PoromechanicsSolver.hpp

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/*
 * ------------------------------------------------------------------------------------------------------------
 * SPDX-License-Identifier: LGPL-2.1-only
 *
 * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
 * Copyright (c) 2018-2024 TotalEnergies
 * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
 * Copyright (c) 2023-2024 Chevron
 * Copyright (c) 2019-     GEOS/GEOSX Contributors
 * All rights reserved
 *
 * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
 * ------------------------------------------------------------------------------------------------------------
 */
 
#ifndef GEOS_PHYSICSSOLVERS_MULTIPHYSICS_POROMECHANICSSOLVER_HPP_
#define GEOS_PHYSICSSOLVERS_MULTIPHYSICS_POROMECHANICSSOLVER_HPP_
 
#include "physicsSolvers/multiphysics/CoupledSolver.hpp"
#include "physicsSolvers/solidMechanics/SolidMechanicsLagrangianFEM.hpp"
#include "physicsSolvers/fluidFlow/FlowSolverBaseFields.hpp"
#include "physicsSolvers/multiphysics/PoromechanicsFields.hpp"
#include "physicsSolvers/solidMechanics/SolidMechanicsFields.hpp"
#include "constitutive/solid/CoupledSolidBase.hpp"
#include "constitutive/contact/HydraulicApertureBase.hpp"
#include "mesh/DomainPartition.hpp"
#include "mesh/utilities/AverageOverQuadraturePointsKernel.hpp"
#include "codingUtilities/Utilities.hpp"
 
namespace geos
{
 
namespace stabilization
{
enum class StabilizationType : integer
{
  None,
  Global,
  Local,
};
 
ENUM_STRINGS( StabilizationType,
              "None",
              "Global",
              "Local" );
}
 
 
template< typename FLOW_SOLVER, typename MECHANICS_SOLVER = SolidMechanicsLagrangianFEM >
class PoromechanicsSolver : public CoupledSolver< FLOW_SOLVER, MECHANICS_SOLVER >
{
public:
 
  using Base = CoupledSolver< FLOW_SOLVER, MECHANICS_SOLVER >;
  using Base::m_solvers;
  using Base::m_dofManager;
  using Base::m_localMatrix;
  using Base::m_rhs;
  using Base::m_solution;
 
  enum class SolverType : integer
  {
    Flow = 0,
    SolidMechanics = 1
  };
 
  static string coupledSolverAttributePrefix() { return "poromechanics"; }
 
  PoromechanicsSolver( const string & name,
                       dataRepository::Group * const parent )
    : Base( name, parent ),
    m_isThermal( 0 ),
    m_performStressInitialization( false )
  {
    this->registerWrapper( viewKeyStruct::isThermalString(), &m_isThermal ).
      setApplyDefaultValue( 0 ).
      setInputFlag( dataRepository::InputFlags::OPTIONAL ).
      setDescription( "Flag indicating whether the problem is thermal or not. Set isThermal=\"1\" to enable the thermal coupling" );
 
    this->registerWrapper( viewKeyStruct::stabilizationTypeString(), &m_stabilizationType ).
      setInputFlag( dataRepository::InputFlags::OPTIONAL ).
      setDescription( "StabilizationType. Options are:\n" +
                      toString( stabilization::StabilizationType::None ) + "- Add no stabilization to mass equation \n" +
                      toString( stabilization::StabilizationType::Global ) + "- Add jump stabilization to all faces \n" +
                      toString( stabilization::StabilizationType::Local ) + "- Add jump stabilization on interior of macro elements" );
 
    this->registerWrapper( viewKeyStruct::stabilizationRegionNamesString(), &m_stabilizationRegionNames ).
      setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
      setInputFlag( dataRepository::InputFlags::OPTIONAL ).
      setDescription( "Regions where stabilization is applied." );
 
    this->registerWrapper( viewKeyStruct::stabilizationMultiplierString(), &m_stabilizationMultiplier ).
      setApplyDefaultValue( 1.0 ).
      setInputFlag( dataRepository::InputFlags::OPTIONAL ).
      setDescription( "Constant multiplier of stabilization strength" );
 
    LinearSolverParameters & linearSolverParameters = this->m_linearSolverParameters.get();
    linearSolverParameters.dofsPerNode = 3;
    linearSolverParameters.multiscale.label = "poro";
  }
 
  virtual void postInputInitialization() override
  {
    Base::postInputInitialization();
 
    GEOS_THROW_IF( this->m_isThermal && !this->flowSolver()->isThermal(),
                   GEOS_FMT( "{} {}: The attribute `{}` of the flow solver must be thermal since the poromechanics solver is thermal",
                             this->getCatalogName(), this->getName(), this->flowSolver()->getName() ),
                   InputError );
 
