elliptic.hh

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/**************************************************************************
 
  The dune-fem module is a module of DUNE (see www.dune-project.org).
  It is based on the dune-grid interface library
  extending the grid interface by a number of discretization algorithms
  for solving non-linear systems of partial differential equations.
 
  Copyright (C) 2003 - 2015 Robert Kloefkorn
  Copyright (C) 2003 - 2010 Mario Ohlberger
  Copyright (C) 2004 - 2015 Andreas Dedner
  Copyright (C) 2005        Adrian Burri
  Copyright (C) 2005 - 2015 Mirko Kraenkel
  Copyright (C) 2006 - 2015 Christoph Gersbacher
  Copyright (C) 2006 - 2015 Martin Nolte
  Copyright (C) 2011 - 2015 Tobias Malkmus
  Copyright (C) 2012 - 2015 Stefan Girke
  Copyright (C) 2013 - 2015 Claus-Justus Heine
  Copyright (C) 2013 - 2014 Janick Gerstenberger
  Copyright (C) 2013        Sven Kaulman
  Copyright (C) 2013        Tom Ranner
  Copyright (C) 2015        Marco Agnese
  Copyright (C) 2015        Martin Alkaemper
 
 
  The dune-fem module is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 2 of
  the License, or (at your option) any later version.
 
  The dune-fem module is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License along
  with this program; if not, write to the Free Software Foundation, Inc.,
  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 
**************************************************************************/
#ifndef DUNE_FEM_SCHEMES_ELLIPTIC_HH
#define DUNE_FEM_SCHEMES_ELLIPTIC_HH
 
#include <cstddef>
 
#include <dune/common/timer.hh>
#include <dune/common/fmatrix.hh>
 
#include <dune/fem/quadrature/cachingquadrature.hh>
#include <dune/fem/operator/common/operator.hh>
#include <dune/fem/operator/common/stencil.hh>
 
#include <dune/fem/common/bindguard.hh>
#include <dune/fem/function/common/localcontribution.hh>
#include <dune/fem/function/localfunction/const.hh>
 
#include <dune/fem/operator/common/differentiableoperator.hh>
#include <dune/fem/operator/common/temporarylocalmatrix.hh>
 
 
// include parameter handling
#include <dune/fem/io/parameter.hh>
#include <dune/fem/io/file/dataoutput.hh>
 
// fempy includes
#include <dune/fempy/quadrature/fempyquadratures.hh>
 
// EllipticOperator
// ----------------
 
template< class DomainDiscreteFunction, class RangeDiscreteFunction, class Model>
struct EllipticOperator
: public virtual Dune::Fem::Operator< DomainDiscreteFunction, RangeDiscreteFunction >
{
  typedef DomainDiscreteFunction DomainFunctionType;
  typedef RangeDiscreteFunction  RangeFunctionType;
  typedef Model                  ModelType;
  typedef Model                  DirichletModelType;
 
  typedef typename DomainFunctionType::DiscreteFunctionSpaceType DomainDiscreteFunctionSpaceType;
  typedef typename DomainFunctionType::LocalFunctionType         DomainLocalFunctionType;
  typedef typename DomainLocalFunctionType::RangeType                    DomainRangeType;
  typedef typename DomainLocalFunctionType::JacobianRangeType            DomainJacobianRangeType;
  typedef typename RangeFunctionType::DiscreteFunctionSpaceType RangeDiscreteFunctionSpaceType;
  typedef typename RangeFunctionType::LocalFunctionType         RangeLocalFunctionType;
  typedef typename RangeLocalFunctionType::RangeType                    RangeRangeType;
  typedef typename RangeLocalFunctionType::JacobianRangeType            RangeJacobianRangeType;
 
