tpfalinearizer.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:
/*
  This file is part of the Open Porous Media project (OPM).
 
  OPM 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.
 
  OPM 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 OPM.  If not, see <http://www.gnu.org/licenses/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef TPFA_LINEARIZER_HH
#define TPFA_LINEARIZER_HH
 
#include <dune/common/version.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <opm/common/Exceptions.hpp>
#include <opm/common/TimingMacros.hpp>
 
#include <opm/grid/utility/SparseTable.hpp>
 
#include <opm/material/common/ConditionalStorage.hpp>
 
#include <opm/input/eclipse/EclipseState/Grid/FaceDir.hpp>
#include <opm/input/eclipse/Schedule/BCProp.hpp>
 
#include <opm/models/blackoil/blackoilproperties.hh>
#include <opm/models/common/multiphasebaseproperties.hh>
#include <opm/models/discretization/common/baseauxiliarymodule.hh>
#include <opm/models/discretization/common/fvbaseproperties.hh>
#include <opm/models/discretization/common/linearizationtype.hh>
#include <opm/simulators/linalg/exportSystem.hpp>
 
#include <cassert>
#include <cstddef>
#include <exception>   // current_exception, rethrow_exception
#include <iostream>
#include <map>
#include <memory>
#include <numeric>
#include <set>
#include <stdexcept>
#include <unordered_map>
#include <vector>
 
#include <fmt/format.h>
 
#include <opm/common/utility/gpuDecorators.hpp>
#if HAVE_CUDA
#if USE_HIP
#include <opm/simulators/linalg/gpuistl_hip/GpuBuffer.hpp>
#include <opm/simulators/linalg/gpuistl_hip/GpuView.hpp>
#include <opm/simulators/linalg/gpuistl_hip/MiniMatrix.hpp>
#include <opm/simulators/linalg/gpuistl_hip/MiniVector.hpp>
#else
#include <opm/simulators/linalg/gpuistl/GpuBuffer.hpp>
#include <opm/simulators/linalg/gpuistl/GpuView.hpp>
#include <opm/simulators/linalg/gpuistl/MiniMatrix.hpp>
#include <opm/simulators/linalg/gpuistl/MiniVector.hpp>
#endif
#endif
 
namespace Opm::Parameters {
 
struct SeparateSparseSourceTerms { static constexpr bool value = false; };
 
} // namespace Opm::Parameters
 
namespace Opm {
 
// forward declarations
template<class TypeTag>
class EcfvDiscretization;
 
// Moved these structs out of the class to make them visible in the GPU code.
template<class Storage = std::vector<int>>
struct FullDomain
{
    Storage cells;
};
 
#if HAVE_CUDA && OPM_IS_COMPILING_WITH_GPU_COMPILER
    FullDomain<gpuistl::GpuBuffer<int>> copy_to_gpu(FullDomain<> CPUDomain)
    {
        if (CPUDomain.cells.size() == 0) {
            OPM_THROW(std::runtime_error, "Cannot copy empty full domain to GPU.");
        }
        return FullDomain<gpuistl::GpuBuffer<int>>{
            gpuistl::GpuBuffer<int>(CPUDomain.cells)
        };
    };
 
    FullDomain<gpuistl::GpuView<int>> make_view(FullDomain<gpuistl::GpuBuffer<int>>& buffer)
    {
        if (buffer.cells.size() == 0) {
            OPM_THROW(std::runtime_error, "Cannot make view of empty full domain buffer.");
        }
        return FullDomain<gpuistl::GpuView<int>>{
            gpuistl::make_view(buffer.cells)
        };
    };
#endif
 
template <class ResidualNBInfoType,class BlockType>
struct NeighborInfoStruct
{
    unsigned int neighbor;
    ResidualNBInfoType res_nbinfo;
    BlockType* matBlockAddress;
 
    template <class OtherBlockType>
    NeighborInfoStruct(const NeighborInfoStruct<ResidualNBInfoType,OtherBlockType>& other)
        : neighbor(other.neighbor)
        , res_nbinfo(other.res_nbinfo)
        , matBlockAddress(nullptr)
    {
        if (other.matBlockAddress) {
            matBlockAddress = reinterpret_cast<BlockType*>(other.matBlockAddress);
        }
    }
 
    template <class PtrType>
    NeighborInfoStruct(unsigned int n, const ResidualNBInfoType& r, PtrType ptr)
        : neighbor(n)
        , res_nbinfo(r)
        , matBlockAddress(static_cast<BlockType*>(ptr))
    {
    }
 
    // Add a default constructor
    NeighborInfoStruct()
        : neighbor(0)
        , res_nbinfo()
        , matBlockAddress(nullptr)
    {
    }
};
 
