discretization/box/fvgridgeometry.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_GRID_FVGEOMETRY_HH
#define DUMUX_DISCRETIZATION_BOX_GRID_FVGEOMETRY_HH
 
#include <unordered_map>
 
#include <dune/geometry/referenceelements.hh>
#include <dune/localfunctions/lagrange/pqkfactory.hh>
 
#include <dumux/discretization/method.hh>
#include <dumux/common/indextraits.hh>
#include <dumux/common/defaultmappertraits.hh>
#include <dumux/discretization/basegridgeometry.hh>
#include <dumux/discretization/checkoverlapsize.hh>
#include <dumux/discretization/box/boxgeometryhelper.hh>
#include <dumux/discretization/box/fvelementgeometry.hh>
#include <dumux/discretization/box/subcontrolvolume.hh>
#include <dumux/discretization/box/subcontrolvolumeface.hh>
 
namespace Dumux {

template<class GridView, class MapperTraits = DefaultMapperTraits<GridView>>
struct BoxDefaultGridGeometryTraits
: public MapperTraits
{
    using SubControlVolume = BoxSubControlVolume<GridView>;
    using SubControlVolumeFace = BoxSubControlVolumeFace<GridView>;
 
    template<class GridGeometry, bool enableCache>
    using LocalView = BoxFVElementGeometry<GridGeometry, enableCache>;
};

template<class Scalar,
         class GridView,
         bool enableGridGeometryCache = false,
         class Traits = BoxDefaultGridGeometryTraits<GridView> >
class BoxFVGridGeometry;

template<class Scalar, class GV, class Traits>
class BoxFVGridGeometry<Scalar, GV, true, Traits>
: public BaseGridGeometry<GV, Traits>
{
    using ThisType = BoxFVGridGeometry<Scalar, GV, true, Traits>;
    using ParentType = BaseGridGeometry<GV, Traits>;
    using GridIndexType = typename IndexTraits<GV>::GridIndex;
    using LocalIndexType = typename IndexTraits<GV>::LocalIndex;
 
    using Element = typename GV::template Codim<0>::Entity;
    using CoordScalar = typename GV::ctype;
    static const int dim = GV::dimension;
    static const int dimWorld = GV::dimensionworld;
 
    using ReferenceElements = typename Dune::ReferenceElements<CoordScalar, dim>;
 
    using GeometryHelper = BoxGeometryHelper<GV, dim,
                                             typename Traits::SubControlVolume,
                                             typename Traits::SubControlVolumeFace>;
 
public:
    static constexpr DiscretizationMethod discMethod = DiscretizationMethod::box;

    using LocalView = typename Traits::template LocalView<ThisType, true>;
    using SubControlVolume = typename Traits::SubControlVolume;
    using SubControlVolumeFace = typename Traits::SubControlVolumeFace;
    using DofMapper = typename Traits::VertexMapper;
    using FeCache = Dune::PQkLocalFiniteElementCache<CoordScalar, Scalar, dim, 1>;
    using GridView = GV;

    BoxFVGridGeometry(const GridView gridView)
    : ParentType(gridView)
    {
        // Check if the overlap size is what we expect
        if (!CheckOverlapSize<DiscretizationMethod::box>::isValid(gridView))
            DUNE_THROW(Dune::InvalidStateException, "The box discretization method only works with zero overlap for parallel computations. "
                                                     << " Set the parameter \"Grid.Overlap\" in the input file.");
    }

    const DofMapper& dofMapper() const
    { return this->vertexMapper(); }

    std::size_t numScv() const
    {  return numScv_; }

    std::size_t numScvf() const
    { return numScvf_; }

    std::size_t numBoundaryScvf() const
    { return numBoundaryScvf_; }

    std::size_t numDofs() const
    { return this->vertexMapper().size(); }

    void update()
    {
        ParentType::update();
 
        scvs_.clear();
        scvfs_.clear();
 
        auto numElements = this->gridView().size(0);
        scvs_.resize(numElements);
        scvfs_.resize(numElements);
        hasBoundaryScvf_.resize(numElements, false);
 
        boundaryDofIndices_.assign(numDofs(), false);
 
        numScv_ = 0;
        numScvf_ = 0;
        numBoundaryScvf_ = 0;
        // Build the SCV and SCV faces
        for (const auto& element : elements(this->gridView()))
        {
            // fill the element map with seeds
            auto eIdx = this->elementMapper().index(element);
 
            // count
            numScv_ += element.subEntities(dim);
            numScvf_ += element.subEntities(dim-1);
 
            // get the element geometry
            auto elementGeometry = element.geometry();
            const auto referenceElement = ReferenceElements::general(elementGeometry.type());
 