    GEOS_THROW_IF( this->solidMechanicsSolver()->timeIntegrationOption() != SolidMechanicsLagrangianFEM::TimeIntegrationOption::QuasiStatic,
                   GEOS_FMT( "{} {}: The attribute `{}` of solid mechanics solver `{}` must be `{}`",
                             this->getCatalogName(), this->getName(),
                             SolidMechanicsLagrangianFEM::viewKeyStruct::timeIntegrationOptionString(),
                             this->solidMechanicsSolver()->getName(),
                             EnumStrings< SolidMechanicsLagrangianFEM::TimeIntegrationOption >::toString( SolidMechanicsLagrangianFEM::TimeIntegrationOption::QuasiStatic ) ),
                   InputError );
 
    setMGRStrategy();
  }
 
  virtual void setConstitutiveNamesCallSuper( ElementSubRegionBase & subRegion ) const override final
  {
    Base::setConstitutiveNamesCallSuper( subRegion );
 
    this->template setConstitutiveName< constitutive::CoupledSolidBase >( subRegion,
                                                                          viewKeyStruct::porousMaterialNamesString(), "coupled solid" );
 
    // This is needed by the way the surface generator currently does things.
    this->template setConstitutiveName< constitutive::PorosityBase >( subRegion,
                                                                      constitutive::CoupledSolidBase::viewKeyStruct::porosityModelNameString(), "porosity" );
 
    if( dynamic_cast< SurfaceElementSubRegion * >( &subRegion ) )
    {
      this->template setConstitutiveName< constitutive::HydraulicApertureBase >( subRegion,
                                                                                 viewKeyStruct::hydraulicApertureRelationNameString(), "hydraulic aperture" );
    }
  }
 
  virtual void initializePreSubGroups() override
  {
    Base::initializePreSubGroups();
 
    GEOS_THROW_IF( m_stabilizationType == stabilization::StabilizationType::Local,
                   this->getWrapperDataContext( viewKeyStruct::stabilizationTypeString() ) <<
                   ": Local stabilization has been temporarily disabled",
                   InputError );
 
    DomainPartition & domain = this->template getGroupByPath< DomainPartition >( "/Problem/domain" );
 
    this->template forDiscretizationOnMeshTargets<>( domain.getMeshBodies(), [&] ( string const &,
                                                                                   MeshLevel & mesh,
                                                                                   string_array const & regionNames )
    {
      ElementRegionManager & elementRegionManager = mesh.getElemManager();
      elementRegionManager.forElementSubRegions< CellElementSubRegion >( regionNames,
                                                                         [&]( localIndex const,
                                                                              ElementSubRegionBase & subRegion )
      {
        if( subRegion.hasField< fields::poromechanics::bulkDensity >() )
        {
          // get the solid model to know the number of quadrature points and resize the bulk density
          constitutive::CoupledSolidBase const & solid =
            this->template getConstitutiveModel< constitutive::CoupledSolidBase >( subRegion,
                                                                                   subRegion.getReference< string >( viewKeyStruct::porousMaterialNamesString() ) );
          subRegion.getField< fields::poromechanics::bulkDensity >().resizeDimension< 1 >( solid.getDensity().size( 1 ) );
        }
      } );
    } );
  }
 
  virtual void registerDataOnMesh( dataRepository::Group & meshBodies ) override
  {
    Base::registerDataOnMesh( meshBodies );
 
    if( this->getNonlinearSolverParameters().m_couplingType == NonlinearSolverParameters::CouplingType::Sequential )
    {
      // to let the solid mechanics solver that there is a pressure and temperature RHS in the mechanics solve
      solidMechanicsSolver()->enableFixedStressPoromechanicsUpdate();
      // to let the flow solver that saving pressure_k and temperature_k is necessary (for the fixed-stress porosity terms)
      flowSolver()->enableFixedStressPoromechanicsUpdate();
    }
 
    if( m_stabilizationType == stabilization::StabilizationType::Global || m_stabilizationType == stabilization::StabilizationType::Local )
    {
      flowSolver()->enableJumpStabilization();
    }
 
    this->forDiscretizationOnMeshTargets( meshBodies, [&] ( string const &,
                                                            MeshLevel & mesh,
                                                            string_array const & regionNames )
    {
      ElementRegionManager & elemManager = mesh.getElemManager();
 
      elemManager.forElementSubRegions< CellElementSubRegion >( regionNames,
                                                                [&]( localIndex const,
                                                                     ElementSubRegionBase & subRegion )
      {
        subRegion.registerWrapper< string >( viewKeyStruct::porousMaterialNamesString() ).
          setPlotLevel( dataRepository::PlotLevel::NOPLOT ).
          setRestartFlags( dataRepository::RestartFlags::NO_WRITE ).
          setSizedFromParent( 0 );
 