#if HAVE_CUDA && OPM_IS_COMPILING_WITH_GPU_COMPILER
namespace  gpuistl {
    template<class MiniMatrixType, class MatrixBlockType, class ResidualNBInfoType>
    auto copy_to_gpu(const SparseTable<NeighborInfoStruct<ResidualNBInfoType, MatrixBlockType>>& cpuNeighborInfoTable)
    {
        // Convert the DUNE FieldMatrix/MatrixBlock to MiniMatrix types
        using StructWithMinimatrix = NeighborInfoStruct<ResidualNBInfoType, MiniMatrixType>;
        std::vector<StructWithMinimatrix> minimatrices(cpuNeighborInfoTable.dataSize());
        size_t idx = 0;
        for (auto e : cpuNeighborInfoTable.dataStorage()) {
            minimatrices[idx++] = StructWithMinimatrix(e);
        }
 
        return SparseTable<StructWithMinimatrix, gpuistl::GpuBuffer>(
            gpuistl::GpuBuffer<StructWithMinimatrix>(minimatrices),
            gpuistl::GpuBuffer<int>(cpuNeighborInfoTable.rowStarts())
        );
    }
}
#endif
 
template<class TypeTag>
class TpfaLinearizer
{
    using Model = GetPropType<TypeTag, Properties::Model>;
    using Problem = GetPropType<TypeTag, Properties::Problem>;
    using Simulator = GetPropType<TypeTag, Properties::Simulator>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Evaluation = GetPropType<TypeTag, Properties::Evaluation>;
 
    using SolutionVector = GetPropType<TypeTag, Properties::SolutionVector>;
    using GlobalEqVector = GetPropType<TypeTag, Properties::GlobalEqVector>;
    using SparseMatrixAdapter = GetPropType<TypeTag, Properties::SparseMatrixAdapter>;
    using EqVector = GetPropType<TypeTag, Properties::EqVector>;
    using Constraints = GetPropType<TypeTag, Properties::Constraints>;
    using Stencil = GetPropType<TypeTag, Properties::Stencil>;
    using LocalResidual = GetPropType<TypeTag, Properties::LocalResidual>;
    using IntensiveQuantities = GetPropType<TypeTag, Properties::IntensiveQuantities>;
    using Indices = GetPropType<TypeTag, Properties::Indices>;
 
    using Element = typename GridView::template Codim<0>::Entity;
    using ElementIterator = typename GridView::template Codim<0>::Iterator;
 
    using Vector = GlobalEqVector;
 
    enum { numEq = getPropValue<TypeTag, Properties::NumEq>() };
    enum { historySize = getPropValue<TypeTag, Properties::TimeDiscHistorySize>() };
    enum { dimWorld = GridView::dimensionworld };
 
    using MatrixBlock = typename SparseMatrixAdapter::MatrixBlock;
    using VectorBlock = Dune::FieldVector<Scalar, numEq>;
    using ADVectorBlock = GetPropType<TypeTag, Properties::RateVector>;
 
#if HAVE_CUDA && OPM_IS_COMPILING_WITH_GPU_COMPILER
    using MatrixBlockGPU = gpuistl::MiniMatrix<Scalar, numEq * numEq>;
    using VectorBlockGPU = gpuistl::MiniVector<Scalar, numEq>;
#endif
 
    static constexpr bool linearizeNonLocalElements =
        getPropValue<TypeTag, Properties::LinearizeNonLocalElements>();
    static constexpr bool enableFullyImplicitThermal = (getPropValue<TypeTag, Properties::EnergyModuleType>() == EnergyModules::FullyImplicitThermal);
    static constexpr bool enableDiffusion = getPropValue<TypeTag, Properties::EnableDiffusion>();
    static constexpr bool enableDispersion = getPropValue<TypeTag, Properties::EnableDispersion>();
    static const bool enableBioeffects = getPropValue<TypeTag, Properties::EnableBioeffects>();
 
    // copying the linearizer is not a good idea
    TpfaLinearizer(const TpfaLinearizer&) = delete;
 
public:
    TpfaLinearizer()
    {
        simulatorPtr_ = nullptr;
        separateSparseSourceTerms_ = Parameters::Get<Parameters::SeparateSparseSourceTerms>();
        exportIndex_=-1;
        exportCount_=-1;
    }
 
    static void registerParameters()
    {
        Parameters::Register<Parameters::SeparateSparseSourceTerms>
            ("Treat well source terms all in one go, instead of on a cell by cell basis.");
    }
 
    void init(Simulator& simulator)
    {
        simulatorPtr_ = &simulator;
        eraseMatrix();
    }
 
    void eraseMatrix()
    {
        jacobian_.reset();
    }
 
    void linearize()
    {
        linearizeDomain();
        linearizeAuxiliaryEquations();
    }
 
    void linearizeDomain()
    {
        int succeeded;
        try {
            linearizeDomain(fullDomain_);
            succeeded = 1;
        }
        catch (const std::exception& e) {
            std::cout << "rank " << simulator_().gridView().comm().rank()
                      << " caught an exception while linearizing:" << e.what()
                      << "\n"  << std::flush;
            succeeded = 0;
        }
        catch (...) {
            std::cout << "rank " << simulator_().gridView().comm().rank()
                      << " caught an exception while linearizing"
                      << "\n"  << std::flush;
            succeeded = 0;
        }
        succeeded = simulator_().gridView().comm().min(succeeded);
 
        if (!succeeded) {
            throw NumericalProblem("A process did not succeed in linearizing the system");
        }
    }
 
    template <class SubDomainType>
    void linearizeDomain(const SubDomainType& domain, const bool isNlddLocalSolve = false)
    {
        OPM_TIMEBLOCK(linearizeDomain);
        // we defer the initialization of the Jacobian matrix until here because the
        // auxiliary modules usually assume the problem, model and grid to be fully
        // initialized...
        if (!jacobian_) {
            initFirstIteration_();
        }
 
