boxlocalassembler.hh

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#ifndef DUMUX_BOX_LOCAL_ASSEMBLER_HH
#define DUMUX_BOX_LOCAL_ASSEMBLER_HH
 
#include <dune/istl/matrixindexset.hh>
#include <dune/istl/bvector.hh>
 
#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/fvlocalassemblerbase.hh>
#include <dumux/assembly/partialreassembler.hh>
#include <dumux/assembly/entitycolor.hh>
#include <dumux/discretization/box/elementsolution.hh>
 
namespace Dumux {

template<class TypeTag, class Assembler, class Implementation, bool implicit>
class BoxLocalAssemblerBase : public FVLocalAssemblerBase<TypeTag, Assembler, Implementation, implicit>
{
    using ParentType = FVLocalAssemblerBase<TypeTag, Assembler, Implementation, implicit>;
    using JacobianMatrix = GetPropType<TypeTag, Properties::JacobianMatrix>;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
    using ElementVolumeVariables = typename GetPropType<TypeTag, Properties::GridVolumeVariables>::LocalView;
 
    enum { numEq = GetPropType<TypeTag, Properties::ModelTraits>::numEq() };
 
public:
 
    using ParentType::ParentType;
 
    void bindLocalViews()
    {
        ParentType::bindLocalViews();
        this->elemBcTypes().update(this->problem(), this->element(), this->fvGeometry());
    }
 

    template <class PartialReassembler = DefaultPartialReassembler>
    void assembleJacobianAndResidual(JacobianMatrix& jac, SolutionVector& res, GridVariables& gridVariables,
                                     const PartialReassembler* partialReassembler = nullptr)
    {
        this->asImp_().bindLocalViews();
        const auto eIdxGlobal = this->assembler().gridGeometry().elementMapper().index(this->element());
        if (partialReassembler
            && partialReassembler->elementColor(eIdxGlobal) == EntityColor::green)
        {
            const auto residual = this->asImp_().evalLocalResidual(); // forward to the internal implementation
            for (const auto& scv : scvs(this->fvGeometry()))
                res[scv.dofIndex()] += residual[scv.localDofIndex()];
        }
        else if (!this->elementIsGhost())
        {
            const auto residual = this->asImp_().assembleJacobianAndResidualImpl(jac, gridVariables, partialReassembler); // forward to the internal implementation
            for (const auto& scv : scvs(this->fvGeometry()))
                res[scv.dofIndex()] += residual[scv.localDofIndex()];
        }
        else
        {
            using GridGeometry = typename GridVariables::GridGeometry;
            using GridView = typename GridGeometry::GridView;
            static constexpr auto dim = GridView::dimension;
 
            int numVerticesLocal = this->element().subEntities(dim);
 
            for (int i = 0; i < numVerticesLocal; ++i) {
                auto vertex = this->element().template subEntity<dim>(i);
 
                if (vertex.partitionType() == Dune::InteriorEntity ||
                    vertex.partitionType() == Dune::BorderEntity)
                {
                    // do not change the non-ghost vertices
                    continue;
                }
 
                // set main diagonal entries for the vertex
                int vIdx = this->assembler().gridGeometry().vertexMapper().index(vertex);
 
                typedef typename JacobianMatrix::block_type BlockType;
                BlockType &J = jac[vIdx][vIdx];
                for (int j = 0; j < BlockType::rows; ++j)
                    J[j][j] = 1.0;
 
                // set residual for the vertex
                res[vIdx] = 0;
            }
        }
 
        auto applyDirichlet = [&] (const auto& scvI,
                                   const auto& dirichletValues,
                                   const auto eqIdx,
                                   const auto pvIdx)
        {
            res[scvI.dofIndex()][eqIdx] = this->curElemVolVars()[scvI].priVars()[pvIdx] - dirichletValues[pvIdx];
 
            auto& row = jac[scvI.dofIndex()];
            for (auto col = row.begin(); col != row.end(); ++col)
                row[col.index()][eqIdx] = 0.0;
 
            jac[scvI.dofIndex()][scvI.dofIndex()][eqIdx][pvIdx] = 1.0;
 
