one-body-sample.cc

#include <Python.h>

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#ifndef HAVE_PYTHON
#error Python is required
#endif

#ifdef HAVE_IPOPT
#undef HAVE_IPOPT
#endif

#ifndef srcdir
#error srcdir unset
#endif

#ifndef DIM
#error DIM unset
#endif

#if !HAVE_ALUGRID
#error ALUGRID is required
#endif

#include <cmath>
#include <exception>
#include <fstream>
#include <iostream>

#include <boost/format.hpp>

#include <dune/common/bitsetvector.hh>
#include <dune/common/exceptions.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/function.hh>
#include <dune/common/fvector.hh>
#include <dune/common/parametertree.hh>
#include <dune/common/parametertreeparser.hh>
#include <dune/common/shared_ptr.hh>

#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wignored-qualifiers"
#include <dune/grid/alugrid.hh>
#pragma clang diagnostic pop

#include <dune/grid/common/mcmgmapper.hh>
#include <dune/grid/utility/structuredgridfactory.hh>
#include <dune/istl/bcrsmatrix.hh>
#include <dune/istl/bvector.hh>
#include <dune/istl/scaledidmatrix.hh>

#include <dune/fufem/assemblers/assembler.hh>
#include <dune/fufem/assemblers/localassemblers/boundarymassassembler.hh>
#include <dune/fufem/assemblers/localassemblers/l2functionalassembler.hh>
#include <dune/fufem/assemblers/localassemblers/massassembler.hh>
#include <dune/fufem/assemblers/localassemblers/stvenantkirchhoffassembler.hh>
#include <dune/fufem/assemblers/localassemblers/viscosityassembler.hh>
#include <dune/fufem/assemblers/localassemblers/vonmisesstressassembler.hh>
#include <dune/fufem/boundarypatch.hh>
#include <dune/fufem/dunepython.hh>
#include <dune/fufem/functions/basisgridfunction.hh>
#include <dune/fufem/functions/constantfunction.hh>

#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wsign-compare"
#include <dune/fufem/functionspacebases/p0basis.hh>
#pragma clang diagnostic pop

#include <dune/fufem/functionspacebases/p1nodalbasis.hh>
#include <dune/fufem/sharedpointermap.hh>
#include <dune/solvers/norms/energynorm.hh>
#include <dune/solvers/norms/sumnorm.hh>
#include <dune/solvers/solvers/loopsolver.hh>
#include <dune/solvers/solvers/solver.hh>
#include <dune/tnnmg/problem-classes/convexproblem.hh>
#include <dune/tnnmg/nonlinearities/zerononlinearity.hh>
#include <dune/tnnmg/problem-classes/blocknonlineartnnmgproblem.hh>

#include <dune/tectonic/myblockproblem.hh>
#include <dune/tectonic/globalnonlinearity.hh>

#include "assemblers.hh"
#include "friction_writer.hh"
#include "solverfactory.hh"
#include "vtk.hh"

#include "enums.hh"
#include "enum_parser.cc"
#include "enum_state_model.cc"
#include "enum_scheme.cc"
#include "enum_verbosity.cc"

#include "timestepping.hh"

#include "state/stateupdater.hh"
#include "state/ruinastateupdater.hh"
#include "state/dieterichstateupdater.hh"

size_t const dims = DIM;

template <class VectorType, class MatrixType, class FunctionType, int dimension>
Dune::shared_ptr<
    TimeSteppingScheme<VectorType, MatrixType, FunctionType, dimension>>
initTimeStepper(Config::scheme scheme,
                FunctionType const &velocityDirichletFunction,
                Dune::BitSetVector<dimension> const &velocityDirichletNodes,
                MatrixType const &massMatrix, MatrixType const &stiffnessMatrix,
                MatrixType const &dampingMatrix, VectorType const &u_initial,
                VectorType const &v_initial, VectorType const &a_initial) {
  switch (scheme) {
    case Config::Newmark:
      return Dune::make_shared<
          Newmark<VectorType, MatrixType, FunctionType, dims>>(
          stiffnessMatrix, massMatrix, dampingMatrix, u_initial, v_initial,
          a_initial, velocityDirichletNodes, velocityDirichletFunction);
    case Config::BackwardEuler:
      return Dune::make_shared<
          BackwardEuler<VectorType, MatrixType, FunctionType, dims>>(
          stiffnessMatrix, massMatrix, dampingMatrix, u_initial, v_initial,
          velocityDirichletNodes, velocityDirichletFunction);
    default:
      assert(false);
  }
}