        // Called here because it is no longer called from linearize_().
        if (isNlddLocalSolve) {
            resetSystem_(domain);
        }
        else {
            resetSystem_();
        }
 
        linearize_(domain, isNlddLocalSolve);
    }
 
    void finalize()
    { jacobian_->finalize(); }
 
    void linearizeAuxiliaryEquations()
    {
        OPM_TIMEBLOCK(linearizeAuxilaryEquations);
        // flush possible local caches into matrix structure
        jacobian_->commit();
 
        auto& model = model_();
        const auto& comm = simulator_().gridView().comm();
        for (unsigned auxModIdx = 0; auxModIdx < model.numAuxiliaryModules(); ++auxModIdx) {
            bool succeeded = true;
            try {
                model.auxiliaryModule(auxModIdx)->linearize(*jacobian_, residual_);
            }
            catch (const std::exception& e) {
                succeeded = false;
 
                std::cout << "rank " << simulator_().gridView().comm().rank()
                          << " caught an exception while linearizing:" << e.what()
                          << "\n"  << std::flush;
            }
 
            succeeded = comm.min(succeeded);
 
            if (!succeeded) {
                throw NumericalProblem("linearization of an auxiliary equation failed");
            }
        }
    }
 
    const SparseMatrixAdapter& jacobian() const
    { return *jacobian_; }
 
    SparseMatrixAdapter& jacobian()
    { return *jacobian_; }
 
    const GlobalEqVector& residual() const
    { return residual_; }
 
    GlobalEqVector& residual()
    { return residual_; }
 
    void exportSystem(const int idx, std::string& tag, const char *path="export")
    {
        const bool export_sparsity = exportIndex_ == -1;
 
        // increment indices and generate tag
        exportCount_ = exportIndex_ == idx ? ++exportCount_ : 0;
        exportIndex_ = idx;
        tag = fmt::format("_{:03d}_{:02d}", exportIndex_, exportCount_);
 
        fmt::print("index = {:d}\n", exportIndex_);
        fmt::print("count = {:d}\n", exportCount_);
 
        Opm::exportSystem(jacobian_->istlMatrix(), residual_, export_sparsity, tag.c_str(), path);
    }
 
    void setLinearizationType(LinearizationType linearizationType)
    { linearizationType_ = linearizationType; }
 
    const LinearizationType& getLinearizationType() const
    { return linearizationType_; }
 
    const auto& getFlowsInfo() const
    { return flowsInfo_; }
 
    const auto& getFloresInfo() const
    { return floresInfo_; }
 
    const auto& getVelocityInfo() const
    { return velocityInfo_; }
 
    const auto& getNeighborInfo() const {
        return neighborInfo_;
    }
 
 
    void updateDiscretizationParameters()
    {
        updateStoredTransmissibilities();
    }
 
    void updateBoundaryConditionData()
    {
        for (auto& bdyInfo : boundaryInfo_) {
            const auto [type, massrateAD] = problem_().boundaryCondition(bdyInfo.cell, bdyInfo.dir);
 
            // Strip the unnecessary (and zero anyway) derivatives off massrate.
            VectorBlock massrate(0.0);
            for (std::size_t ii = 0; ii < massrate.size(); ++ii) {
                massrate[ii] = massrateAD[ii].value();
            }
            if (type != BCType::NONE) {
                const auto& exFluidState = problem_().boundaryFluidState(bdyInfo.cell, bdyInfo.dir);
                bdyInfo.bcdata.type = type;
                bdyInfo.bcdata.massRate = massrate;
                bdyInfo.bcdata.exFluidState = exFluidState;
            }
        }
    }
 
    std::map<unsigned, Constraints> constraintsMap() const
    { return {}; }
 
    template <class SubDomainType>
    void resetSystem_(const SubDomainType& domain)
    {
        if (!jacobian_) {
            initFirstIteration_();
        }
        for (int globI : domain.cells) {
            residual_[globI] = 0.0;
            jacobian_->clearRow(globI, 0.0);
        }
    }
 
private:
    Simulator& simulator_()
    { return *simulatorPtr_; }
 
    const Simulator& simulator_() const
    { return *simulatorPtr_; }
 
    Problem& problem_()
    { return simulator_().problem(); }
 
    const Problem& problem_() const
    { return simulator_().problem(); }
 
    Model& model_()
    { return simulator_().model(); }
 
    const Model& model_() const
    { return simulator_().model(); }
 
    const GridView& gridView_() const
    { return problem_().gridView(); }
 
    void initFirstIteration_()
    {
        // initialize the BCRS matrix for the Jacobian of the residual function
        createMatrix_();
 