            // if a periodic dof has Dirichlet values also apply the same Dirichlet values to the other dof
            if (this->assembler().gridGeometry().dofOnPeriodicBoundary(scvI.dofIndex()))
            {
                const auto periodicDof = this->assembler().gridGeometry().periodicallyMappedDof(scvI.dofIndex());
                res[periodicDof][eqIdx] = this->curElemVolVars()[scvI].priVars()[pvIdx] - dirichletValues[pvIdx];
                const auto end = jac[periodicDof].end();
                for (auto it = jac[periodicDof].begin(); it != end; ++it)
                    (*it) = periodicDof != it.index() ? 0.0 : 1.0;
            }
        };
 
        this->asImp_().enforceDirichletConstraints(applyDirichlet);
    }

    void assembleJacobian(JacobianMatrix& jac, GridVariables& gridVariables)
    {
        this->asImp_().bindLocalViews();
        this->asImp_().assembleJacobianAndResidualImpl(jac, gridVariables); // forward to the internal implementation
 
        auto applyDirichlet = [&] (const auto& scvI,
                                   const auto& dirichletValues,
                                   const auto eqIdx,
                                   const auto pvIdx)
        {
            auto& row = jac[scvI.dofIndex()];
            for (auto col = row.begin(); col != row.end(); ++col)
                row[col.index()][eqIdx] = 0.0;
 
            jac[scvI.dofIndex()][scvI.dofIndex()][eqIdx][pvIdx] = 1.0;
        };
 
        this->asImp_().enforceDirichletConstraints(applyDirichlet);
    }

    void assembleResidual(SolutionVector& res)
    {
        this->asImp_().bindLocalViews();
        const auto residual = this->evalLocalResidual();
 
        for (const auto& scv : scvs(this->fvGeometry()))
            res[scv.dofIndex()] += residual[scv.localDofIndex()];
 
        auto applyDirichlet = [&] (const auto& scvI,
                                   const auto& dirichletValues,
                                   const auto eqIdx,
                                   const auto pvIdx)
        {
            res[scvI.dofIndex()][eqIdx] = this->curElemVolVars()[scvI].priVars()[pvIdx] - dirichletValues[pvIdx];
        };
 
        this->asImp_().enforceDirichletConstraints(applyDirichlet);
    }

    template<typename ApplyFunction>
    void enforceDirichletConstraints(const ApplyFunction& applyDirichlet)
    {
        // enforce Dirichlet boundary conditions
        this->asImp_().evalDirichletBoundaries(applyDirichlet);
        // take care of internal Dirichlet constraints (if enabled)
        this->asImp_().enforceInternalDirichletConstraints(applyDirichlet);
    }

    template< typename ApplyDirichletFunctionType >
    void evalDirichletBoundaries(ApplyDirichletFunctionType applyDirichlet)
    {
        // enforce Dirichlet boundaries by overwriting partial derivatives with 1 or 0
        // and set the residual to (privar - dirichletvalue)
        if (this->elemBcTypes().hasDirichlet())
        {
            for (const auto& scvI : scvs(this->fvGeometry()))
            {
                const auto bcTypes = this->elemBcTypes()[scvI.localDofIndex()];
                if (bcTypes.hasDirichlet())
                {
                    const auto dirichletValues = this->problem().dirichlet(this->element(), scvI);
 
                    // set the Dirichlet conditions in residual and jacobian
                    for (int eqIdx = 0; eqIdx < numEq; ++eqIdx)
                    {
                        if (bcTypes.isDirichlet(eqIdx))
                        {
                            const auto pvIdx = bcTypes.eqToDirichletIndex(eqIdx);
                            assert(0 <= pvIdx && pvIdx < numEq);
                            applyDirichlet(scvI, dirichletValues, eqIdx, pvIdx);
                        }
                    }
                }
            }
        }
    }
 
};

template<class TypeTag, class Assembler, DiffMethod diffMethod = DiffMethod::numeric, bool implicit = true>
class BoxLocalAssembler;

template<class TypeTag, class Assembler>
class BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, /*implicit=*/true>
: public BoxLocalAssemblerBase<TypeTag, Assembler,
                              BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, true>, true>
{
    using ThisType = BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, true>;
    using ParentType = BoxLocalAssemblerBase<TypeTag, Assembler, ThisType, true>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using JacobianMatrix = GetPropType<TypeTag, Properties::JacobianMatrix>;
    using LocalResidual = GetPropType<TypeTag, Properties::LocalResidual>;
    using ElementResidualVector = typename LocalResidual::ElementResidualVector;
 
    enum { numEq = GetPropType<TypeTag, Properties::ModelTraits>::numEq() };
    enum { dim = GetPropType<TypeTag, Properties::GridView>::dimension };
 
    static constexpr bool enableGridFluxVarsCache = getPropValue<TypeTag, Properties::EnableGridFluxVariablesCache>();
 
public:
 
    using ParentType::ParentType;

    template <class PartialReassembler = DefaultPartialReassembler>
    ElementResidualVector assembleJacobianAndResidualImpl(JacobianMatrix& A, GridVariables& gridVariables,
                                                          const PartialReassembler* partialReassembler = nullptr)
    {
        // get some aliases for convenience
        const auto& element = this->element();
        const auto& fvGeometry = this->fvGeometry();
        const auto& curSol = this->curSol();
        auto&& curElemVolVars = this->curElemVolVars();
 
