subdomainfclocalassembler.hh

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#ifndef DUMUX_MULTIDOMAIN_FACECENTERED_LOCAL_ASSEMBLER_HH
#define DUMUX_MULTIDOMAIN_FACECENTERED_LOCAL_ASSEMBLER_HH
 
#include <dune/common/indices.hh>
#include <dune/common/hybridutilities.hh>
#include <dune/grid/common/gridenums.hh> // for GhostEntity
 
#include <dumux/common/properties.hh>
#include <dumux/common/parameters.hh>
#include <dumux/common/numericdifferentiation.hh>
#include <dumux/assembly/numericepsilon.hh>
#include <dumux/assembly/diffmethod.hh>
#include <dumux/assembly/fclocalassembler.hh>
 
namespace Dumux {

template<std::size_t id, class TypeTag, class Assembler, class Implementation, DiffMethod dm, bool implicit>
class SubDomainFaceCenteredLocalAssemblerBase : public FaceCenteredLocalAssembler<TypeTag, Assembler, dm, implicit, Implementation>
{
    using ParentType = FaceCenteredLocalAssembler<TypeTag, Assembler, dm, implicit, Implementation>;
 
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using SolutionVector = typename Assembler::SolutionVector;
    using SubSolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
 
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using GridVolumeVariables = typename GridVariables::GridVolumeVariables;
    using ElementVolumeVariables = typename GridVolumeVariables::LocalView;
    using ElementFluxVariablesCache = typename GridVariables::GridFluxVariablesCache::LocalView;
    using Scalar = typename GridVariables::Scalar;
 
    using GridGeometry = typename GridVariables::GridGeometry;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolume = typename GridGeometry::SubControlVolume;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
    using CouplingManager = typename Assembler::CouplingManager;
 
    static constexpr auto numEq = GetPropType<TypeTag, Properties::ModelTraits>::numEq();
 
public:
    static constexpr auto domainId = typename Dune::index_constant<id>();
    using ParentType::ParentType;
    using ElementResidualVector = typename ParentType::LocalResidual::ElementResidualVector;
 
    // the constructor
    explicit SubDomainFaceCenteredLocalAssemblerBase(const Assembler& assembler,
                                                     const Element& element,
                                                     const SolutionVector& curSol,
                                                     CouplingManager& couplingManager)
    : ParentType(assembler,
                 element,
                 curSol,
                 localView(assembler.gridGeometry(domainId)),
                 localView(assembler.gridVariables(domainId).curGridVolVars()),
                 localView(assembler.gridVariables(domainId).prevGridVolVars()),
                 localView(assembler.gridVariables(domainId).gridFluxVarsCache()),
                 assembler.localResidual(domainId),
                 (element.partitionType() == Dune::GhostEntity))
    , couplingManager_(couplingManager)
    {}

    template<class JacobianMatrixRow, class GridVariablesTuple>
    void assembleJacobianAndResidual(JacobianMatrixRow& jacRow, SubSolutionVector& res, GridVariablesTuple& gridVariables)
    {
        auto assembleCouplingBlocks = [&](const auto& residual)
        {
            // assemble the coupling blocks
            using namespace Dune::Hybrid;
            forEach(integralRange(Dune::Hybrid::size(jacRow)), [&](auto&& i)
            {
                if (i != id)
                    this->assembleJacobianCoupling(i, jacRow, residual, gridVariables);
            });
        };
 
        // the coupled model does not support partial reassembly yet
        const DefaultPartialReassembler* noReassembler = nullptr;
        ParentType::assembleJacobianAndResidual(jacRow[domainId], res, *std::get<domainId>(gridVariables), noReassembler, assembleCouplingBlocks);
    }

    template<std::size_t otherId, class JacRow, class GridVariables,
             typename std::enable_if_t<(otherId == id), int> = 0>
    void assembleJacobianCoupling(Dune::index_constant<otherId> domainJ, JacRow& jacRow,
                                  const ElementResidualVector& res, GridVariables& gridVariables)
    {}

    template<std::size_t otherId, class JacRow, class GridVariables,
             typename std::enable_if_t<(otherId != id), int> = 0>
    void assembleJacobianCoupling(Dune::index_constant<otherId> domainJ, JacRow& jacRow,
                                  const ElementResidualVector& res, GridVariables& gridVariables)
    {
        this->asImp_().assembleJacobianCoupling(domainJ, jacRow[domainJ], res, *std::get<domainId>(gridVariables));
    }

    ElementResidualVector evalLocalSourceResidual(const Element& element, const ElementVolumeVariables& elemVolVars) const
    {
        // initialize the residual vector for all scvs in this element
        ElementResidualVector residual(this->fvGeometry().numScv());
 