        // initialize the Jacobian matrix and the vector for the residual function
        residual_.resize(model_().numTotalDof());
        resetSystem_();
 
        // initialize the sparse tables for Flows and Flores
        createFlows_();
    }
 
    // Construct the BCRS matrix for the Jacobian of the residual function
    void createMatrix_()
    {
        OPM_TIMEBLOCK(createMatrix);
        if (!neighborInfo_.empty()) {
            // It is ok to call this function multiple times, but it
            // should not do anything if already called.
            return;
        }
        const auto& model = model_();
        Stencil stencil(gridView_(), model_().dofMapper());
 
        // for the main model, find out the global indices of the neighboring degrees of
        // freedom of each primary degree of freedom
        using NeighborSet = std::set<unsigned>;
        std::vector<NeighborSet> sparsityPattern(model.numTotalDof());
        const Scalar gravity = problem_().gravity()[dimWorld - 1];
        unsigned numCells = model.numTotalDof();
        neighborInfo_.reserve(numCells, 6 * numCells);
        std::vector<NeighborInfoCPU> loc_nbinfo;
        for (const auto& elem : elements(gridView_())) {
            stencil.update(elem);
 
            for (unsigned primaryDofIdx = 0; primaryDofIdx < stencil.numPrimaryDof(); ++primaryDofIdx) {
                const unsigned myIdx = stencil.globalSpaceIndex(primaryDofIdx);
                loc_nbinfo.resize(stencil.numDof() - 1); // Do not include the primary dof in neighborInfo_
 
                for (unsigned dofIdx = 0; dofIdx < stencil.numDof(); ++dofIdx) {
                    const unsigned neighborIdx = stencil.globalSpaceIndex(dofIdx);
                    sparsityPattern[myIdx].insert(neighborIdx);
                    if (dofIdx > 0) {
                        const Scalar trans = problem_().transmissibility(myIdx, neighborIdx);
                        const auto scvfIdx = dofIdx - 1;
                        const auto& scvf = stencil.interiorFace(scvfIdx);
                        const Scalar area = scvf.area();
                        const Scalar Vin = problem_().model().dofTotalVolume(myIdx);
                        const Scalar Vex = problem_().model().dofTotalVolume(neighborIdx);
                        const Scalar zIn = problem_().dofCenterDepth(myIdx);
                        const Scalar zEx = problem_().dofCenterDepth(neighborIdx);
                        const Scalar dZg = (zIn - zEx)*gravity;
                        const Scalar thpres = problem_().thresholdPressure(myIdx, neighborIdx);
                        const auto dirId = scvf.dirId();
                        auto faceDir = dirId < 0 ? FaceDir::DirEnum::Unknown
                                                 : FaceDir::FromIntersectionIndex(dirId);
                        ResidualNBInfo nbinfo{trans, area, thpres, dZg, faceDir, Vin, Vex, {}, {}, {}, {}};
                        if constexpr (enableFullyImplicitThermal) {
                            nbinfo.inAlpha = problem_().thermalHalfTransmissibility(myIdx, neighborIdx);
                            nbinfo.outAlpha = problem_().thermalHalfTransmissibility(neighborIdx, myIdx);
                        }
                        if constexpr (enableDiffusion) {
                            nbinfo.diffusivity = problem_().diffusivity(myIdx, neighborIdx);
                        }
                        if constexpr (enableDispersion) {
                            nbinfo.dispersivity = problem_().dispersivity(myIdx, neighborIdx);
                        }
                        loc_nbinfo[dofIdx - 1] = NeighborInfoCPU{neighborIdx, nbinfo, nullptr};
                    }
                }
                neighborInfo_.appendRow(loc_nbinfo.begin(), loc_nbinfo.end());
                if (problem_().nonTrivialBoundaryConditions()) {
                    for (unsigned bfIndex = 0; bfIndex < stencil.numBoundaryFaces(); ++bfIndex) {
                        const auto& bf = stencil.boundaryFace(bfIndex);
                        const int dir_id = bf.dirId();
                        // not for NNCs
                        if (dir_id < 0) {
                            continue;
                        }
                        const auto [type, massrateAD] = problem_().boundaryCondition(myIdx, dir_id);
                        // Strip the unnecessary (and zero anyway) derivatives off massrate.
                        VectorBlock massrate(0.0);
                        for (std::size_t ii = 0; ii < massrate.size(); ++ii) {
                            massrate[ii] = massrateAD[ii].value();
                        }
                        const auto& exFluidState = problem_().boundaryFluidState(myIdx, dir_id);
                        BoundaryConditionData bcdata{type,
                                                     massrate,
                                                     exFluidState.pvtRegionIndex(),
                                                     bfIndex,
                                                     bf.area(),
                                                     bf.integrationPos()[dimWorld - 1],
                                                     exFluidState};
                        boundaryInfo_.push_back({myIdx, dir_id, bfIndex, bcdata});
                    }
                }
            }
        }
 