        // get the vector of the actual element residuals
        const auto origResiduals = this->evalLocalResidual();

        //                                                                                              //
        // Calculate derivatives of all dofs in stencil with respect to the dofs in the element. In the //
        // neighboring elements we do so by computing the derivatives of the fluxes which depend on the //
        // actual element. In the actual element we evaluate the derivative of the entire residual.     //
        //                                                                                              //
 
        // create the element solution
        auto elemSol = elementSolution(element, curSol, fvGeometry.gridGeometry());
 
        // create the vector storing the partial derivatives
        ElementResidualVector partialDerivs(element.subEntities(dim));
 
        // calculation of the derivatives
        for (auto&& scv : scvs(fvGeometry))
        {
            // dof index and corresponding actual pri vars
            const auto dofIdx = scv.dofIndex();
            auto& curVolVars = this->getVolVarAccess(gridVariables.curGridVolVars(), curElemVolVars, scv);
            const VolumeVariables origVolVars(curVolVars);
 
            // calculate derivatives w.r.t to the privars at the dof at hand
            for (int pvIdx = 0; pvIdx < numEq; pvIdx++)
            {
                partialDerivs = 0.0;
 
                auto evalResiduals = [&](Scalar priVar)
                {
                    // update the volume variables and compute element residual
                    elemSol[scv.localDofIndex()][pvIdx] = priVar;
                    curVolVars.update(elemSol, this->problem(), element, scv);
                    return this->evalLocalResidual();
                };
 
                // derive the residuals numerically
                static const NumericEpsilon<Scalar, numEq> eps_{this->problem().paramGroup()};
                static const int numDiffMethod = getParamFromGroup<int>(this->problem().paramGroup(), "Assembly.NumericDifferenceMethod");
                NumericDifferentiation::partialDerivative(evalResiduals, elemSol[scv.localDofIndex()][pvIdx], partialDerivs, origResiduals,
                                                          eps_(elemSol[scv.localDofIndex()][pvIdx], pvIdx), numDiffMethod);
 
                // update the global stiffness matrix with the current partial derivatives
                for (auto&& scvJ : scvs(fvGeometry))
                {
                    // don't add derivatives for green vertices
                    if (!partialReassembler
                        || partialReassembler->vertexColor(scvJ.dofIndex()) != EntityColor::green)
                    {
                        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[scvJ.dofIndex()][dofIdx][eqIdx][pvIdx] += partialDerivs[scvJ.localDofIndex()][eqIdx];
                        }
                    }
                }
 
                // restore the original state of the scv's volume variables
                curVolVars = origVolVars;
 
                // restore the original element solution
                elemSol[scv.localDofIndex()][pvIdx] = curSol[scv.dofIndex()][pvIdx];
                // TODO additional dof dependencies
            }
        }
        return origResiduals;
    }
 
}; // implicit BoxAssembler with numeric Jacobian

template<class TypeTag, class Assembler>
class BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, /*implicit=*/false>
: public BoxLocalAssemblerBase<TypeTag, Assembler,
                              BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, false>, false>
{
    using ThisType = BoxLocalAssembler<TypeTag, Assembler, DiffMethod::numeric, false>;
    using ParentType = BoxLocalAssemblerBase<TypeTag, Assembler, ThisType, false>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using VolumeVariables = GetPropType<TypeTag, Properties::VolumeVariables>;
    using JacobianMatrix = GetPropType<TypeTag, Properties::JacobianMatrix>;
    using LocalResidual = GetPropType<TypeTag, Properties::LocalResidual>;
    using ElementResidualVector = typename LocalResidual::ElementResidualVector;
 
    enum { numEq = GetPropType<TypeTag, Properties::ModelTraits>::numEq() };
    enum { dim = GetPropType<TypeTag, Properties::GridView>::dimension };
 
public:
 
    using ParentType::ParentType;

    template <class PartialReassembler = DefaultPartialReassembler>
    ElementResidualVector assembleJacobianAndResidualImpl(JacobianMatrix& A, GridVariables& gridVariables,
                                                          const PartialReassembler* partialReassembler = nullptr)
    {
        if (partialReassembler)
            DUNE_THROW(Dune::NotImplemented, "partial reassembly for explicit time discretization");
 