        // evaluate the volume terms (storage + source terms)
        // forward to the local residual specialized for the discretization methods
        for (auto&& scv : scvs(this->fvGeometry()))
        {
            const auto& curVolVars = elemVolVars[scv];
            auto source = this->localResidual().computeSource(problem(), element, this->fvGeometry(), elemVolVars, scv);
            source *= -scv.volume()*curVolVars.extrusionFactor();
            residual[scv.localDofIndex()] = std::move(source);
        }
 
        return residual;
    }

    ElementResidualVector evalLocalSourceResidual(const Element& neighbor) const
    { return this->evalLocalSourceResidual(neighbor, implicit ? this->curElemVolVars() : this->prevElemVolVars()); }

    void bindLocalViews()
    {
        // get some references for convenience
        const auto& element = this->element();
        const auto& curSol = this->curSol(domainId);
        auto&& fvGeometry = this->fvGeometry();
        auto&& curElemVolVars = this->curElemVolVars();
        auto&& elemFluxVarsCache = this->elemFluxVarsCache();
 
        // bind the caches
        couplingManager_.bindCouplingContext(domainId, element, this->assembler());
        fvGeometry.bind(element);
 
        if (implicit)
        {
            curElemVolVars.bind(element, fvGeometry, curSol);
            elemFluxVarsCache.bind(element, fvGeometry, curElemVolVars);
            if (!this->assembler().isStationaryProblem())
                this->prevElemVolVars().bindElement(element, fvGeometry, this->assembler().prevSol()[domainId]);
        }
        else
        {
            auto& prevElemVolVars = this->prevElemVolVars();
            const auto& prevSol = this->assembler().prevSol()[domainId];
 
            curElemVolVars.bindElement(element, fvGeometry, curSol);
            prevElemVolVars.bind(element, fvGeometry, prevSol);
            elemFluxVarsCache.bind(element, fvGeometry, prevElemVolVars);
        }
 
        this->elemBcTypes().update(problem(), this->element(), this->fvGeometry());
    }

    template<std::size_t i = domainId>
    const Problem& problem(Dune::index_constant<i> dId = domainId) const
    { return this->assembler().problem(domainId); }

    template<std::size_t i = domainId>
    const auto& curSol(Dune::index_constant<i> dId = domainId) const
    { return ParentType::curSol()[dId]; }

    CouplingManager& couplingManager()
    { return couplingManager_; }
 
private:
    CouplingManager& couplingManager_; 
};

template<std::size_t id, class TypeTag, class Assembler, DiffMethod DM = DiffMethod::numeric, bool implicit = true>
class SubDomainFaceCenteredLocalAssembler;

template<std::size_t id, class TypeTag, class Assembler>
class SubDomainFaceCenteredLocalAssembler<id, TypeTag, Assembler, DiffMethod::numeric, /*implicit=*/true>
: public SubDomainFaceCenteredLocalAssemblerBase<id, TypeTag, Assembler,
             SubDomainFaceCenteredLocalAssembler<id, TypeTag, Assembler, DiffMethod::numeric, true>, DiffMethod::numeric, /*implicit=*/true>
{
    using ThisType = SubDomainFaceCenteredLocalAssembler<id, TypeTag, Assembler, DiffMethod::numeric, /*implicit=*/true>;
    using ParentType = SubDomainFaceCenteredLocalAssemblerBase<id, TypeTag, Assembler, ThisType, DiffMethod::numeric, /*implicit=*/true>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
 
    using GridGeometry = GetPropType<TypeTag, Properties::GridGeometry>;
    using FVElementGeometry = typename GridGeometry::LocalView;
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
    using SubControlVolume = typename FVElementGeometry::SubControlVolume;
 
    enum { numEq = GetPropType<TypeTag, Properties::ModelTraits>::numEq() };
    enum { dim = GridView::dimension };
 
    static constexpr bool enableGridFluxVarsCache = getPropValue<TypeTag, Properties::EnableGridFluxVariablesCache>();
    static constexpr bool enableGridVolVarsCache = getPropValue<TypeTag, Properties::EnableGridVolumeVariablesCache>();
    static constexpr auto domainI = Dune::index_constant<id>();
 
public:
    using ParentType::ParentType;
    using ElementResidualVector = typename ParentType::LocalResidual::ElementResidualVector;

    template<class ElemSol>
    void maybeUpdateCouplingContext(const SubControlVolume& scv, ElemSol& elemSol, const int pvIdx)
    {
        this->couplingManager().updateCouplingContext(domainI, *this, domainI, scv.dofIndex(), elemSol[scv.localDofIndex()], pvIdx);
    }

    template<class JacobianMatrixDiagBlock, class GridVariables>
    void maybeEvalAdditionalDomainDerivatives(const ElementResidualVector& origResiduals, const JacobianMatrixDiagBlock& A, GridVariables& gridVariables)
    {
        this->couplingManager().evalAdditionalDomainDerivatives(domainI, *this, origResiduals, A, gridVariables);
    }

    template<std::size_t otherId, class JacobianBlock, class GridVariables>
    void assembleJacobianCoupling(Dune::index_constant<otherId> domainJ, JacobianBlock& A,
                                  const ElementResidualVector& res, GridVariables& gridVariables)
    {
        // Calculate derivatives of all dofs in the element with respect to all dofs in the coupling stencil. //
 
        // get some aliases for convenience
        const auto& element = this->element();
        const auto& fvGeometry = this->fvGeometry();
        auto&& curElemVolVars = this->curElemVolVars();
        auto&& elemFluxVarsCache = this->elemFluxVarsCache();
 