template <class SingletonVectorType, class VectorType>
Dune::shared_ptr<StateUpdater<SingletonVectorType, VectorType>>
initStateUpdater(Config::stateModel model,
                 SingletonVectorType const &alpha_initial,
                 Dune::BitSetVector<1> const &frictionalNodes,
                 FrictionData const &fd) {
  switch (model) {
    case Config::Dieterich:
      return Dune::make_shared<
          DieterichStateUpdater<SingletonVectorType, VectorType>>(
          alpha_initial, frictionalNodes, fd.L);
    case Config::Ruina:
      return Dune::make_shared<
          RuinaStateUpdater<SingletonVectorType, VectorType>>(
          alpha_initial, frictionalNodes, fd.L);
    default:
      assert(false);
  }
}

void initPython() {
  Python::start();

  Python::run("import sys");
  Python::run("sys.path.append('" srcdir "')");
}

int main(int argc, char *argv[]) {
  try {
    Dune::ParameterTree parset;
    Dune::ParameterTreeParser::readINITree(srcdir "/one-body-sample.parset",
                                           parset);
    Dune::ParameterTreeParser::readOptions(argc, argv, parset);

    using SmallVector = Dune::FieldVector<double, dims>;
    using SmallMatrix = Dune::FieldMatrix<double, dims, dims>;
    using SmallSingletonMatrix = Dune::FieldMatrix<double, 1, 1>;
    using MatrixType = Dune::BCRSMatrix<SmallMatrix>;
    using SingletonMatrixType = Dune::BCRSMatrix<SmallSingletonMatrix>;
    using VectorType = Dune::BlockVector<SmallVector>;
    using SingletonVectorType = Dune::BlockVector<Dune::FieldVector<double, 1>>;
    using NonlinearityType = Dune::GlobalNonlinearity<MatrixType, VectorType>;

    auto const E = parset.get<double>("body.E");
    auto const nu = parset.get<double>("body.nu");

    // {{{ Set up grid
    using GridType =
        Dune::ALUGrid<dims, dims, Dune::simplex, Dune::nonconforming>;

    Dune::FieldVector<typename GridType::ctype, dims> lowerLeft(0);
    Dune::FieldVector<typename GridType::ctype, dims> upperRight(1);
    upperRight[0] = parset.get<size_t>("body.width");
    upperRight[1] = parset.get<size_t>("body.height");

    Dune::shared_ptr<GridType> grid;
    {
      Dune::array<unsigned int, dims> elements;
      std::fill(elements.begin(), elements.end(), 1);
      elements[0] = parset.get<size_t>("body.width");
      elements[1] = parset.get<size_t>("body.height");

      grid = Dune::StructuredGridFactory<GridType>::createSimplexGrid(
          lowerLeft, upperRight, elements);
    }

    auto const refinements = parset.get<size_t>("grid.refinements");
    grid->globalRefine(refinements);
    size_t const fineVertexCount = grid->size(grid->maxLevel(), dims);

    using GridView = GridType::LeafGridView;
    GridView const leafView = grid->leafView();
    // }}}

    // Set up bases
    using P0Basis = P0Basis<GridView, double>;
    using P1Basis = P1NodalBasis<GridView, double>;
    P0Basis const p0Basis(leafView);
    P1Basis const p1Basis(leafView);
    Assembler<P0Basis, P0Basis> const p0Assembler(p0Basis, p0Basis);
    Assembler<P1Basis, P1Basis> const p1Assembler(p1Basis, p1Basis);