        // get some aliases for convenience
        const auto& element = this->element();
        const auto& fvGeometry = this->fvGeometry();
        const auto& curSol = this->curSol();
        auto&& curElemVolVars = this->curElemVolVars();
 
        // get the vecor of the acutal element residuals
        const auto origResiduals = this->evalLocalResidual();
        const auto origStorageResiduals = this->evalLocalStorageResidual();

        //                                                                                              //
        // Calculate derivatives of all dofs in stencil with respect to the dofs in the element. In the //
        // neighboring elements we do so by computing the derivatives of the fluxes which depend on the //
        // actual element. In the actual element we evaluate the derivative of the entire residual.     //
        //                                                                                              //
 
        // create the element solution
        auto elemSol = elementSolution(element, curSol, fvGeometry.gridGeometry());
 
        // create the vector storing the partial derivatives
        ElementResidualVector partialDerivs(element.subEntities(dim));
 
        // calculation of the derivatives
        for (auto&& scv : scvs(fvGeometry))
        {
            // dof index and corresponding actual pri vars
            const auto dofIdx = scv.dofIndex();
            auto& curVolVars = this->getVolVarAccess(gridVariables.curGridVolVars(), curElemVolVars, scv);
            const VolumeVariables origVolVars(curVolVars);
 
            // calculate derivatives w.r.t to the privars at the dof at hand
            for (int pvIdx = 0; pvIdx < numEq; pvIdx++)
            {
                partialDerivs = 0.0;
 
                auto evalStorage = [&](Scalar priVar)
                {
                    // auto partialDerivsTmp = partialDerivs;
                    elemSol[scv.localDofIndex()][pvIdx] = priVar;
                    curVolVars.update(elemSol, this->problem(), element, scv);
                    return this->evalLocalStorageResidual();
                };
 
                // derive the residuals numerically
                static const NumericEpsilon<Scalar, numEq> eps_{this->problem().paramGroup()};
                static const int numDiffMethod = getParamFromGroup<int>(this->problem().paramGroup(), "Assembly.NumericDifferenceMethod");
                NumericDifferentiation::partialDerivative(evalStorage, elemSol[scv.localDofIndex()][pvIdx], partialDerivs, origStorageResiduals,
                                                          eps_(elemSol[scv.localDofIndex()][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[dofIdx][dofIdx][eqIdx][pvIdx] += partialDerivs[scv.localDofIndex()][eqIdx];
                }
 
                // restore the original state of the scv's volume variables
                curVolVars = origVolVars;
 
                // restore the original element solution
                elemSol[scv.localDofIndex()][pvIdx] = curSol[scv.dofIndex()][pvIdx];
                // TODO additional dof dependencies
            }
        }
        return origResiduals;
    }
}; // explicit BoxAssembler with numeric Jacobian

template<class TypeTag, class Assembler>
class BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, /*implicit=*/true>
: public BoxLocalAssemblerBase<TypeTag, Assembler,
                              BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, true>, true>
{
    using ThisType = BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, true>;
    using ParentType = BoxLocalAssemblerBase<TypeTag, Assembler, ThisType, true>;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using JacobianMatrix = GetPropType<TypeTag, Properties::JacobianMatrix>;
    using LocalResidual = GetPropType<TypeTag, Properties::LocalResidual>;
    using ElementResidualVector = typename LocalResidual::ElementResidualVector;
 
public:
 
    using ParentType::ParentType;

    template <class PartialReassembler = DefaultPartialReassembler>
    ElementResidualVector assembleJacobianAndResidualImpl(JacobianMatrix& A, GridVariables& gridVariables,
                                                          const PartialReassembler* partialReassembler = nullptr)
    {
        if (partialReassembler)
            DUNE_THROW(Dune::NotImplemented, "partial reassembly for analytic differentiation");
 
        // get some aliases for convenience
        const auto& element = this->element();
        const auto& fvGeometry = this->fvGeometry();
        const auto& problem = this->problem();
        const auto& curElemVolVars = this->curElemVolVars();
        const auto& elemFluxVarsCache = this->elemFluxVarsCache();
 
        // get the vecor of the acutal element residuals
        const auto origResiduals = this->evalLocalResidual();

        //                                                                                              //
        // Calculate derivatives of all dofs in stencil with respect to the dofs in the element. In the //
        // neighboring elements we do so by computing the derivatives of the fluxes which depend on the //
        // actual element. In the actual element we evaluate the derivative of the entire residual.     //
        //                                                                                              //
 
        // calculation of the source and storage derivatives
        for (const auto& scv : scvs(fvGeometry))
        {
            // dof index and corresponding actual pri vars
            const auto dofIdx = scv.dofIndex();
            const auto& volVars = curElemVolVars[scv];
 