        // the solution vector of the other domain
        const auto& curSolJ = this->curSol(domainJ);
 
        // convenience lambda for call to update self
        auto updateCoupledVariables = [&] ()
        {
            // Update ourself after the context has been modified. Depending on the
            // type of caching, other objects might have to be updated. All ifs can be optimized away.
            if constexpr (enableGridFluxVarsCache)
            {
                if constexpr (enableGridVolVarsCache)
                    this->couplingManager().updateCoupledVariables(domainI, *this, gridVariables.curGridVolVars(), gridVariables.gridFluxVarsCache());
                else
                    this->couplingManager().updateCoupledVariables(domainI, *this, curElemVolVars, gridVariables.gridFluxVarsCache());
            }
            else
            {
                if constexpr (enableGridVolVarsCache)
                    this->couplingManager().updateCoupledVariables(domainI, *this, gridVariables.curGridVolVars(), elemFluxVarsCache);
                else
                    this->couplingManager().updateCoupledVariables(domainI, *this, curElemVolVars, elemFluxVarsCache);
            }
        };
 
        for (const auto& scv : scvs(fvGeometry))
        {
            const auto& stencil = this->couplingManager().couplingStencil(domainI, element, scv, domainJ);
 
            for (const auto globalJ : stencil)
            {
                const auto origResidual = this->couplingManager().evalCouplingResidual(domainI, *this, scv, domainJ, globalJ); // TODO is this necessary?
                // undeflected privars and privars to be deflected
                const auto origPriVarsJ = curSolJ[globalJ];
                auto priVarsJ = origPriVarsJ;
 
                for (int pvIdx = 0; pvIdx < JacobianBlock::block_type::cols; ++pvIdx)
                {
                    auto evalCouplingResidual = [&](Scalar priVar)
                    {
                        priVarsJ[pvIdx] = priVar;
                        this->couplingManager().updateCouplingContext(domainI, *this, domainJ, globalJ, priVarsJ, pvIdx);
                        updateCoupledVariables();
                        return this->couplingManager().evalCouplingResidual(domainI, *this, scv, domainJ, globalJ);
                    };
 
                    // derive the residuals numerically
                    ElementResidualVector partialDerivs(element.subEntities(1));
 
                    const auto& paramGroup = this->assembler().problem(domainJ).paramGroup();
                    static const int numDiffMethod = getParamFromGroup<int>(paramGroup, "Assembly.NumericDifferenceMethod");
                    static const auto epsCoupl = this->couplingManager().numericEpsilon(domainJ, paramGroup);
 
                    NumericDifferentiation::partialDerivative(evalCouplingResidual, origPriVarsJ[pvIdx], partialDerivs, origResidual,
                                                              epsCoupl(origPriVarsJ[pvIdx], pvIdx), numDiffMethod);
 
                    // update the global stiffness matrix with the current partial derivatives
                    for (int eqIdx = 0; eqIdx < numEq; eqIdx++)
                    {
                        // A[i][col][eqIdx][pvIdx] is the rate of change of
                        // the residual of equation 'eqIdx' at dof 'i'
                        // depending on the primary variable 'pvIdx' at dof
                        // 'col'.
                        A[scv.dofIndex()][globalJ][eqIdx][pvIdx] += partialDerivs[scv.localDofIndex()][eqIdx];
                    }
 
                    // handle Dirichlet boundary conditions
                    // TODO internal constraints
                    if (scv.boundary() && this->elemBcTypes().hasDirichlet())
                    {
                        const auto bcTypes = this->elemBcTypes()[fvGeometry.frontalScvfOnBoundary(scv).localIndex()];
                        if (bcTypes.hasDirichlet())
                        {
                            // If the dof is coupled by a Dirichlet condition,
                            // set the derived value only once (i.e. overwrite existing values).
                            // For other dofs, add the contribution of the partial derivative.
                            for (int eqIdx = 0; eqIdx < numEq; ++eqIdx)
                            {
                                for (int pvIdx = 0; pvIdx < JacobianBlock::block_type::cols; ++pvIdx)
                                {
                                    if (bcTypes.isCouplingDirichlet(eqIdx))
                                        A[scv.dofIndex()][globalJ][eqIdx][pvIdx] = partialDerivs[scv.localDofIndex()][pvIdx];
                                    else if (bcTypes.isDirichlet(eqIdx))
                                        A[scv.dofIndex()][globalJ][eqIdx][pvIdx] = 0.0;
                                }
                            }
                        }
                    }
 
                    // restore the current element solution
                    priVarsJ[pvIdx] = origPriVarsJ[pvIdx];
 
                    // restore the undeflected state of the coupling context
                    this->couplingManager().updateCouplingContext(domainI, *this, domainJ, globalJ, priVarsJ, pvIdx);
                }
 
                // Restore original state of the flux vars cache and/or vol vars.
                // This has to be done in case they depend on variables of domainJ before
                // we continue with the numeric derivative w.r.t the next globalJ. Otherwise,
                // the next "origResidual" will be incorrect.
                updateCoupledVariables();
            }
        }
    }
};
 
} // end namespace Dumux
 
#endif