        // add the additional neighbors and degrees of freedom caused by the auxiliary
        // equations
        const std::size_t numAuxMod = model.numAuxiliaryModules();
        for (unsigned auxModIdx = 0; auxModIdx < numAuxMod; ++auxModIdx) {
            model.auxiliaryModule(auxModIdx)->addNeighbors(sparsityPattern);
        }
 
        // allocate raw matrix
        jacobian_ = std::make_unique<SparseMatrixAdapter>(simulator_());
        diagMatAddress_.resize(numCells);
        // create matrix structure based on sparsity pattern
        jacobian_->reserve(sparsityPattern);
        for (unsigned globI = 0; globI < numCells; globI++) {
            const auto& nbInfos = neighborInfo_[globI];
            diagMatAddress_[globI] = jacobian_->blockAddress(globI, globI);
            for (auto& nbInfo : nbInfos) {
                nbInfo.matBlockAddress = jacobian_->blockAddress(nbInfo.neighbor, globI);
            }
        }
 
        // Create dummy full domain.
        fullDomain_.cells.resize(numCells);
        std::iota(fullDomain_.cells.begin(), fullDomain_.cells.end(), 0);
    }
 
    // reset the global linear system of equations.
    void resetSystem_()
    {
        residual_ = 0.0;
        // zero all matrix entries
        jacobian_->clear();
    }
 
    // Initialize the flows, flores, and velocity sparse tables
    void createFlows_()
    {
        OPM_TIMEBLOCK(createFlows);
        // If FLOWS/FLORES is set in any RPTRST in the schedule, then we initializate the sparse tables
        // For now, do the same also if any block flows are requested (TODO: only save requested cells...)
        // If DISPERC is in the deck, we initialize the sparse table here as well.
        const bool anyFlows = simulator_().problem().eclWriter().outputModule().getFlows().anyFlows() ||
                              simulator_().problem().eclWriter().outputModule().getFlows().hasBlockFlows();
        const bool anyFlores = simulator_().problem().eclWriter().outputModule().getFlows().anyFlores();
        const bool dispersionActive = simulator_().vanguard().eclState().getSimulationConfig().rock_config().dispersion();
        if (((!anyFlows || !flowsInfo_.empty()) && (!anyFlores || !floresInfo_.empty())) && (!dispersionActive && !enableBioeffects)) {
            return;
        }
        const auto& model = model_();
        const auto& nncOutput = simulator_().problem().eclWriter().getOutputNnc();
        Stencil stencil(gridView_(), model_().dofMapper());
        const unsigned numCells = model.numTotalDof();
        std::unordered_multimap<int, std::pair<int, int>> nncIndices;
        std::vector<FlowInfo> loc_flinfo;
        std::vector<VelocityInfo> loc_vlinfo;
        unsigned int nncId = 0;
        VectorBlock flow(0.0);
 
        // Create a nnc structure to use fast lookup
        for (unsigned nncIdx = 0; nncIdx < nncOutput.size(); ++nncIdx) {
            const int ci1 = nncOutput[nncIdx].cell1;
            const int ci2 = nncOutput[nncIdx].cell2;
            nncIndices.emplace(ci1, std::make_pair(ci2, nncIdx));
        }
 
        if (anyFlows) {
            flowsInfo_.reserve(numCells, 6 * numCells);
        }
        if (anyFlores) {
            floresInfo_.reserve(numCells, 6 * numCells);
        }
        if (dispersionActive || enableBioeffects) {
            velocityInfo_.reserve(numCells, 6 * numCells);
        }
 
        for (const auto& elem : elements(gridView_())) {
            stencil.update(elem);
            for (unsigned primaryDofIdx = 0; primaryDofIdx < stencil.numPrimaryDof(); ++primaryDofIdx) {
                const unsigned myIdx = stencil.globalSpaceIndex(primaryDofIdx);
                const int numFaces = stencil.numBoundaryFaces() + stencil.numInteriorFaces();
                loc_flinfo.resize(numFaces);
                loc_vlinfo.resize(stencil.numDof() - 1);
 
                for (unsigned dofIdx = 0; dofIdx < stencil.numDof(); ++dofIdx) {
                    const unsigned neighborIdx = stencil.globalSpaceIndex(dofIdx);
                    if (dofIdx > 0) {
                        const auto scvfIdx = dofIdx - 1;
                        const auto& scvf = stencil.interiorFace(scvfIdx);
                        int faceId = scvf.dirId();
                        const int cartMyIdx = simulator_().vanguard().cartesianIndex(myIdx);
                        const int cartNeighborIdx = simulator_().vanguard().cartesianIndex(neighborIdx);
                        const auto& range = nncIndices.equal_range(cartMyIdx);
                        for (auto it = range.first; it != range.second; ++it) {
                            if (it->second.first == cartNeighborIdx){
                                // -1 gives problem since is used for the nncInput from the deck
                                faceId = -2;
                                // the index is stored to be used for writting the outputs
                                nncId = it->second.second;
                            }
                        }
                        loc_flinfo[dofIdx - 1] = FlowInfo{faceId, flow, nncId};
                        loc_vlinfo[dofIdx - 1] = VelocityInfo{flow};
                    }
                }
 