    // Set up the boundary
    Dune::BitSetVector<dims> velocityDirichletNodes(fineVertexCount, false);
    Dune::BitSetVector<dims> const &displacementDirichletNodes =
        velocityDirichletNodes;
    Dune::BitSetVector<dims> accelerationDirichletNodes(fineVertexCount, false);
    Dune::BitSetVector<1> neumannNodes(fineVertexCount, false);
    Dune::BitSetVector<1> frictionalNodes(fineVertexCount, false);

    VectorType vertexCoordinates(fineVertexCount);
    {
      Dune::MultipleCodimMultipleGeomTypeMapper<
          GridView, Dune::MCMGVertexLayout> const vertexMapper(leafView);
      for (auto it = leafView.begin<dims>(); it != leafView.end<dims>(); ++it) {
        assert(it->geometry().corners() == 1);
        size_t const id = vertexMapper.map(*it);
        vertexCoordinates[id] = it->geometry().corner(0);
        auto const &localCoordinates = vertexCoordinates[id];

        // lower face
        if (localCoordinates[1] == lowerLeft[1]) {
          frictionalNodes[id] = true;
          velocityDirichletNodes[id][1] = true;
        }

        // upper face
        else if (localCoordinates[1] == upperRight[1])
          velocityDirichletNodes[id] = true;

        // right face (except for both corners)
        else if (localCoordinates[0] == upperRight[0])
          ;

        // left face (except for both corners)
        else if (localCoordinates[0] == lowerLeft[0])
          ;
      }
    }
    BoundaryPatch<GridView> const frictionalBoundary(leafView, frictionalNodes);

    // Set up functions for time-dependent boundary conditions
    using FunctionType = Dune::VirtualFunction<double, double>;
    using FunctionMap = SharedPointerMap<std::string, FunctionType>;
    FunctionMap functions;
    {
      initPython();
      Python::import("one-body-sample")
          .get("Functions")
          .toC<typename FunctionMap::Base>(functions);
    }
    auto const &velocityDirichletFunction =
                   functions.get("velocityDirichletCondition"),
               &neumannFunction = functions.get("neumannCondition");

    // Set up normal stress, mass matrix, and gravity functional
    double normalStress;
    MatrixType M;
    EnergyNorm<MatrixType, VectorType> const MNorm(M);
    VectorType gravityFunctional;
    {
      double const gravity = 9.81;
      double const density = parset.get<double>("body.density");
      {
        MassAssembler<GridType, P1Basis::LocalFiniteElement,
                      P1Basis::LocalFiniteElement,
                      Dune::ScaledIdentityMatrix<double, dims>> const localMass;
        p1Assembler.assembleOperator(localMass, M);
        M *= density;
      }
      {
        double volume = 1.0;
        for (size_t i = 0; i < dims; ++i)
          volume *= (upperRight[i] - lowerLeft[i]);

        double area = 1.0;
        for (size_t i = 0; i < dims; ++i)
          if (i != 1)
            area *= (upperRight[i] - lowerLeft[i]);

        // volume * gravity * density / area    = normal stress
        // V      * g       * rho     / A       = sigma_n
        // m^d    * N/kg    * kg/m^d  / m^(d-1) = N/m^(d-1)
        normalStress = volume * gravity * density / area;
      }
      {
        SmallVector weightedGravitationalDirection(0);
        weightedGravitationalDirection[1] = -density * gravity;
        ConstantFunction<SmallVector, SmallVector> const gravityFunction(
            weightedGravitationalDirection);
        L2FunctionalAssembler<GridType, P1Basis::LocalFiniteElement,
                              SmallVector>
        gravityFunctionalAssembler(gravityFunction);
        p1Assembler.assembleFunctional(gravityFunctionalAssembler,
                                       gravityFunctional);
      }
    }
    FrictionData const frictionData(parset.sub("boundary.friction"),
                                    normalStress);

    MatrixType A;
    EnergyNorm<MatrixType, VectorType> const ANorm(A);
    {
      StVenantKirchhoffAssembler<GridType, P1Basis::LocalFiniteElement,
                                 P1Basis::LocalFiniteElement> const
      localStiffness(E, nu);
      p1Assembler.assembleOperator(localStiffness, A);
    }
    MatrixType C;
    {
      ViscosityAssembler<GridType, P1Basis::LocalFiniteElement,
                         P1Basis::LocalFiniteElement> const
      localViscosity(parset.get<double>("body.shearViscosity"),
                     parset.get<double>("body.bulkViscosity"));
      p1Assembler.assembleOperator(localViscosity, C);
    }