            // instantiate the geometry helper
            GeometryHelper geometryHelper(elementGeometry);
 
            // construct the sub control volumes
            scvs_[eIdx].resize(elementGeometry.corners());
            for (LocalIndexType scvLocalIdx = 0; scvLocalIdx < elementGeometry.corners(); ++scvLocalIdx)
            {
                const auto dofIdxGlobal = this->vertexMapper().subIndex(element, scvLocalIdx, dim);
 
                scvs_[eIdx][scvLocalIdx] = SubControlVolume(geometryHelper,
                                                            scvLocalIdx,
                                                            eIdx,
                                                            dofIdxGlobal);
            }
 
            // construct the sub control volume faces
            LocalIndexType scvfLocalIdx = 0;
            scvfs_[eIdx].resize(element.subEntities(dim-1));
            for (; scvfLocalIdx < element.subEntities(dim-1); ++scvfLocalIdx)
            {
                // find the global and local scv indices this scvf is belonging to
                std::vector<LocalIndexType> localScvIndices({static_cast<LocalIndexType>(referenceElement.subEntity(scvfLocalIdx, dim-1, 0, dim)),
                                                             static_cast<LocalIndexType>(referenceElement.subEntity(scvfLocalIdx, dim-1, 1, dim))});
 
                scvfs_[eIdx][scvfLocalIdx] = SubControlVolumeFace(geometryHelper,
                                                                  element,
                                                                  elementGeometry,
                                                                  scvfLocalIdx,
                                                                  std::move(localScvIndices),
                                                                  false);
            }
 
            // construct the sub control volume faces on the domain boundary
            for (const auto& intersection : intersections(this->gridView(), element))
            {
                if (intersection.boundary() && !intersection.neighbor())
                {
                    const auto isGeometry = intersection.geometry();
                    hasBoundaryScvf_[eIdx] = true;
 
                    // count
                    numScvf_ += isGeometry.corners();
                    numBoundaryScvf_ += isGeometry.corners();
 
                    for (unsigned int isScvfLocalIdx = 0; isScvfLocalIdx < isGeometry.corners(); ++isScvfLocalIdx)
                    {
                        // find the scvs this scvf is belonging to
                        const LocalIndexType insideScvIdx = static_cast<LocalIndexType>(referenceElement.subEntity(intersection.indexInInside(), 1, isScvfLocalIdx, dim));
                        std::vector<LocalIndexType> localScvIndices = {insideScvIdx, insideScvIdx};
 
                        scvfs_[eIdx].emplace_back(geometryHelper,
                                                  intersection,
                                                  isGeometry,
                                                  isScvfLocalIdx,
                                                  scvfLocalIdx,
                                                  std::move(localScvIndices),
                                                  true);
 
                        // increment local counter
                        scvfLocalIdx++;
                    }
 
                    // add all vertices on the intersection to the set of
                    // boundary vertices
                    const auto fIdx = intersection.indexInInside();
                    const auto numFaceVerts = referenceElement.size(fIdx, 1, dim);
                    for (int localVIdx = 0; localVIdx < numFaceVerts; ++localVIdx)
                    {
                        const auto vIdx = referenceElement.subEntity(fIdx, 1, localVIdx, dim);
                        const auto vIdxGlobal = this->vertexMapper().subIndex(element, vIdx, dim);
                        boundaryDofIndices_[vIdxGlobal] = true;
                    }
                }
 
                // inform the grid geometry if we have periodic boundaries
                else if (intersection.boundary() && intersection.neighbor())
                {
                    this->setPeriodic();
 
                    // find the mapped periodic vertex of all vertices on periodic boundaries
                    const auto fIdx = intersection.indexInInside();
                    const auto numFaceVerts = referenceElement.size(fIdx, 1, dim);
                    const auto eps = 1e-7*(elementGeometry.corner(1) - elementGeometry.corner(0)).two_norm();
                    for (int localVIdx = 0; localVIdx < numFaceVerts; ++localVIdx)
                    {
                        const auto vIdx = referenceElement.subEntity(fIdx, 1, localVIdx, dim);
                        const auto vIdxGlobal = this->vertexMapper().subIndex(element, vIdx, dim);
                        const auto vPos = elementGeometry.corner(vIdx);
 
