discretization/box/fvelementgeometry.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
//
// SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_DISCRETIZATION_BOX_FV_ELEMENT_GEOMETRY_HH
#define DUMUX_DISCRETIZATION_BOX_FV_ELEMENT_GEOMETRY_HH
 
#include <optional>
#include <span>
#include <utility>
#include <unordered_map>
#include <array>
#include <vector>
 
#include <dune/geometry/type.hh>
#include <dune/localfunctions/lagrange/pqkfactory.hh>
#include <dune/common/reservedvector.hh>
 
#include <dumux/common/indextraits.hh>
#include <dumux/discretization/scvandscvfiterators.hh>
#include <dumux/discretization/box/boxgeometryhelper.hh>
#include <dumux/discretization/cvfe/localdof.hh>
#include <dumux/discretization/cvfe/interpolationpointdata.hh>
#include <dumux/discretization/cvfe/quadraturerules.hh>
 
namespace Dumux {

template<class GG, bool enableGridGeometryCache>
class BoxFVElementGeometry;

template<class GG>
class BoxFVElementGeometry<GG, true>
{
    using GridView = typename GG::GridView;
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
    using GridIndexType = typename IndexTraits<GridView>::GridIndex;
    using LocalIndexType = typename IndexTraits<GridView>::LocalIndex;
    using CoordScalar = typename GridView::ctype;
    using FeLocalBasis = typename GG::FeCache::FiniteElementType::Traits::LocalBasisType;
    using GGCache = typename GG::Cache;
    using GeometryHelper = typename GGCache::GeometryHelper;
    using DofHelper = typename GGCache::DofHelper;
 
    using BaseIpData = CVFE::InterpolationPointData<
                        typename GridView::template Codim<0>::Entity::Geometry::LocalCoordinate,
                        typename GridView::template Codim<0>::Entity::Geometry::GlobalCoordinate
                        >;
 
public:
    using Element = typename GridView::template Codim<0>::Entity;
    using SubControlVolume = typename GG::SubControlVolume;
    using SubControlVolumeFace = typename GG::SubControlVolumeFace;
    using GridGeometry = GG;
    using BoundaryFace = typename GG::BoundaryFace;
    using ScvQuadratureRule = typename GG::ScvQuadratureRule;
    using ScvfQuadratureRule = typename GG::ScvfQuadratureRule;
    static constexpr std::size_t maxNumElementScvs = (1<<dim);

    BoxFVElementGeometry(const GGCache& ggCache)
    : ggCache_(&ggCache) {}

    const SubControlVolume& scv(LocalIndexType scvIdx) const
    {
        return ggCache_->scvs(eIdx_)[scvIdx];
    }

    const SubControlVolumeFace& scvf(LocalIndexType scvfIdx) const
    {
        return ggCache_->scvfs(eIdx_)[scvfIdx];
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolume>::const_iterator>
    scvs(const BoxFVElementGeometry& fvGeometry)
    {
        using Iter = typename std::vector<SubControlVolume>::const_iterator;
        const auto& s = fvGeometry.ggCache_->scvs(fvGeometry.eIdx_);
        return Dune::IteratorRange<Iter>(s.begin(), s.end());
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolumeFace>::const_iterator>
    scvfs(const BoxFVElementGeometry& fvGeometry)
    {
        using Iter = typename std::vector<SubControlVolumeFace>::const_iterator;
        const auto& s = fvGeometry.ggCache_->scvfs(fvGeometry.eIdx_);
        return Dune::IteratorRange<Iter>(s.begin(), s.end());
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolumeFace>::const_iterator>
    scvfs(const BoxFVElementGeometry& fvGeometry, const BoundaryFace& boundaryFace)
    {
        using Iter = typename std::vector<SubControlVolumeFace>::const_iterator;
        const auto& s = fvGeometry.ggCache_->scvfs(fvGeometry.eIdx_);
        const auto& range = fvGeometry.ggCache_->boundaryFaceScvfRanges(fvGeometry.eIdx_)[boundaryFace.index()];
        return Dune::IteratorRange<Iter>(s.begin() + range[0], s.begin() + range[0] + range[1]);
    }

