletVertices(Python::evaluate(lambda));

    // Same for the Neumann boundary
    lambda = std::string("lambda x: (") + parameterSet.get<std::string>("neumannVerticesPredicate", "0") + std::string(")");
    PythonFunction<FieldVector<double,dim>, int> pythonNeumannVertices(Python::evaluate(lambda));

    for (; vIt!=vEndIt; ++vIt) {

        int isDirichlet;
        pythonDirichletVertices.evaluate(vIt->geometry().corner(0), isDirichlet);
        dirichletVertices[indexSet.index(*vIt)] = isDirichlet;

        int isNeumann;
        pythonNeumannVertices.evaluate(vIt->geometry().corner(0), isNeumann);
        neumannNodes[indexSet.index(*vIt)] = isNeumann;

    }

    BoundaryPatch<GridView> dirichletBoundary(gridView, dirichletVertices);
    BoundaryPatch<GridView> neumannBoundary(gridView, neumannNodes);

    if (mpiHelper.rank()==0)
      std::cout << "Neumann boundary has " << neumannBoundary.numFaces() << " faces\n";


    BitSetVector<1> dirichletNodes(feBasis.size(), false);
    constructBoundaryDofs(dirichletBoundary,feBasis,dirichletNodes);

    BitSetVector<blocksize> dirichletDofs(feBasis.size(), false);
    for (size_t i=0; i<feBasis.size(); i++)
      if (dirichletNodes[i][0])
        for (int j=0; j<5; j++)
          dirichletDofs[i][j] = true;

    // //////////////////////////
    //   Initial iterate
    // //////////////////////////

    SolutionType x(feBasis.size());

    Identity identity;
    std::vector<FieldVector<double,3> > v;
    Functions::interpolate(feBasis, v, identity);

    for (size_t i=0; i<x.size(); i++)
      x[i].r = v[i];

    ////////////////////////////////////////////////////////
    //   Main homotopy loop
    ////////////////////////////////////////////////////////

    // Output initial iterate (of homotopy loop)
    CosseratVTKWriter<GridType>::write<FEBasis>(feBasis,x, resultPath + "cosserat_homotopy_0");

    for (int i=0; i<numHomotopySteps; i++) {

        double homotopyParameter = (i+1)*(1.0/numHomotopySteps);
        if (mpiHelper.rank()==0)
            std::cout << "Homotopy step: " << i << ",    parameter: " << homotopyParameter << std::endl;


    // ////////////////////////////////////////////////////////////
    //   Create an assembler for the energy functional
    // ////////////////////////////////////////////////////////////

    const ParameterTree& materialParameters = parameterSet.sub("materialParameters");
    shared_ptr<NeumannFunction> neumannFunction;
    if (parameterSet.hasKey("neumannValues"))
        neumannFunction = make_shared<NeumannFunction>(parameterSet.get<FieldVector<double,3> >("neumannValues"),
                                                       homotopyParameter);


        if (mpiHelper.rank() == 0) {
            std::cout << "Material parameters:" << std::endl;
            materialParameters.report();
        }

    // Assembler using ADOL-C
    CosseratEnergyLocalStiffness<GridView,
                                 FEBasis::LocalFiniteElement,
                                 3,adouble> cosseratEnergyADOLCLocalStiffness(materialParameters,
                                                                              &neumannBoundary,
                                                                              neumannFunction.get());
    LocalGeodesicFEADOLCStiffness<GridView,
                                  FEBasis::LocalFiniteElement,
                                  TargetSpace> localGFEADOLCStiffness(&cosseratEnergyADOLCLocalStiffness);

    GeodesicFEAssembler<FEBasis,TargetSpace> assembler(gridView, &localGFEADOLCStiffness);

    // /////////////////////////////////////////////////
    //   Create a Riemannian trust-region solver
    // /////////////////////////////////////////////////

    RiemannianTrustRegionSolver<GridType,TargetSpace> solver;
    solver.setup(*grid,
                 &assembler,
                 x,
                 dirichletDofs,
                 tolerance,
                 maxTrustRegionSteps,
                 initialTrustRegionRadius,
                 multigridIterations,
                 mgTolerance,
                 mu, nu1, nu2,
                 baseIterations,
                 baseTolerance,
                 instrumented);

        ////////////////////////////////////////////////////////
        //   Set Dirichlet values
        ////////////////////////////////////////////////////////

        TwistedStripDeformationDirichletValues deformationDirichletValues(upper,homotopyParameter);
        std::vector<FieldVector<double,3> > ddV;
        Functions::interpolate(feBasis, ddV, deformationDirichletValues, dirichletDofs);


        TwistedStripOrientationDirichletValues orientationDirichletValues(upper,homotopyParameter);
        std::vector<FieldMatrix<double,3,3> > dOV;
        Functions::interpolate(feBasis, dOV, orientationDirichletValues, dirichletDofs);

        for (size_t j=0; j<x.size(); j++)
          if (dirichletNodes[j][0])
          {
            x[j].r = ddV[j];
            x[j].q.set(dOV[j]);
          }

        // /////////////////////////////////////////////////////
        //   Solve!
        // /////////////////////////////////////////////////////

        solver.setInitialIterate(x);
        solver.solve();

        x = solver.getSol();

        // Output result of each homotopy step
        std::stringstream iAsAscii;
        iAsAscii << i+1;
        CosseratVTKWriter<GridType>::write<FEBasis>(feBasis,x, resultPath + "cosserat_homotopy_" + iAsAscii.str());

    }

    // //////////////////////////////
    //   Output result
    // //////////////////////////////

    CosseratVTKWriter<GridType>::write<FEBasis>(feBasis,x, resultPath + "cosserat");

    // finally: compute the average deformation of the Neumann boundary
    // That is what we need for the locking tests
    FieldVector<double,3> averageDef(0);
    for (size_t i=0; i<x.size(); i++)
        if (neumannNodes[i][0])
            averageDef += x[i].r;
    averageDef /= neumannNodes.count();

    if (mpiHelper.rank()==0)
    {
    std::cout << "mu_c = " << parameterSet.get<double>("materialParameters.mu_c") << "  "
              << "kappa = " << parameterSet.get<double>("materialParameters.kappa") << "  "
              << numLevels << " levels,  average deflection: " << averageDef << std::endl;
    }

    // //////////////////////////////
 } catch (Exception e) {

    std::cout << e << std::endl;

 }