                        const auto& outside = intersection.outside();
                        const auto outsideGeometry = outside.geometry();
                        for (const auto& isOutside : intersections(this->gridView(), outside))
                        {
                            // only check periodic vertices of the periodic neighbor
                            if (isOutside.boundary() && isOutside.neighbor())
                            {
                                const auto fIdxOutside = isOutside.indexInInside();
                                const auto numFaceVertsOutside = referenceElement.size(fIdxOutside, 1, dim);
                                for (int localVIdxOutside = 0; localVIdxOutside < numFaceVertsOutside; ++localVIdxOutside)
                                {
                                    const auto vIdxOutside = referenceElement.subEntity(fIdxOutside, 1, localVIdxOutside, dim);
                                    const auto vPosOutside = outsideGeometry.corner(vIdxOutside);
                                    const auto shift = std::abs((this->bBoxMax()-this->bBoxMin())*intersection.centerUnitOuterNormal());
                                    if (std::abs((vPosOutside-vPos).two_norm() - shift) < eps)
                                        periodicVertexMap_[vIdxGlobal] = this->vertexMapper().subIndex(outside, vIdxOutside, dim);
                                }
                            }
                        }
                    }
                }
            }
        }
 
        // error check: periodic boundaries currently don't work for box in parallel
        if (this->isPeriodic() && this->gridView().comm().size() > 1)
            DUNE_THROW(Dune::NotImplemented, "Periodic boundaries for box method for parallel simulations!");
    }

    const FeCache& feCache() const
    { return feCache_; }

    const std::vector<SubControlVolume>& scvs(GridIndexType eIdx) const
    { return scvs_[eIdx]; }

    const std::vector<SubControlVolumeFace>& scvfs(GridIndexType eIdx) const
    { return scvfs_[eIdx]; }

    bool dofOnBoundary(GridIndexType dofIdx) const
    { return boundaryDofIndices_[dofIdx]; }

    bool dofOnPeriodicBoundary(GridIndexType dofIdx) const
    { return periodicVertexMap_.count(dofIdx); }

    GridIndexType periodicallyMappedDof(GridIndexType dofIdx) const
    { return periodicVertexMap_.at(dofIdx); }

    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
    { return periodicVertexMap_; }

    bool hasBoundaryScvf(GridIndexType eIdx) const
    { return hasBoundaryScvf_[eIdx]; }
 
private:
 
    const FeCache feCache_;
 
    std::vector<std::vector<SubControlVolume>> scvs_;
    std::vector<std::vector<SubControlVolumeFace>> scvfs_;
    // TODO do we need those?
    std::size_t numScv_;
    std::size_t numScvf_;
    std::size_t numBoundaryScvf_;
 
    // vertices on the boudary
    std::vector<bool> boundaryDofIndices_;
    std::vector<bool> hasBoundaryScvf_;
 
    // a map for periodic boundary vertices
    std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap_;
};

template<class Scalar, class GV, class Traits>
class BoxFVGridGeometry<Scalar, GV, false, Traits>
: public BaseGridGeometry<GV, Traits>
{
    using ThisType = BoxFVGridGeometry<Scalar, GV, false, Traits>;
    using ParentType = BaseGridGeometry<GV, Traits>;
    using GridIndexType = typename IndexTraits<GV>::GridIndex;
 
    static const int dim = GV::dimension;
    static const int dimWorld = GV::dimensionworld;
 
    using Element = typename GV::template Codim<0>::Entity;
    using CoordScalar = typename GV::ctype;
 
    using ReferenceElements = typename Dune::ReferenceElements<CoordScalar, dim>;
 
public:
    static constexpr DiscretizationMethod discMethod = DiscretizationMethod::box;

    using LocalView = typename Traits::template LocalView<ThisType, false>;
    using SubControlVolume = typename Traits::SubControlVolume;
    using SubControlVolumeFace = typename Traits::SubControlVolumeFace;
    using DofMapper = typename Traits::VertexMapper;
    using FeCache = Dune::PQkLocalFiniteElementCache<CoordScalar, Scalar, dim, 1>;
    using GridView = GV;

    BoxFVGridGeometry(const GridView gridView)
    : ParentType(gridView)
    {
        // Check if the overlap size is what we expect
        if (!CheckOverlapSize<DiscretizationMethod::box>::isValid(gridView))
            DUNE_THROW(Dune::InvalidStateException, "The box discretization method only works with zero overlap for parallel computations. "
                                                     << " Set the parameter \"Grid.Overlap\" in the input file.");
    }

    const DofMapper& dofMapper() const
    { return this->vertexMapper(); }

    std::size_t numScv() const
    {  return numScv_; }

    std::size_t numScvf() const
    { return numScvf_; }

    std::size_t numBoundaryScvf() const
    { return numBoundaryScvf_; }

    std::size_t numDofs() const
    { return this->vertexMapper().size(); }

    void update()
    {
        ParentType::update();
 
        boundaryDofIndices_.assign(numDofs(), false);
 