    friend inline std::ranges::view auto
    boundaryFaces(const BoxFVElementGeometry& fvGeometry)
    {
        const auto& v = fvGeometry.ggCache_->boundaryFaces(fvGeometry.eIdx_);
        return std::ranges::views::all(v);
    }

    friend inline auto localDofs(const BoxFVElementGeometry& fvGeometry, const BoundaryFace& boundaryFace)
    { return DofHelper::localDofsOnBoundaryFace(fvGeometry, boundaryFace); }

    const FeLocalBasis& feLocalBasis() const
    {
        return gridGeometry().feCache().get(element_->type()).localBasis();
    }

    const auto& feLocalCoefficients() const
    {
        return gridGeometry().feCache().get(element_->type()).localCoefficients();
    }

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

    std::size_t numScv() const
    {
        return ggCache_->scvs(eIdx_).size();
    }

    std::size_t numScvf() const
    {
        return ggCache_->scvfs(eIdx_).size();
    }

    BoxFVElementGeometry bind(const Element& element) &&
    {
        this->bindElement(element);
        return std::move(*this);
    }

    void bind(const Element& element) &
    { this->bindElement(element); }

    BoxFVElementGeometry bindElement(const Element& element) &&
    {
        this->bindElement(element);
        return std::move(*this);
    }

    void bindElement(const Element& element) &
    {
        element_ = element;
        elementGeometry_.emplace(element.geometry());
        // cache element index
        eIdx_ = gridGeometry().elementMapper().index(element);
    }

    bool isBound() const
    { return static_cast<bool>(element_); }

    const Element& element() const
    { return *element_; }

    const typename Element::Geometry& elementGeometry() const
    { return *elementGeometry_; }

    GridIndexType elementIndex() const
    { return eIdx_; }

    std::size_t intersectionIndex(const SubControlVolumeFace& scvf) const
    {
        const auto localScvfIdx = scvf.index() - GeometryHelper::numInteriorScvf(element().type());
        return ggCache_->scvfBoundaryGeometryKeys(eIdx_)[localScvfIdx][0];
    }

    const GridGeometry& gridGeometry() const
    { return ggCache_->gridGeometry(); }

    const GridGeometry& gridDiscretization() const
    { return ggCache_->gridGeometry(); }

    bool hasBoundaryScvf() const
    { return ggCache_->hasBoundaryScvf(eIdx_); }

    bool hasBoundaryFaces() const
    { return hasBoundaryScvf(); }

    const BoundaryFace& boundaryFace(LocalIndexType bfIdx) const
    { return ggCache_->boundaryFaces(eIdx_)[bfIdx]; }

    typename SubControlVolume::Traits::Geometry geometry(const SubControlVolume& scv) const
    {
        assert(isBound());
        return { Dune::GeometryTypes::cube(dim), GeometryHelper(*elementGeometry_).getScvCorners(scv.indexInElement()) };
    }

    typename SubControlVolumeFace::Traits::Geometry geometry(const SubControlVolumeFace& scvf) const
    {
        assert(isBound());
        const GeometryHelper geometryHelper(*elementGeometry_);
        if (scvf.boundary())
        {
            const auto localBoundaryIndex = scvf.index() - geometryHelper.numInteriorScvf();
            const auto& key = ggCache_->scvfBoundaryGeometryKeys(eIdx_)[localBoundaryIndex];
            return { Dune::GeometryTypes::cube(dim-1), geometryHelper.getBoundaryScvfCorners(key[0], key[1]) };
        }
        else
            return { Dune::GeometryTypes::cube(dim-1), geometryHelper.getScvfCorners(scvf.index()) };
    }