                for (unsigned bdfIdx = 0; bdfIdx < stencil.numBoundaryFaces(); ++bdfIdx) {
                    const auto& scvf = stencil.boundaryFace(bdfIdx);
                    const int faceId = scvf.dirId();
                    loc_flinfo[stencil.numInteriorFaces() + bdfIdx] = FlowInfo{faceId, flow, nncId};
                }
 
                if (anyFlows) {
                    flowsInfo_.appendRow(loc_flinfo.begin(), loc_flinfo.end());
                }
                if (anyFlores) {
                    floresInfo_.appendRow(loc_flinfo.begin(), loc_flinfo.end());
                }
                if (dispersionActive || enableBioeffects) {
                    velocityInfo_.appendRow(loc_vlinfo.begin(), loc_vlinfo.end());
                }
            }
        }
    }
 
public:
    void setResAndJacobi(VectorBlock& res, MatrixBlock& bMat, const ADVectorBlock& resid) const
    {
        for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx) {
            res[eqIdx] = resid[eqIdx].value();
        }
 
        for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx) {
            for (unsigned pvIdx = 0; pvIdx < numEq; ++pvIdx) {
                // A[dofIdx][focusDofIdx][eqIdx][pvIdx] is the partial derivative of
                // the residual function 'eqIdx' for the degree of freedom 'dofIdx'
                // with regard to the focus variable 'pvIdx' of the degree of freedom
                // 'focusDofIdx'
                bMat[eqIdx][pvIdx] = resid[eqIdx].derivative(pvIdx);
            }
        }
    }
 
    void updateFlowsInfo()
    {
        OPM_TIMEBLOCK(updateFlows);
        const bool enableFlows = simulator_().problem().eclWriter().outputModule().getFlows().hasFlows() ||
                                 simulator_().problem().eclWriter().outputModule().getFlows().hasBlockFlows();
        const bool enableFlores = simulator_().problem().eclWriter().outputModule().getFlows().hasFlores();
        if (!enableFlows && !enableFlores) {
            return;
        }
        const unsigned int numCells = model_().numTotalDof();
#ifdef _OPENMP
#pragma omp parallel for
#endif
        for (unsigned globI = 0; globI < numCells; ++globI) {
            OPM_TIMEBLOCK_LOCAL(linearizationForEachCell, Subsystem::Assembly);
            const auto& nbInfos = neighborInfo_[globI];
            ADVectorBlock adres(0.0);
            ADVectorBlock darcyFlux(0.0);
            const IntensiveQuantities& intQuantsIn = model_().intensiveQuantities(globI, /*timeIdx*/ 0);
            // Flux term.
            {
                OPM_TIMEBLOCK_LOCAL(fluxCalculationForEachCell, Subsystem::Assembly);
                short loc = 0;
                for (const auto& nbInfo : nbInfos) {
                    OPM_TIMEBLOCK_LOCAL(fluxCalculationForEachFace, Subsystem::Assembly);
                    const unsigned globJ = nbInfo.neighbor;
                    assert(globJ != globI);
                    adres = 0.0;
                    darcyFlux = 0.0;
                    const IntensiveQuantities& intQuantsEx = model_().intensiveQuantities(globJ, /*timeIdx*/ 0);
                    LocalResidual::computeFlux(adres, darcyFlux, globI, globJ, intQuantsIn,
                                               intQuantsEx, nbInfo.res_nbinfo, problem_().moduleParams());
                    adres *= nbInfo.res_nbinfo.faceArea;
                    if (enableFlows) {
                        for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx) {
                            flowsInfo_[globI][loc].flow[eqIdx] = adres[eqIdx].value();
                        }
                    }
                    if (enableFlores) {
                        for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx) {
                            floresInfo_[globI][loc].flow[eqIdx] = darcyFlux[eqIdx].value();
                        }
                    }
                    ++loc;
                }
            }
        }
 
        // Boundary terms. Only looping over cells with nontrivial bcs.
        for (const auto& bdyInfo : boundaryInfo_) {
            if (bdyInfo.bcdata.type == BCType::NONE) {
                continue;
            }
 
            ADVectorBlock adres(0.0);
            const unsigned globI = bdyInfo.cell;
            const auto& nbInfos = neighborInfo_[globI];
            const IntensiveQuantities& insideIntQuants = model_().intensiveQuantities(globI, /*timeIdx*/ 0);
            LocalResidual::computeBoundaryFlux(adres, problem_(), bdyInfo.bcdata, insideIntQuants, globI);
            adres *= bdyInfo.bcdata.faceArea;
            const unsigned bfIndex = bdyInfo.bfIndex;
            if (enableFlows) {
                for (unsigned eqIdx = 0; eqIdx < numEq; ++eqIdx) {
                    flowsInfo_[globI][nbInfos.size() + bfIndex].flow[eqIdx] = adres[eqIdx].value();
                }
            }
            // TODO also store Flores?
        }
    }
 
private:
    template <class SubDomainType>
    void linearize_(const SubDomainType& domain, bool isNlddLocalSolve)
    {
        // This check should be removed once this is addressed by
        // for example storing the previous timesteps' values for
        // rsmax (for DRSDT) and similar.
        if (!problem_().recycleFirstIterationStorage()) {
            if (!model_().storeIntensiveQuantities() && !model_().enableStorageCache()) {
                OPM_THROW(std::runtime_error, "Must have cached either IQs or storage when we cannot recycle.");
            }
        }
 