        // save global data on the grid's scvs and scvfs
        // TODO do we need those information?
        numScv_ = 0;
        numScvf_ = 0;
        numBoundaryScvf_ = 0;
        for (const auto& element : elements(this->gridView()))
        {
            numScv_ += element.subEntities(dim);
            numScvf_ += element.subEntities(dim-1);
 
            const auto elementGeometry = element.geometry();
            const auto referenceElement = ReferenceElements::general(elementGeometry.type());
 
            // store the sub control volume face indices on the domain boundary
            for (const auto& intersection : intersections(this->gridView(), element))
            {
                if (intersection.boundary() && !intersection.neighbor())
                {
                    const auto isGeometry = intersection.geometry();
                    numScvf_ += isGeometry.corners();
                    numBoundaryScvf_ += isGeometry.corners();
 
                    // add all vertices on the intersection to the set of
                    // boundary vertices
                    const auto fIdx = intersection.indexInInside();
                    const auto numFaceVerts = referenceElement.size(fIdx, 1, dim);
                    for (int localVIdx = 0; localVIdx < numFaceVerts; ++localVIdx)
                    {
                        const auto vIdx = referenceElement.subEntity(fIdx, 1, localVIdx, dim);
                        const auto vIdxGlobal = this->vertexMapper().subIndex(element, vIdx, dim);
                        boundaryDofIndices_[vIdxGlobal] = true;
                    }
                }
 
                // inform the grid geometry if we have periodic boundaries
                else if (intersection.boundary() && intersection.neighbor())
                {
                    this->setPeriodic();
 
                    // find the mapped periodic vertex of all vertices on periodic boundaries
                    const auto fIdx = intersection.indexInInside();
                    const auto numFaceVerts = referenceElement.size(fIdx, 1, dim);
                    const auto eps = 1e-7*(elementGeometry.corner(1) - elementGeometry.corner(0)).two_norm();
                    for (int localVIdx = 0; localVIdx < numFaceVerts; ++localVIdx)
                    {
                        const auto vIdx = referenceElement.subEntity(fIdx, 1, localVIdx, dim);
                        const auto vIdxGlobal = this->vertexMapper().subIndex(element, vIdx, dim);
                        const auto vPos = elementGeometry.corner(vIdx);
 
                        const auto& outside = intersection.outside();
                        const auto outsideGeometry = outside.geometry();
                        for (const auto& isOutside : intersections(this->gridView(), outside))
                        {
                            // only check periodic vertices of the periodic neighbor
                            if (isOutside.boundary() && isOutside.neighbor())
                            {
                                const auto fIdxOutside = isOutside.indexInInside();
                                const auto numFaceVertsOutside = referenceElement.size(fIdxOutside, 1, dim);
                                for (int localVIdxOutside = 0; localVIdxOutside < numFaceVertsOutside; ++localVIdxOutside)
                                {
                                    const auto vIdxOutside = referenceElement.subEntity(fIdxOutside, 1, localVIdxOutside, dim);
                                    const auto vPosOutside = outsideGeometry.corner(vIdxOutside);
                                    const auto shift = std::abs((this->bBoxMax()-this->bBoxMin())*intersection.centerUnitOuterNormal());
                                    if (std::abs((vPosOutside-vPos).two_norm() - shift) < eps)
                                        periodicVertexMap_[vIdxGlobal] = this->vertexMapper().subIndex(outside, vIdxOutside, dim);
                                }
                            }
                        }
                    }
                }
            }
        }
 
        // error check: periodic boundaries currently don't work for box in parallel
        if (this->isPeriodic() && this->gridView().comm().size() > 1)
            DUNE_THROW(Dune::NotImplemented, "Periodic boundaries for box method for parallel simulations!");
    }

    const FeCache& feCache() const
    { return feCache_; }

    bool dofOnBoundary(GridIndexType dofIdx) const
    { return boundaryDofIndices_[dofIdx]; }

    bool dofOnPeriodicBoundary(GridIndexType dofIdx) const
    { return periodicVertexMap_.count(dofIdx); }

    GridIndexType periodicallyMappedDof(GridIndexType dofIdx) const
    { return periodicVertexMap_.at(dofIdx); }

    const std::unordered_map<GridIndexType, GridIndexType>& periodicVertexMap() const
    { return periodicVertexMap_; }
 
private:
 
    const FeCache feCache_;
 
    // Information on the global number of geometries
    // TODO do we need those information?
    std::size_t numScv_;
    std::size_t numScvf_;
    std::size_t numBoundaryScvf_;
 
    // vertices on the boudary
    std::vector<bool> boundaryDofIndices_;
 
    // a map for periodic boundary vertices
    std::unordered_map<GridIndexType, GridIndexType> periodicVertexMap_;
};
 
} // end namespace Dumux
 
#endif