    SingletonMatrixType frictionalBoundaryMassMatrix;
    EnergyNorm<SingletonMatrixType, SingletonVectorType> const stateEnergyNorm(
        frictionalBoundaryMassMatrix);
    {
      BoundaryMassAssembler<
          GridType, BoundaryPatch<GridView>, P1Basis::LocalFiniteElement,
          P1Basis::LocalFiniteElement, SmallSingletonMatrix> const
      frictionalBoundaryMassAssembler(frictionalBoundary);
      p1Assembler.assembleOperator(frictionalBoundaryMassAssembler,
                                   frictionalBoundaryMassMatrix);
    }
    // Q: Does it make sense to weigh them in this manner?
    SumNorm<VectorType> const AMNorm(1.0, ANorm, 1.0, MNorm);

    auto const nodalIntegrals =
        assembleFrictionWeightsal<GridView, SmallVector>(leafView, p1Assembler,
                                                         frictionalNodes);
    auto myGlobalNonlinearity = assembleNonlinearity<MatrixType, VectorType>(
        frictionalNodes, *nodalIntegrals, frictionData);

    // Problem formulation: right-hand side
    auto const createRHS = [&](double _relativeTime, VectorType &_ell) {
      assembleNeumann(leafView, p1Assembler, neumannNodes, _ell,
                      neumannFunction, _relativeTime);
      _ell += gravityFunctional;
    };
    VectorType ell(fineVertexCount);
    createRHS(0.0, ell);

    // {{{ Initial conditions
    SingletonVectorType alpha_initial(fineVertexCount);
    alpha_initial =
        std::log(parset.get<double>("boundary.friction.initialState"));

    using LinearFactoryType = SolverFactory<
        dims, BlockNonlinearTNNMGProblem<ConvexProblem<
                  ZeroNonlinearity<SmallVector, SmallMatrix>, MatrixType>>,
        GridType>;
    ZeroNonlinearity<SmallVector, SmallMatrix> zeroNonlinearity;

    // Solve the stationary problem
    VectorType u_initial(fineVertexCount);
    u_initial = 0.0;
    {
      LinearFactoryType displacementFactory(parset.sub("solver.tnnmg"), // FIXME
                                            refinements, *grid,
                                            displacementDirichletNodes);
      auto multigridStep = displacementFactory.getSolver();

      typename LinearFactoryType::ConvexProblemType convexProblem(
          1.0, A, zeroNonlinearity, ell, u_initial);
      typename LinearFactoryType::BlockProblemType initialDisplacementProblem(
          parset, convexProblem);

      auto const &localParset = parset.sub("u0.solver");
      multigridStep->setProblem(u_initial, initialDisplacementProblem);
      LoopSolver<VectorType> initialDisplacementProblemSolver(
          multigridStep, localParset.get<size_t>("maximumIterations"),
          localParset.get<double>("tolerance"), &ANorm,
          localParset.get<Solver::VerbosityMode>("verbosity"),
          false); // absolute error

      initialDisplacementProblemSolver.preprocess();
      initialDisplacementProblemSolver.solve();
    }
    VectorType v_initial(fineVertexCount);
    v_initial = 0.0;
    {
      // Prescribe a homogeneous velocity field in the x-direction
      // This way, the initial condition for v and the Dirichlet
      // condition match up at t=0
      double v_initial_const;
      velocityDirichletFunction.evaluate(0.0, v_initial_const);
      for (auto &x : v_initial)
        x[0] = v_initial_const;
    }
    VectorType a_initial(fineVertexCount);
    a_initial = 0.0;
    {
      /* We solve Au + Cv + Ma + Psi(v) = ell, thus
                                     Ma = - (Au + Cv + Psi(v) - ell)
      */
      VectorType accelerationRHS(fineVertexCount);
      {
        accelerationRHS = 0.0;
        Arithmetic::addProduct(accelerationRHS, A, u_initial);
        Arithmetic::addProduct(accelerationRHS, C, v_initial);
        myGlobalNonlinearity->updateLogState(alpha_initial);
        // NOTE: We assume differentiability of Psi at v0 here!
        myGlobalNonlinearity->addGradient(v_initial, accelerationRHS);
        accelerationRHS -= ell;
        accelerationRHS *= -1.0;
      }
      LinearFactoryType accelerationFactory(parset.sub("solver.tnnmg"), // FIXME
                                            refinements, *grid,
                                            accelerationDirichletNodes);
      auto multigridStep = accelerationFactory.getSolver();