    typename BoundaryFace::Traits::Geometry geometry(const BoundaryFace& boundaryFace) const
    {
        assert(isBound());
        const auto& elemGeo = elementGeometry();
        const auto faceGeoInRef = referenceElement(elemGeo).template geometry<1>(boundaryFace.intersectionIndex());
        typename BoundaryFace::Traits::CornerStorage corners;
        for (int i = 0; i < faceGeoInRef.corners(); ++i)
            corners.push_back(elemGeo.global(faceGeoInRef.corner(i)));
        return { faceGeoInRef.type(), corners };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const SubControlVolume& scv)
    {
        const auto type = fvGeometry.element().type();
        const auto& localKey = fvGeometry.gridGeometry().feCache().get(type).localCoefficients().localKey(scv.localDofIndex());
 
        return CVFE::LocalDofInterpolationPointData{ DofHelper::localDofPosition(type, localKey), scv.dofPosition(), scv.localDofIndex() };
    }

    template<class LocalDof>
    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const LocalDof& localDof)
    {
        const auto type = fvGeometry.element().type();
        const auto& localKey = fvGeometry.gridGeometry().feCache().get(type).localCoefficients().localKey(localDof.index());
        const auto& localPos = DofHelper::localDofPosition(type, localKey);
 
        return CVFE::LocalDofInterpolationPointData{ localPos, fvGeometry.elementGeometry().global(localPos), localDof.index() };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const typename Element::Geometry::GlobalCoordinate& globalPos)
    {
        // Create ipData that does not automatically calculate the local position but only if it is called
        return CVFE::InterpolationPointDataLocalMapping{
            [&] (const typename Element::Geometry::GlobalCoordinate& pos)
            { return fvGeometry.elementGeometry().local(pos); },
            globalPos
        };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const SubControlVolumeFace& scvf)
    {
        return CVFE::FaceInterpolationPointData<BaseIpData, LocalIndexType>
                    { scvf.unitOuterNormal(), scvf.index(), fvGeometry.elementGeometry().local(scvf.ipGlobal()), scvf.ipGlobal() };
    }
 
private:
    const GGCache* ggCache_;
    GridIndexType eIdx_;
 
    std::optional<Element> element_;
    std::optional<typename Element::Geometry> elementGeometry_;
};

template<class GG>
class BoxFVElementGeometry<GG, false>
{
    using GridView = typename GG::GridView;
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
    using GridIndexType = typename IndexTraits<GridView>::GridIndex;
    using LocalIndexType = typename IndexTraits<GridView>::LocalIndex;
    using CoordScalar = typename GridView::ctype;
    using FeLocalBasis = typename GG::FeCache::FiniteElementType::Traits::LocalBasisType;
    using GGCache = typename GG::Cache;
    using GeometryHelper = typename GGCache::GeometryHelper;
    using DofHelper = typename GGCache::DofHelper;
 
    using BaseIpData = CVFE::InterpolationPointData<
                        typename GridView::template Codim<0>::Entity::Geometry::LocalCoordinate,
                        typename GridView::template Codim<0>::Entity::Geometry::GlobalCoordinate
                        >;
 
public:
    using Element = typename GridView::template Codim<0>::Entity;
    using SubControlVolume = typename GG::SubControlVolume;
    using SubControlVolumeFace = typename GG::SubControlVolumeFace;
    using GridGeometry = GG;
    using BoundaryFace = typename GG::BoundaryFace;
    using ScvQuadratureRule = typename GG::ScvQuadratureRule;
    using ScvfQuadratureRule = typename GG::ScvfQuadratureRule;
    static constexpr std::size_t maxNumElementScvs = (1<<dim);