  // the following types must be identical for domain and range
  typedef typename RangeDiscreteFunctionSpaceType::IteratorType IteratorType;
  typedef typename IteratorType::Entity       EntityType;
  typedef typename EntityType::Geometry       GeometryType;
  typedef typename RangeDiscreteFunctionSpaceType::DomainType DomainType;
  typedef typename RangeDiscreteFunctionSpaceType::GridPartType  GridPartType;
  typedef typename GridPartType::IntersectionIteratorType IntersectionIteratorType;
  typedef typename IntersectionIteratorType::Intersection IntersectionType;
 
  typedef Dune::Fem::CachingQuadrature< GridPartType, 0, Dune::FemPy::FempyQuadratureTraits > QuadratureType;
  typedef Dune::Fem::CachingQuadrature< GridPartType, 1, Dune::FemPy::FempyQuadratureTraits > FaceQuadratureType;
 
  EllipticOperator ( const RangeDiscreteFunctionSpaceType &rangeSpace,
                     ModelType &model,
                     const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : model_( model ),
      dSpace_(rangeSpace), rSpace_(rangeSpace)
  {}
  EllipticOperator ( const DomainDiscreteFunctionSpaceType &dSpace,
                     const RangeDiscreteFunctionSpaceType &rSpace,
                     ModelType &model,
                     const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : model_( model ),
      dSpace_(dSpace), rSpace_(rSpace),
      interiorOrder_(-1), surfaceOrder_(-1)
  {}
 
  virtual void operator() ( const DomainFunctionType &u, RangeFunctionType &w ) const
  { apply(u,w); }
  template <class GF>
  void operator()( const GF &u, RangeFunctionType &w ) const
  { apply(u,w); }
  template <class GF>
  void apply( const GF &u, RangeFunctionType &w ) const;
 
  const DomainDiscreteFunctionSpaceType& domainSpace() const
  {
    return dSpace_;
  }
  const RangeDiscreteFunctionSpaceType& rangeSpace() const
  {
    return rSpace_;
  }
  const ModelType &model () const { return model_; }
  ModelType &model () { return model_; }
 
  void setQuadratureOrders(unsigned int interior, unsigned int surface)
  {
    interiorOrder_ = interior;
    surfaceOrder_ = surface;
  }
 
protected:
  int interiorOrder_, surfaceOrder_;
private:
  ModelType &model_;
  const DomainDiscreteFunctionSpaceType &dSpace_;
  const RangeDiscreteFunctionSpaceType &rSpace_;
};
 
 
 
// DifferentiableEllipticOperator
// ------------------------------
 
template< class JacobianOperator, class Model >
struct DifferentiableEllipticOperator
: public EllipticOperator< typename JacobianOperator::DomainFunctionType, typename JacobianOperator::RangeFunctionType, Model >,
  public Dune::Fem::DifferentiableOperator< JacobianOperator >
{
  typedef EllipticOperator< typename JacobianOperator::DomainFunctionType, typename JacobianOperator::RangeFunctionType, Model > BaseType;
 
  typedef JacobianOperator JacobianOperatorType;
 
  typedef typename BaseType::DomainFunctionType DomainFunctionType;
  typedef typename BaseType::RangeFunctionType  RangeFunctionType;
  typedef typename BaseType::ModelType ModelType;
 
  typedef typename DomainFunctionType::DiscreteFunctionSpaceType DomainDiscreteFunctionSpaceType;
  typedef typename DomainFunctionType::LocalFunctionType         DomainLocalFunctionType;
  typedef typename DomainLocalFunctionType::RangeType                    DomainRangeType;
  typedef typename DomainLocalFunctionType::JacobianRangeType            DomainJacobianRangeType;
  typedef typename RangeFunctionType::DiscreteFunctionSpaceType RangeDiscreteFunctionSpaceType;
  typedef typename RangeFunctionType::LocalFunctionType         RangeLocalFunctionType;
  typedef typename RangeLocalFunctionType::RangeType                    RangeRangeType;
  typedef typename RangeLocalFunctionType::JacobianRangeType            RangeJacobianRangeType;
 
  // the following types must be identical for domain and range
  typedef typename RangeDiscreteFunctionSpaceType::IteratorType IteratorType;
  typedef typename IteratorType::Entity       EntityType;
  typedef typename EntityType::Geometry       GeometryType;
  typedef typename RangeDiscreteFunctionSpaceType::DomainType DomainType;
  typedef typename RangeDiscreteFunctionSpaceType::GridPartType  GridPartType;
  typedef typename GridPartType::IntersectionIteratorType IntersectionIteratorType;
  typedef typename IntersectionIteratorType::Intersection IntersectionType;
 
  typedef typename BaseType::QuadratureType QuadratureType;
  // quadrature for faces - used for Neuman b.c.
  typedef typename BaseType::FaceQuadratureType FaceQuadratureType;
 