        // This is needed by the way the surface generator currently does things.
        subRegion.registerWrapper< string >( constitutive::CoupledSolidBase::viewKeyStruct::porosityModelNameString() ).
          setPlotLevel( dataRepository::PlotLevel::NOPLOT ).
          setRestartFlags( dataRepository::RestartFlags::NO_WRITE ).
          setSizedFromParent( 0 );
 
        // register the bulk density for use in the solid mechanics solver
        // ideally we would resize it here as well, but the solid model name is not available yet (see below)
        subRegion.registerField< fields::poromechanics::bulkDensity >( this->getName() );
 
        if( m_stabilizationType == stabilization::StabilizationType::Global || m_stabilizationType == stabilization::StabilizationType::Local )
        {
          subRegion.registerField< fields::flow::macroElementIndex >( this->getName());
          subRegion.registerField< fields::flow::elementStabConstant >( this->getName());
        }
      } );
    } );
  }
 
  virtual void implicitStepSetup( real64 const & time_n,
                                  real64 const & dt,
                                  DomainPartition & domain ) override
  {
    flowSolver()->setKeepVariablesConstantDuringInitStep( m_performStressInitialization );
 
    if( this->m_stabilizationType == stabilization::StabilizationType::Global || this->m_stabilizationType == stabilization::StabilizationType::Local )
    {
      this->updateStabilizationParameters( domain );
    }
 
    Base::implicitStepSetup( time_n, dt, domain );
  }
 
  virtual void setupDofs( DomainPartition const & domain,
                          DofManager & dofManager ) const override
  {
    // note that the order of operations matters a lot here (for instance for the MGR labels)
    // we must set up dofs for solid mechanics first, and then for flow
    // that's the reason why this function is here and not in CoupledSolvers.hpp
    solidMechanicsSolver()->setupDofs( domain, dofManager );
    flowSolver()->setupDofs( domain, dofManager );
    this->setupCoupling( domain, dofManager );
  }
 
  virtual void setupCoupling( DomainPartition const & GEOS_UNUSED_PARAM( domain ),
                              DofManager & dofManager ) const override
  {
    dofManager.addCoupling( fields::solidMechanics::totalDisplacement::key(),
                            getFlowDofKey(),
                            DofManager::Connector::Elem );
  }
 
  virtual void assembleSystem( real64 const time,
                               real64 const dt,
                               DomainPartition & domain,
                               DofManager const & dofManager,
                               CRSMatrixView< real64, globalIndex const > const & localMatrix,
                               arrayView1d< real64 > const & localRhs ) override
  {
    GEOS_MARK_FUNCTION;
 
    // Steps 1 and 2: compute element-based terms (mechanics and local flow terms)
    assembleElementBasedTerms( time,
                               dt,
                               domain,
                               dofManager,
                               localMatrix,
                               localRhs );
 
    // Step 3: compute the fluxes (face-based contributions)
 
    if( m_stabilizationType == stabilization::StabilizationType::Global ||
        m_stabilizationType == stabilization::StabilizationType::Local )
    {
      this->flowSolver()->assembleStabilizedFluxTerms( dt,
                                                       domain,
                                                       dofManager,
                                                       localMatrix,
                                                       localRhs );
    }
    else
    {
      this->flowSolver()->assembleFluxTerms( dt,
                                             domain,
                                             dofManager,
                                             localMatrix,
                                             localRhs );
    }
  }
 
  virtual void assembleElementBasedTerms( real64 const time_n,
                                          real64 const dt,
                                          DomainPartition & domain,
                                          DofManager const & dofManager,
                                          CRSMatrixView< real64, globalIndex const > const & localMatrix,
                                          arrayView1d< real64 > const & localRhs ) = 0;
 
  virtual bool checkSequentialConvergence( integer const cycleNumber,
                                           integer const iter,
                                           real64 const & time_n,
                                           real64 const & dt,
                                           DomainPartition & domain ) override
  {
    // always force outer loop for initialization
    auto & subcycling = this->getNonlinearSolverParameters().m_subcyclingOption;
    auto const subcycling_orig = subcycling;
    if( m_performStressInitialization )
      subcycling = 1;
    bool isConverged = Base::checkSequentialConvergence( cycleNumber, iter, time_n, dt, domain );
 
    // restore original
    subcycling = subcycling_orig;
 
    return isConverged;
  }
 
  MECHANICS_SOLVER * solidMechanicsSolver() const
  {
    return std::get< toUnderlying( SolverType::SolidMechanics ) >( m_solvers );
  }
 
  FLOW_SOLVER * flowSolver() const
  {
    return std::get< toUnderlying( SolverType::Flow ) >( m_solvers );
  }
 