    BoxFVElementGeometry(const GGCache& ggCache)
    : ggCache_(&ggCache) {}

    const SubControlVolume& scv(LocalIndexType scvIdx) const
    {
        return scvs_[scvIdx];
    }

    const SubControlVolumeFace& scvf(LocalIndexType scvfIdx) const
    {
        return scvfs_[scvfIdx];
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolume>::const_iterator>
    scvs(const BoxFVElementGeometry& fvGeometry)
    {
        using Iter = typename std::vector<SubControlVolume>::const_iterator;
        return Dune::IteratorRange<Iter>(fvGeometry.scvs_.begin(), fvGeometry.scvs_.end());
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolumeFace>::const_iterator>
    scvfs(const BoxFVElementGeometry& fvGeometry)
    {
        using Iter = typename std::vector<SubControlVolumeFace>::const_iterator;
        return Dune::IteratorRange<Iter>(fvGeometry.scvfs_.begin(), fvGeometry.scvfs_.end());
    }

    friend inline Dune::IteratorRange<typename std::vector<SubControlVolumeFace>::const_iterator>
    scvfs(const BoxFVElementGeometry& fvGeometry, const BoundaryFace& boundaryFace)
    {
        using Iter = typename std::vector<SubControlVolumeFace>::const_iterator;
        const auto& range = fvGeometry.boundaryFaceScvfRanges_[boundaryFace.index()];
        return Dune::IteratorRange<Iter>(fvGeometry.scvfs_.begin() + range[0], fvGeometry.scvfs_.begin() + range[0] + range[1]);
    }

    friend inline std::ranges::view auto
    boundaryFaces(const BoxFVElementGeometry& fvGeometry)
    { return std::ranges::views::all(fvGeometry.boundaryFaces_); }

    friend inline auto localDofs(const BoxFVElementGeometry& fvGeometry, const BoundaryFace& boundaryFace)
    { return DofHelper::localDofsOnBoundaryFace(fvGeometry, boundaryFace); }

    const FeLocalBasis& feLocalBasis() const
    {
        return gridGeometry().feCache().get(element_->type()).localBasis();
    }

    const auto& feLocalCoefficients() const
    {
        return gridGeometry().feCache().get(element_->type()).localCoefficients();
    }

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

    std::size_t numScv() const
    {
        return scvs_.size();
    }

    std::size_t numScvf() const
    {
        return scvfs_.size();
    }

    BoxFVElementGeometry bind(const Element& element) &&
    {
        this->bindElement(element);
        return std::move(*this);
    }

    void bind(const Element& element) &
    { this->bindElement(element); }

    BoxFVElementGeometry bindElement(const Element& element) &&
    {
        this->bindElement(element);
        return std::move(*this);
    }

    void bindElement(const Element& element) &
    {
        element_ = element;
        eIdx_ = gridGeometry().elementMapper().index(element);
        elementGeometry_.emplace(element.geometry());
        makeElementGeometries_();
    }

    bool isBound() const
    { return static_cast<bool>(element_); }

    const Element& element() const
    { return *element_; }

    const typename Element::Geometry& elementGeometry() const
    { return *elementGeometry_; }

    GridIndexType elementIndex() const
    { return eIdx_; }

    std::size_t intersectionIndex(const SubControlVolumeFace& scvf) const
    {
        const auto localScvfIdx = scvf.index() - GeometryHelper::numInteriorScvf(element().type());
        return scvfBoundaryGeometryKeys_[localScvfIdx][0];
    }

    const GridGeometry& gridGeometry() const
    { return ggCache_->gridGeometry(); }

    const GridGeometry& gridDiscretization() const
    { return ggCache_->gridGeometry(); }

    bool hasBoundaryScvf() const
    { return hasBoundaryScvf_; }

    bool hasBoundaryFaces() const
    { return hasBoundaryScvf(); }

    const BoundaryFace& boundaryFace(LocalIndexType bfIdx) const
    { return boundaryFaces_[bfIdx]; }

    typename SubControlVolume::Traits::Geometry geometry(const SubControlVolume& scv) const
    {
        assert(isBound());
        return { Dune::GeometryTypes::cube(dim), GeometryHelper(*elementGeometry_).getScvCorners(scv.indexInElement()) };
    }