      typename LinearFactoryType::ConvexProblemType convexProblem(
          1.0, M, zeroNonlinearity, accelerationRHS, a_initial);
      typename LinearFactoryType::BlockProblemType initialAccelerationProblem(
          parset, convexProblem);

      auto const &localParset = parset.sub("a0.solver");
      multigridStep->setProblem(a_initial, initialAccelerationProblem);
      LoopSolver<VectorType> initialAccelerationProblemSolver(
          multigridStep, localParset.get<size_t>("maximumIterations"),
          localParset.get<double>("tolerance"), &MNorm,
          localParset.get<Solver::VerbosityMode>("verbosity"),
          false); // absolute error

      initialAccelerationProblemSolver.preprocess();
      initialAccelerationProblemSolver.solve();
    }
    // }}}
    FrictionWriter<Dune::BitSetVector<1>> writer(frictionData, frictionalNodes);
    writer.writeInfo(alpha_initial, u_initial, v_initial);

    // Set up TNNMG solver
    using NonlinearFactoryType = SolverFactory<
        dims,
        MyBlockProblem<ConvexProblem<
            Dune::GlobalNonlinearity<MatrixType, VectorType>, MatrixType>>,
        GridType>;
    NonlinearFactoryType factory(parset.sub("solver.tnnmg"), refinements, *grid,
                                 velocityDirichletNodes);
    auto multigridStep = factory.getSolver();

    {
      std::fstream vertexCoordinateWriter("coordinates", std::fstream::out);
      for (size_t i = 0; i < fineVertexCount; ++i)
        if (frictionalNodes[i][0])
          vertexCoordinateWriter << vertexCoordinates[i] << std::endl;
      vertexCoordinateWriter.close();
    }
    std::fstream iterationWriter("iterations", std::fstream::out),
        relaxationWriter("relaxation", std::fstream::out);

    auto timeSteppingScheme =
        initTimeStepper(parset.get<Config::scheme>("timeSteps.scheme"),
                        velocityDirichletFunction, velocityDirichletNodes, M, A,
                        C, u_initial, v_initial, a_initial);
    auto stateUpdater = initStateUpdater<SingletonVectorType, VectorType>(
        parset.get<Config::stateModel>("boundary.friction.stateModel"),
        alpha_initial, frictionalNodes, frictionData);

    VectorType v = v_initial;
    SingletonVectorType alpha(fineVertexCount);

    auto const timesteps = parset.get<size_t>("timeSteps.number"),
               maximumStateFPI = parset.get<size_t>("v.fpi.maximumIterations"),
               maximumIterations =
                   parset.get<size_t>("v.solver.maximumIterations");
    auto const tau = parset.get<double>("problem.finalTime") / timesteps,
               tolerance = parset.get<double>("v.solver.tolerance"),
               fixedPointTolerance = parset.get<double>("v.fpi.tolerance"),
               relaxation = parset.get<double>("v.fpi.relaxation"),
               requiredReduction =
                   parset.get<double>("v.fpi.requiredReduction");
    auto const printProgress = parset.get<bool>("io.printProgress");
    auto const verbosity =
        parset.get<Solver::VerbosityMode>("v.solver.verbosity");
    for (size_t run = 1; run <= timesteps; ++run) {
      if (printProgress)
        std::cout << boost::format("%7d ") % run << " " << std::flush;

      stateUpdater->nextTimeStep();
      timeSteppingScheme->nextTimeStep();

      auto const relativeTime = double(run) / double(timesteps);
      createRHS(relativeTime, ell);