        OPM_TIMEBLOCK(linearize);
 
        // We do not call resetSystem_() here, since that will set
        // the full system to zero, not just our part.
        // Instead, that must be called before starting the linearization.
        const bool dispersionActive = simulator_().vanguard().eclState().getSimulationConfig().rock_config().dispersion();
        const unsigned int numCells = domain.cells.size();
 
        // Fetch timestepsize used later in accumulation term.
        const double dt = simulator_().timeStepSize();
 
#ifdef _OPENMP
#pragma omp parallel for
#endif
        for (unsigned ii = 0; ii < numCells; ++ii) {
            OPM_TIMEBLOCK_LOCAL(linearizationForEachCell, Subsystem::Assembly);
            const unsigned globI = domain.cells[ii];
            const auto& nbInfos = neighborInfo_[globI];
            VectorBlock res(0.0);
            MatrixBlock bMat(0.0);
            ADVectorBlock adres(0.0);
            ADVectorBlock darcyFlux(0.0);
            const IntensiveQuantities& intQuantsIn = model_().intensiveQuantities(globI, /*timeIdx*/ 0);
 
            // Flux term.
            {
                OPM_TIMEBLOCK_LOCAL(fluxCalculationForEachCell, Subsystem::Assembly);
                short loc = 0;
                for (const auto& nbInfo : nbInfos) {
                    OPM_TIMEBLOCK_LOCAL(fluxCalculationForEachFace, Subsystem::Assembly);
                    const unsigned globJ = nbInfo.neighbor;
                    assert(globJ != globI);
                    res = 0.0;
                    bMat = 0.0;
                    adres = 0.0;
                    darcyFlux = 0.0;
                    const IntensiveQuantities& intQuantsEx = model_().intensiveQuantities(globJ, /*timeIdx*/ 0);
                    LocalResidual::computeFlux(adres, darcyFlux, globI, globJ, intQuantsIn, intQuantsEx,
                                               nbInfo.res_nbinfo, problem_().moduleParams());
                    adres *= nbInfo.res_nbinfo.faceArea;
                    if (dispersionActive || enableBioeffects) {
                        for (unsigned phaseIdx = 0; phaseIdx < numEq; ++phaseIdx) {
                            velocityInfo_[globI][loc].velocity[phaseIdx] =
                                darcyFlux[phaseIdx].value() / nbInfo.res_nbinfo.faceArea;
                        }
                    }
                    setResAndJacobi(res, bMat, adres);
                    residual_[globI] += res;
                    //SparseAdapter syntax:  jacobian_->addToBlock(globI, globI, bMat);
                    *diagMatAddress_[globI] += bMat;
                    bMat *= -1.0;
                    //SparseAdapter syntax: jacobian_->addToBlock(globJ, globI, bMat);
                    *nbInfo.matBlockAddress += bMat;
                    ++loc;
                }
            }
 
            // Accumulation term.
            const double volume = model_().dofTotalVolume(globI);
            const Scalar storefac = volume / dt;
            adres = 0.0;
            {
                OPM_TIMEBLOCK_LOCAL(computeStorage, Subsystem::Assembly);
                LocalResidual::computeStorage(adres, intQuantsIn);
            }
            setResAndJacobi(res, bMat, adres);
            // Either use cached storage term, or compute it on the fly.
            if (model_().enableStorageCache()) {
                // The cached storage for timeIdx 0 (current time) is not
                // used, but after storage cache is shifted at the end of the
                // timestep, it will become cached storage for timeIdx 1.
                model_().updateCachedStorage(globI, /*timeIdx=*/0, res);
                // We should not update the storage cache here for NLDD local solves.
                // This will reset the start-of-step storage to incorrect numbers when
                // we do local solves, where the iteration number will start from 0,
                // but the starting state may not be identical to the start-of-step state.
                // Note that a full assembly must be done before local solves
                // otherwise this will be left un-updated.
                if (model_().newtonMethod().numIterations() == 0 && !isNlddLocalSolve) {
                    // Need to update the storage cache.
                    if (problem_().recycleFirstIterationStorage()) {
                        // Assumes nothing have changed in the system which
                        // affects masses calculated from primary variables.
                        model_().updateCachedStorage(globI, /*timeIdx=*/1, res);
                    }
                    else {
                        Dune::FieldVector<Scalar, numEq> tmp;
                        const IntensiveQuantities intQuantOld = model_().intensiveQuantities(globI, 1);
                        LocalResidual::computeStorage(tmp, intQuantOld);
                        model_().updateCachedStorage(globI, /*timeIdx=*/1, tmp);
                    }
                }
                res -= model_().cachedStorage(globI, 1);
            }
            else {
                OPM_TIMEBLOCK_LOCAL(computeStorage0, Subsystem::Assembly);
                Dune::FieldVector<Scalar, numEq> tmp;
                const IntensiveQuantities intQuantOld = model_().intensiveQuantities(globI, 1);
                LocalResidual::computeStorage(tmp, intQuantOld);
                // assume volume do not change
                res -= tmp;
            }
            res *= storefac;
            bMat *= storefac;
            residual_[globI] += res;
            //SparseAdapter syntax: jacobian_->addToBlock(globI, globI, bMat);
            *diagMatAddress_[globI] += bMat;
 