    typename SubControlVolumeFace::Traits::Geometry geometry(const SubControlVolumeFace& scvf) const
    {
        assert(isBound());
        const GeometryHelper geometryHelper(*elementGeometry_);
        if (scvf.boundary())
        {
            const auto localBoundaryIndex = scvf.index() - geometryHelper.numInteriorScvf();
            const auto& key = scvfBoundaryGeometryKeys_[localBoundaryIndex];
            return { Dune::GeometryTypes::cube(dim-1), geometryHelper.getBoundaryScvfCorners(key[0], key[1]) };
        }
        else
            return { Dune::GeometryTypes::cube(dim-1), geometryHelper.getScvfCorners(scvf.index()) };
    }

    typename BoundaryFace::Traits::Geometry geometry(const BoundaryFace& boundaryFace) const
    {
        assert(isBound());
        const auto& elemGeo = elementGeometry();
        const auto faceGeoInRef = referenceElement(elemGeo).template geometry<1>(boundaryFace.intersectionIndex());
        typename BoundaryFace::Traits::CornerStorage corners;
        for (int i = 0; i < faceGeoInRef.corners(); ++i)
            corners.push_back(elemGeo.global(faceGeoInRef.corner(i)));
        return { faceGeoInRef.type(), corners };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const SubControlVolume& scv)
    {
        const auto type = fvGeometry.element().type();
        const auto& localKey = fvGeometry.gridGeometry().feCache().get(type).localCoefficients().localKey(scv.localDofIndex());
 
        return CVFE::LocalDofInterpolationPointData{ DofHelper::localDofPosition(type, localKey), scv.dofPosition(), scv.localDofIndex() };
    }

    template<class LocalDof>
    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const LocalDof& localDof)
    {
        const auto type = fvGeometry.element().type();
        const auto& localKey = fvGeometry.gridGeometry().feCache().get(type).localCoefficients().localKey(localDof.index());
        const auto& localPos = DofHelper::localDofPosition(type, localKey);
 
        return CVFE::LocalDofInterpolationPointData{ localPos, fvGeometry.elementGeometry().global(localPos), localDof.index() };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const typename Element::Geometry::GlobalCoordinate& globalPos)
    {
        // Create ipData that does not automatically calculate the local position but only if it is called
        return CVFE::InterpolationPointDataLocalMapping{
            [&] (const typename Element::Geometry::GlobalCoordinate& pos) { return fvGeometry.elementGeometry().local(pos); },
            globalPos
        };
    }

    friend inline auto ipData(const BoxFVElementGeometry& fvGeometry, const SubControlVolumeFace& scvf)
    {
        return CVFE::FaceInterpolationPointData<BaseIpData, LocalIndexType>
                    { scvf.unitOuterNormal(), scvf.index(), fvGeometry.elementGeometry().local(scvf.ipGlobal()), scvf.ipGlobal() };
    }
 
private:
    void makeElementGeometries_()
    {
        hasBoundaryScvf_ = false;
        boundaryFaces_.clear();
        boundaryFaceScvfRanges_.clear();
 
        // get the element geometry
        const auto& element = *element_;
        const auto& elementGeometry = *elementGeometry_;
        const auto refElement = referenceElement(elementGeometry);
 
        // get the sub control volume geometries of this element
        GeometryHelper geometryHelper(elementGeometry);
 
        // construct the sub control volumes
        scvs_.resize(elementGeometry.corners());
        for (LocalIndexType scvLocalIdx = 0; scvLocalIdx < elementGeometry.corners(); ++scvLocalIdx)
        {
            // get associated dof index
            const auto dofIdxGlobal = gridGeometry().vertexMapper().subIndex(element, scvLocalIdx, dim);
 
            // add scv to the local container
            scvs_[scvLocalIdx] = SubControlVolume(
                geometryHelper.getScvCorners(scvLocalIdx),
                scvLocalIdx,
                eIdx_,
                dofIdxGlobal
            );
        }
 