            // derivative of this scv residual w.r.t the d.o.f. of the same scv (because of mass lumping)
            // only if the problem is instationary we add derivative of storage term
            // TODO if e.g. porosity depends on all dofs in the element, we would have off-diagonal matrix entries!?
            if (!this->assembler().isStationaryProblem())
                this->localResidual().addStorageDerivatives(A[dofIdx][dofIdx],
                                                            problem,
                                                            element,
                                                            fvGeometry,
                                                            volVars,
                                                            scv);
 
            // derivative of this scv residual w.r.t the d.o.f. of the same scv (because of mass lumping)
            // add source term derivatives
            this->localResidual().addSourceDerivatives(A[dofIdx][dofIdx],
                                                       problem,
                                                       element,
                                                       fvGeometry,
                                                       volVars,
                                                       scv);
        }
 
        // localJacobian[scvIdx][otherScvIdx][eqIdx][priVarIdx] of the fluxes
        for (const auto& scvf : scvfs(fvGeometry))
        {
            if (!scvf.boundary())
            {
                // add flux term derivatives
                this->localResidual().addFluxDerivatives(A,
                                                         problem,
                                                         element,
                                                         fvGeometry,
                                                         curElemVolVars,
                                                         elemFluxVarsCache,
                                                         scvf);
            }
 
            // the boundary gets special treatment to simplify
            // for the user
            else
            {
                const auto& insideScv = fvGeometry.scv(scvf.insideScvIdx());
                if (this->elemBcTypes()[insideScv.localDofIndex()].hasNeumann())
                {
                    // add flux term derivatives
                    this->localResidual().addRobinFluxDerivatives(A[insideScv.dofIndex()],
                                                                  problem,
                                                                  element,
                                                                  fvGeometry,
                                                                  curElemVolVars,
                                                                  elemFluxVarsCache,
                                                                  scvf);
                }
            }
        }
 
        return origResiduals;
    }
 
}; // implicit BoxAssembler with analytic Jacobian

template<class TypeTag, class Assembler>
class BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, /*implicit=*/false>
: public BoxLocalAssemblerBase<TypeTag, Assembler,
                              BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, false>, false>
{
    using ThisType = BoxLocalAssembler<TypeTag, Assembler, DiffMethod::analytic, false>;
    using ParentType = BoxLocalAssemblerBase<TypeTag, Assembler, ThisType, false>;
    using GridVariables = GetPropType<TypeTag, Properties::GridVariables>;
    using JacobianMatrix = GetPropType<TypeTag, Properties::JacobianMatrix>;
    using LocalResidual = GetPropType<TypeTag, Properties::LocalResidual>;
    using ElementResidualVector = typename LocalResidual::ElementResidualVector;
 
public:
 
    using ParentType::ParentType;

    template <class PartialReassembler = DefaultPartialReassembler>
    ElementResidualVector assembleJacobianAndResidualImpl(JacobianMatrix& A, GridVariables& gridVariables,
                                                          const PartialReassembler* partialReassembler = nullptr)
    {
        if (partialReassembler)
            DUNE_THROW(Dune::NotImplemented, "partial reassembly for explicit time discretization");
 
        // get some aliases for convenience
        const auto& element = this->element();
        const auto& fvGeometry = this->fvGeometry();
        const auto& problem = this->problem();
        const auto& curElemVolVars = this->curElemVolVars();
 
        // get the vecor of the acutal element residuals
        const auto origResiduals = this->evalLocalResidual();

        //                                                                                              //
        // Calculate derivatives of all dofs in stencil with respect to the dofs in the element. In the //
        // neighboring elements we do so by computing the derivatives of the fluxes which depend on the //
        // actual element. In the actual element we evaluate the derivative of the entire residual.     //
        //                                                                                              //
 
        // calculation of the source and storage derivatives
        for (const auto& scv : scvs(fvGeometry))
        {
            // dof index and corresponding actual pri vars
            const auto dofIdx = scv.dofIndex();
            const auto& volVars = curElemVolVars[scv];
 
            // derivative of this scv residual w.r.t the d.o.f. of the same scv (because of mass lumping)
            // only if the problem is instationary we add derivative of storage term
            this->localResidual().addStorageDerivatives(A[dofIdx][dofIdx],
                                                        problem,
                                                        element,
                                                        fvGeometry,
                                                        volVars,
                                                        scv);
        }
 
        return origResiduals;
    }
 
}; // explicit BoxAssembler with analytic Jacobian
 
} // end namespace Dumux
 
#endif