      MatrixType velocityMatrix;
      VectorType velocityRHS(fineVertexCount);
      VectorType velocityIterate(fineVertexCount);

      stateUpdater->setup(tau);
      timeSteppingScheme->setup(ell, tau, relativeTime, velocityRHS,
                                velocityIterate, velocityMatrix);

      LoopSolver<VectorType> velocityProblemSolver(
          multigridStep, maximumIterations, tolerance, &AMNorm, verbosity,
          false); // absolute error

      size_t iterationCounter;
      auto solveVelocityProblem = [&](VectorType &_velocityIterate,
                                      SingletonVectorType const &_alpha) {
        myGlobalNonlinearity->updateLogState(_alpha);

        // NIT: Do we really need to pass u here?
        typename NonlinearFactoryType::ConvexProblemType const convexProblem(
            1.0, velocityMatrix, *myGlobalNonlinearity, velocityRHS,
            _velocityIterate);
        typename NonlinearFactoryType::BlockProblemType velocityProblem(
            parset, convexProblem);
        multigridStep->setProblem(_velocityIterate, velocityProblem);

        velocityProblemSolver.preprocess();
        velocityProblemSolver.solve();
        iterationCounter = velocityProblemSolver.getResult().iterations;
      };

      // Since the velocity explodes in the quasistatic case, use the
      // displacement as a convergence criterion
      // Q: is this reasonable?
      VectorType u;
      VectorType u_saved;
      SingletonVectorType alpha_saved;
      double lastStateCorrection;
      for (size_t stateFPI = 1; stateFPI <= maximumStateFPI; ++stateFPI) {
        stateUpdater->solve(v);
        stateUpdater->extractLogState(alpha);

        if (stateFPI == 1)
          relaxationWriter << "N ";
        else {
          double const stateCorrection =
              stateEnergyNorm.diff(alpha, alpha_saved);
          if (stateFPI <= 2 // lastStateCorrection is only set for stateFPI > 2
              or stateCorrection < requiredReduction * lastStateCorrection)
            relaxationWriter << "N ";
          else {
            alpha *= (1.0 - relaxation);
            Arithmetic::addProduct(alpha, relaxation, alpha_saved);
            relaxationWriter << "Y ";
          }
          lastStateCorrection = stateCorrection;
        }

        solveVelocityProblem(velocityIterate, alpha);
        timeSteppingScheme->postProcess(velocityIterate);
        timeSteppingScheme->extractDisplacement(u);
        timeSteppingScheme->extractVelocity(v);

        iterationWriter << iterationCounter << " ";
        if (printProgress)
          std::cout << '.' << std::flush;

        if (stateFPI > 1) {
          double const velocityCorrection = AMNorm.diff(u_saved, u);
          if (velocityCorrection < fixedPointTolerance)
            break;
        }
        if (stateFPI == maximumStateFPI)
          DUNE_THROW(Dune::Exception, "FPI failed to converge");

        alpha_saved = alpha;
        u_saved = u;
      }
      if (printProgress)
        std::cout << std::endl;

      writer.writeInfo(alpha, u, v);
      iterationWriter << std::endl;
      relaxationWriter << std::endl;

      if (parset.get<bool>("io.writeVTK")) {
        auto const gridDisplacement =
            Dune::make_shared<BasisGridFunction<P1Basis, VectorType> const>(
                p1Basis, u);
        SingletonVectorType vonMisesStress;
        VonMisesStressAssembler<GridType, P0Basis::LocalFiniteElement>
        localStressAssembler(E, nu, gridDisplacement);
        p0Assembler.assembleFunctional(localStressAssembler, vonMisesStress);

        writeVtk(p1Basis, u, alpha, p0Basis, vonMisesStress,
                 (boost::format("obs%d") % run).str());
      }
    }
    iterationWriter.close();
    relaxationWriter.close();

    Python::stop();
  }
  catch (Dune::Exception &e) {
    Dune::derr << "Dune reported error: " << e << std::endl;
  }
  catch (std::exception &e) {
    std::cerr << "Standard exception: " << e.what() << std::endl;
  }
}