        // construct the sub control volume faces
        const auto numInnerScvf = geometryHelper.numInteriorScvf();
        scvfs_.resize(numInnerScvf);
        scvfBoundaryGeometryKeys_.clear();
 
        LocalIndexType scvfLocalIdx = 0;
        for (; scvfLocalIdx < numInnerScvf; ++scvfLocalIdx)
        {
            // find the local scv indices this scvf is connected to
            std::array<LocalIndexType, 2> localScvIndices{{
                static_cast<LocalIndexType>(refElement.subEntity(scvfLocalIdx, dim-1, 0, dim)),
                static_cast<LocalIndexType>(refElement.subEntity(scvfLocalIdx, dim-1, 1, dim))
            }};
 
            const auto& corners = geometryHelper.getScvfCorners(scvfLocalIdx);
            scvfs_[scvfLocalIdx] = SubControlVolumeFace(
                corners,
                geometryHelper.normal(corners, localScvIndices),
                element,
                scvfLocalIdx,
                std::move(localScvIndices)
            );
        }
 
        // construct the sub control volume faces on the domain boundary
        LocalIndexType numBoundaryFaces = 0;
        for (const auto& intersection : intersections(gridGeometry().gridView(), element))
        {
            if (intersection.boundary() && !intersection.neighbor())
            {
                const auto isGeometry = intersection.geometry();
                hasBoundaryScvf_ = true;
 
                // add one boundary face per boundary intersection
                boundaryFaces_.push_back(BoundaryFace{
                    isGeometry.center(),
                    isGeometry.volume(),
                    intersection.centerUnitOuterNormal(),
                    numBoundaryFaces++,
                    static_cast<LocalIndexType>(intersection.indexInInside()),
                    typename BoundaryFace::Traits::BoundaryFlag{intersection}
                });
 
                // record the scvf subrange for this boundary face: {offset, count}
                boundaryFaceScvfRanges_.push_back(std::array<LocalIndexType, 2>{{
                    scvfLocalIdx,
                    static_cast<LocalIndexType>(isGeometry.corners())
                }});
 
                for (unsigned int isScvfLocalIdx = 0; isScvfLocalIdx < isGeometry.corners(); ++isScvfLocalIdx)
                {
                    // find the scv this scvf is connected to
                    const LocalIndexType insideScvIdx = static_cast<LocalIndexType>(refElement.subEntity(intersection.indexInInside(), 1, isScvfLocalIdx, dim));
                    std::array<LocalIndexType, 2> localScvIndices{{insideScvIdx, insideScvIdx}};
 
                    scvfs_.emplace_back(
                        geometryHelper.getBoundaryScvfCorners(intersection.indexInInside(), isScvfLocalIdx),
                        intersection.centerUnitOuterNormal(),
                        intersection,
                        isScvfLocalIdx,
                        scvfLocalIdx,
                        std::move(localScvIndices)
                    );
 
                    scvfBoundaryGeometryKeys_.emplace_back(std::array<LocalIndexType, 2>{{
                        static_cast<LocalIndexType>(intersection.indexInInside()),
                        static_cast<LocalIndexType>(isScvfLocalIdx)
                    }});
 
                    // increment local counter
                    scvfLocalIdx++;
                }
            }
        }
    }

    GridIndexType eIdx_;
    std::optional<Element> element_;
    std::optional<typename Element::Geometry> elementGeometry_;

    const GGCache* ggCache_;

    std::vector<SubControlVolume> scvs_;
    std::vector<SubControlVolumeFace> scvfs_;
    std::vector<std::array<LocalIndexType, 2>> scvfBoundaryGeometryKeys_;
    Dune::ReservedVector<BoundaryFace, 2*dim> boundaryFaces_;
    Dune::ReservedVector<std::array<LocalIndexType, 2>, 2*dim> boundaryFaceScvfRanges_;
 
    bool hasBoundaryScvf_ = false;
};
 
} // end namespace Dumux
 
#endif