  DifferentiableEllipticOperator ( const RangeDiscreteFunctionSpaceType &space,
                                   ModelType &model,
                                   const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
  : BaseType( space, space, model, parameter )
  {}
  DifferentiableEllipticOperator ( const DomainDiscreteFunctionSpaceType &dSpace,
                                   const RangeDiscreteFunctionSpaceType &rSpace,
                                   ModelType &model,
                                   const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
  : BaseType( dSpace, rSpace, model, parameter )
  {}
 
  void jacobian ( const DomainFunctionType &u, JacobianOperatorType &jOp ) const
  { assemble(u,jOp); }
  template <class GridFunctionType>
  void jacobian ( const GridFunctionType &u, JacobianOperatorType &jOp ) const
  { assemble(u,jOp); }
  template <class GridFunctionType>
  void assemble ( const GridFunctionType &u, JacobianOperatorType &jOp ) const;
  using BaseType::operator();
 
  using BaseType::model;
  using BaseType::interiorOrder_;
  using BaseType::surfaceOrder_;
};
 
 
 
// Implementation of EllipticOperator
// ----------------------------------
 
template< class DomainDiscreteFunction, class RangeDiscreteFunction, class Model >
template<class GF>
void EllipticOperator< DomainDiscreteFunction, RangeDiscreteFunction, Model >
  ::apply( const GF &u, RangeFunctionType &w ) const
{
  w.clear();
  // get discrete function space
  const RangeDiscreteFunctionSpaceType &dfSpace = w.space();
 
  // get local representation of the discrete functions
  Dune::Fem::ConstLocalFunction< GF > uLocal( u );
  Dune::Fem::AddLocalContribution< RangeFunctionType > wLocal( w );
 
  // iterate over grid
  for( const EntityType &entity : dfSpace )
  {
    if( !model().init( entity ) )
      continue;
 
    // get elements geometry
    const GeometryType &geometry = entity.geometry();
 
    auto uGuard = Dune::Fem::bindGuard( uLocal, entity );
    auto wGuard = Dune::Fem::bindGuard( wLocal, entity );
 
    // obtain quadrature order
    const int quadOrder = interiorOrder_==-1?
      uLocal.order() + wLocal.order() : interiorOrder_;
 
    { // element integral
      QuadratureType quadrature( entity, quadOrder );
      const size_t numQuadraturePoints = quadrature.nop();
      for( size_t pt = 0; pt < numQuadraturePoints; ++pt )
      {
        const typename QuadratureType::CoordinateType &x = quadrature.point( pt );
        const double weight = quadrature.weight( pt ) * geometry.integrationElement( x );
 
        DomainRangeType vu;
        uLocal.evaluate( quadrature[ pt ], vu );
        DomainJacobianRangeType du;
        uLocal.jacobian( quadrature[ pt ], du );
 
        // compute mass contribution (studying linear case so linearizing around zero)
        RangeRangeType avu( 0 );
        model().source( quadrature[ pt ], vu, du, avu );
        avu *= weight;
        // add to local functional wLocal.axpy( quadrature[ pt ], avu );
 
        RangeJacobianRangeType adu( 0 );
        // apply diffusive flux
        model().flux( quadrature[ pt ], vu, du, adu );
        adu *= weight;
 