            // Cell-wise source terms.
            // This will include well sources if SeparateSparseSourceTerms is false.
            res = 0.0;
            bMat = 0.0;
            adres = 0.0;
            if (separateSparseSourceTerms_) {
                LocalResidual::computeSourceDense(adres, problem_(), intQuantsIn, globI, 0);
            }
            else {
                LocalResidual::computeSource(adres, problem_(), intQuantsIn, globI, 0);
            }
            adres *= -volume;
            setResAndJacobi(res, bMat, adres);
            residual_[globI] += res;
            //SparseAdapter syntax: jacobian_->addToBlock(globI, globI, bMat);
            *diagMatAddress_[globI] += bMat;
        } // end of loop for cell globI.
 
        // Add sparse source terms. For now only wells.
        if (separateSparseSourceTerms_) {
            problem_().wellModel().addReservoirSourceTerms(residual_, diagMatAddress_);
        }
 
        // Boundary terms. Only looping over cells with nontrivial bcs.
        for (const auto& bdyInfo : boundaryInfo_) {
            if (bdyInfo.bcdata.type == BCType::NONE) {
                continue;
            }
 
            VectorBlock res(0.0);
            MatrixBlock bMat(0.0);
            ADVectorBlock adres(0.0);
            const unsigned globI = bdyInfo.cell;
            const IntensiveQuantities& insideIntQuants = model_().intensiveQuantities(globI, /*timeIdx*/ 0);
            LocalResidual::computeBoundaryFlux(adres, problem_(), bdyInfo.bcdata, insideIntQuants, globI);
            adres *= bdyInfo.bcdata.faceArea;
            setResAndJacobi(res, bMat, adres);
            residual_[globI] += res;
            *diagMatAddress_[globI] += bMat;
        }
    }
 
    void updateStoredTransmissibilities()
    {
        if (neighborInfo_.empty()) {
            // This function was called before createMatrix_() was called.
            // We call initFirstIteration_(), not createMatrix_(), because
            // that will also initialize the residual consistently.
            initFirstIteration_();
        }
 
        const unsigned numCells = model_().numTotalDof();
#ifdef _OPENMP
#pragma omp parallel for
#endif
        for (unsigned globI = 0; globI < numCells; globI++) {
            auto nbInfos = neighborInfo_[globI]; // nbInfos will be a SparseTable<...>::mutable_iterator_range.
            for (auto& nbInfo : nbInfos) {
                const unsigned globJ = nbInfo.neighbor;
                nbInfo.res_nbinfo.trans = problem_().transmissibility(globI, globJ);
            }
        }
    }
 
    Simulator* simulatorPtr_{};
 
    // the jacobian matrix
    std::unique_ptr<SparseMatrixAdapter> jacobian_{};
 
    // the right-hand side
    GlobalEqVector residual_;
 
    LinearizationType linearizationType_{};
 
    using ResidualNBInfo = typename LocalResidual::ResidualNBInfo;
    using NeighborInfoCPU = NeighborInfoStruct<ResidualNBInfo, MatrixBlock>;
 
    SparseTable<NeighborInfoCPU> neighborInfo_{};
    std::vector<MatrixBlock*> diagMatAddress_{};
 
    struct FlowInfo
    {
        int faceId;
        VectorBlock flow;
        unsigned int nncId;
    };
    SparseTable<FlowInfo> flowsInfo_;
    SparseTable<FlowInfo> floresInfo_;
 
    struct VelocityInfo
    {
        VectorBlock velocity;
    };
    SparseTable<VelocityInfo> velocityInfo_;
 
    using ScalarFluidState = typename IntensiveQuantities::ScalarFluidState;
    struct BoundaryConditionData
    {
        BCType type;
        VectorBlock massRate;
        unsigned pvtRegionIdx;
        unsigned boundaryFaceIndex;
        double faceArea;
        double faceZCoord;
        ScalarFluidState exFluidState;
    };
 
    struct BoundaryInfo
    {
        unsigned int cell;
        int dir;
        unsigned int bfIndex;
        BoundaryConditionData bcdata;
    };
    std::vector<BoundaryInfo> boundaryInfo_;
 
    bool separateSparseSourceTerms_ = false;
 
    FullDomain<> fullDomain_;
 
    int exportIndex_;
    int exportCount_;
};
} // namespace Opm
 
#endif // TPFA_LINEARIZER