        // add to local function
        wLocal.axpy( quadrature[ pt ], avu, adu );
      }
    }
 
    if( model().hasNeumanBoundary() && entity.hasBoundaryIntersections() )
    {
      const IntersectionIteratorType iitend = dfSpace.gridPart().iend( entity );
      for( IntersectionIteratorType iit = dfSpace.gridPart().ibegin( entity ); iit != iitend; ++iit )
      {
        const IntersectionType &intersection = *iit;
        if( !intersection.boundary() )
          continue;
 
        std::array<int,RangeRangeType::dimension> components(0);
 
        const bool hasDirichletComponent = model().isDirichletIntersection( intersection, components );
 
        const auto &intersectionGeometry = intersection.geometry();
        const int quadOrder = surfaceOrder_==-1?
          uLocal.order() + wLocal.order() : surfaceOrder_;
        FaceQuadratureType quadInside( dfSpace.gridPart(), intersection, quadOrder, FaceQuadratureType::INSIDE );
        const std::size_t numQuadraturePoints = quadInside.nop();
        for( std::size_t pt = 0; pt < numQuadraturePoints; ++pt )
        {
          const auto &x = quadInside.localPoint( pt );
          double weight = quadInside.weight( pt ) * intersectionGeometry.integrationElement( x );
          DomainRangeType vu;
          uLocal.evaluate( quadInside[ pt ], vu );
          RangeRangeType alpha( 0 );
          model().alpha( quadInside[ pt ], vu, alpha );
          alpha *= weight;
          for( int k = 0; k < RangeRangeType::dimension; ++k )
            if( hasDirichletComponent && components[ k ] )
              alpha[ k ] = 0;
          wLocal.axpy( quadInside[ pt ], alpha );
        }
      }
    }
  }
 
  w.communicate();
}
 
 
 
// Implementation of DifferentiableEllipticOperator
// ------------------------------------------------
 
template< class JacobianOperator, class Model >
template<class GF>
void DifferentiableEllipticOperator< JacobianOperator, Model >
  ::assemble ( const GF &u, JacobianOperator &jOp ) const
{
  // std::cout << "starting assembly\n";
  // Dune::Timer timer;
  typedef typename DomainDiscreteFunctionSpaceType::BasisFunctionSetType DomainBasisFunctionSetType;
  typedef typename RangeDiscreteFunctionSpaceType::BasisFunctionSetType  RangeBasisFunctionSetType;
  typedef Dune::Fem::TemporaryLocalMatrix< DomainDiscreteFunctionSpaceType, RangeDiscreteFunctionSpaceType > TmpLocalMatrixType;
 
  const DomainDiscreteFunctionSpaceType &domainSpace = jOp.domainSpace();
  const RangeDiscreteFunctionSpaceType  &rangeSpace = jOp.rangeSpace();
 
  Dune::Fem::DiagonalStencil<DomainDiscreteFunctionSpaceType,RangeDiscreteFunctionSpaceType> stencil( domainSpace, rangeSpace );
  jOp.reserve(stencil);
  jOp.clear();
  TmpLocalMatrixType jLocal( domainSpace, rangeSpace );
 
  const int domainBlockSize = domainSpace.localBlockSize; // is equal to 1 for scalar functions
  std::vector< typename DomainLocalFunctionType::RangeType >         phi( domainSpace.blockMapper().maxNumDofs()*domainBlockSize );
  std::vector< typename DomainLocalFunctionType::JacobianRangeType > dphi( domainSpace.blockMapper().maxNumDofs()*domainBlockSize );
  const int rangeBlockSize = rangeSpace.localBlockSize; // is equal to 1 for scalar functions
  std::vector< typename RangeLocalFunctionType::RangeType >         rphi( rangeSpace.blockMapper().maxNumDofs()*rangeBlockSize );
  std::vector< typename RangeLocalFunctionType::JacobianRangeType > rdphi( rangeSpace.blockMapper().maxNumDofs()*rangeBlockSize );
 
  Dune::Fem::ConstLocalFunction< GF > uLocal( u );
  // std::cout << "   in assembly: start element loop size=" << rangeSpace.gridPart().grid().size(0) << " time=  " << timer.elapsed() << std::endl;;
  for( const EntityType &entity : rangeSpace )
  {
    if( !model().init( entity ) )
      continue;
 
    const GeometryType &geometry = entity.geometry();
 
    auto uGuard = Dune::Fem::bindGuard( uLocal, entity );
    jLocal.bind( entity, entity );
    jLocal.clear();
 
    const DomainBasisFunctionSetType &domainBaseSet = jLocal.domainBasisFunctionSet();
    const RangeBasisFunctionSetType &rangeBaseSet  = jLocal.rangeBasisFunctionSet();
    const std::size_t domainNumBasisFunctions = domainBaseSet.size();
 
    const int quadOrder = interiorOrder_==-1?
      domainSpace.order() + rangeSpace.order() : interiorOrder_;
    QuadratureType quadrature( entity, quadOrder );
    const size_t numQuadraturePoints = quadrature.nop();
    for( size_t pt = 0; pt < numQuadraturePoints; ++pt )
    {
      const typename QuadratureType::CoordinateType &x = quadrature.point( pt );
      const double weight = quadrature.weight( pt ) * geometry.integrationElement( x );
 
      // evaluate all basis functions at given quadrature point
      domainBaseSet.evaluateAll( quadrature[ pt ], phi );
      rangeBaseSet.evaluateAll( quadrature[ pt ], rphi );
 
      // evaluate jacobians of all basis functions at given quadrature point
      domainBaseSet.jacobianAll( quadrature[ pt ], dphi );
      rangeBaseSet.jacobianAll( quadrature[ pt ], rdphi );
 
      // get value for linearization
      DomainRangeType u0;
      DomainJacobianRangeType jacU0;
      uLocal.evaluate( quadrature[ pt ], u0 );
      uLocal.jacobian( quadrature[ pt ], jacU0 );
 
      RangeRangeType aphi( 0 );
      RangeJacobianRangeType adphi( 0 );
      for( std::size_t localCol = 0; localCol < domainNumBasisFunctions; ++localCol )
      {
        // if mass terms or right hand side is present
        model().linSource( u0, jacU0, quadrature[ pt ], phi[ localCol ], dphi[localCol], aphi );
 
        // if gradient term is present
        model().linFlux( u0, jacU0, quadrature[ pt ], phi[ localCol ], dphi[ localCol ], adphi );
 
        // get column object and call axpy method
        jLocal.column( localCol ).axpy( rphi, rdphi, aphi, adphi, weight );
      }
    }
 
    if( model().hasNeumanBoundary() && entity.hasBoundaryIntersections() )
    {
      const IntersectionIteratorType iitend = rangeSpace.gridPart().iend( entity );
      for( IntersectionIteratorType iit = rangeSpace.gridPart().ibegin( entity ); iit != iitend; ++iit ) // looping over intersections
      {
        const IntersectionType &intersection = *iit;
        if( !intersection.boundary() )
          continue;
 
        std::array<int,RangeRangeType::dimension> components(0);
        bool hasDirichletComponent = model().isDirichletIntersection( intersection, components );
 
        const auto &intersectionGeometry = intersection.geometry();
        const int quadOrder = surfaceOrder_==-1?
          domainSpace.order() + rangeSpace.order() : surfaceOrder_;
        FaceQuadratureType quadInside( rangeSpace.gridPart(), intersection, quadOrder, FaceQuadratureType::INSIDE );
        const std::size_t numQuadraturePoints = quadInside.nop();
        for( std::size_t pt = 0; pt < numQuadraturePoints; ++pt )
        {
          const auto &x = quadInside.localPoint( pt );
          const double weight = quadInside.weight( pt ) * intersectionGeometry.integrationElement( x );
          DomainRangeType u0;
          uLocal.evaluate( quadInside[ pt ], u0 );
          domainBaseSet.evaluateAll( quadInside[ pt ], phi );
          for( std::size_t localCol = 0; localCol < domainNumBasisFunctions; ++localCol )
          {
            RangeRangeType alpha( 0 );
            model().linAlpha( u0,quadInside[ pt ], phi[ localCol ], alpha );
            for( int k = 0; k < RangeRangeType::dimension; ++k )
              if( hasDirichletComponent && components[ k ] )
                alpha[ k ] = 0;
            jLocal.column( localCol ).axpy( phi, alpha, weight );
          }
        }
      }
    }
    jOp.addLocalMatrix( entity, entity, jLocal );
    jLocal.unbind();
  } // end grid traversal
  // std::cout << "   in assembly: final    " << timer.elapsed() << std::endl;;
  jOp.flushAssembly();
}
#endif // #ifndef DUNE_FEM_SCHEMES_ELLIPTIC_HH