  /*
   * @brief Utility function to set the stress initialization flag
   * @param[in] performStressInitialization true if the solver has to initialize stress, false otherwise
   */
  void setStressInitialization( bool const performStressInitialization )
  {
    m_performStressInitialization = performStressInitialization;
    solidMechanicsSolver()->setStressInitialization( performStressInitialization );
  }
 
  struct viewKeyStruct : Base::viewKeyStruct
  {
    constexpr static char const * porousMaterialNamesString() { return "porousMaterialNames"; }
 
    constexpr static char const * isThermalString() { return "isThermal"; }
 
    constexpr static char const * stabilizationTypeString() {return "stabilizationType"; }
 
    constexpr static const char * stabilizationRegionNamesString() {return "stabilizationRegionNames"; }
 
    constexpr static const char * stabilizationMultiplierString() {return "stabilizationMultiplier"; }
 
    static constexpr char const * hydraulicApertureRelationNameString() {return "hydraulicApertureRelationName"; }
 
  };
 
  void updateStabilizationParameters( DomainPartition & domain ) const
  {
    // Step 1: we loop over the regions where stabilization is active and collect their name
    set< string > regionFilter;
    for( string const & regionName : m_stabilizationRegionNames )
    {
      regionFilter.insert( regionName );
    }
 
    // Step 2: loop over target regions of solver, and tag the elements belonging to the stabilization regions
    this->template forDiscretizationOnMeshTargets<>( domain.getMeshBodies(), [&] ( string const &,
                                                                                   MeshLevel & mesh,
                                                                                   string_array const & targetRegionNames )
    {
      //keep only target regions in filter
      string_array filteredTargetRegionNames;
      filteredTargetRegionNames.reserve( targetRegionNames.size() );
 
      for( string const & targetRegionName : targetRegionNames )
      {
        if( regionFilter.count( targetRegionName ) )
        {
          filteredTargetRegionNames.emplace_back( targetRegionName );
        }
      }
 
      // Loop over elements and update stabilization constant
      mesh.getElemManager().forElementSubRegions( filteredTargetRegionNames, [&]( localIndex const,
                                                                                  ElementSubRegionBase & subRegion )
      {
        arrayView1d< integer > const macroElementIndex = subRegion.getField< fields::flow::macroElementIndex >();
        arrayView1d< real64 > const elementStabConstant = subRegion.getField< fields::flow::elementStabConstant >();
 
        constitutive::CoupledSolidBase const & porousSolid =
          this->template getConstitutiveModel< constitutive::CoupledSolidBase >( subRegion,
                                                                                 subRegion.getReference< string >( viewKeyStruct::porousMaterialNamesString() ) );
 
        arrayView1d< real64 const > const bulkModulus = porousSolid.getBulkModulus();
        arrayView1d< real64 const > const shearModulus = porousSolid.getShearModulus();
        arrayView1d< real64 const > const biotCoefficient = porousSolid.getBiotCoefficient();
 
        real64 const stabilizationMultiplier = m_stabilizationMultiplier;
 
        forAll< parallelDevicePolicy<> >( subRegion.size(), [bulkModulus,
                                                             shearModulus,
                                                             biotCoefficient,
                                                             stabilizationMultiplier,
                                                             macroElementIndex,
                                                             elementStabConstant] GEOS_HOST_DEVICE ( localIndex const ei )
 
        {
          real64 const bM = bulkModulus[ei];
          real64 const sM = shearModulus[ei];
          real64 const bC = biotCoefficient[ei];
 
          macroElementIndex[ei] = 1;
          elementStabConstant[ei] = stabilizationMultiplier * 9.0 * (bC * bC) / (32.0 * (10.0 * sM / 3.0 + bM));
        } );
      } );
    } );
 
  }
 
  void updateBulkDensity( DomainPartition & domain )
  {
    this->template forDiscretizationOnMeshTargets<>( domain.getMeshBodies(), [&]( string const &,
                                                                                  MeshLevel & mesh,
                                                                                  string_array const & regionNames )
    {
      mesh.getElemManager().forElementSubRegions< CellElementSubRegion >( regionNames, [&]( localIndex const,
                                                                                            auto & subRegion )
      {
        // update the bulk density
        // TODO: ideally, we would not recompute the bulk density, but a more general "rhs" containing the body force and the
        // pressure/temperature terms
        updateBulkDensity( subRegion );
      } );
    } );
  }
 
protected:
 
  virtual void initializePostInitialConditionsPreSubGroups() override
  {
    Base::initializePostInitialConditionsPreSubGroups();
 
    string_array const & poromechanicsTargetRegionNames =
      this->template getReference< string_array >( PhysicsSolverBase::viewKeyStruct::targetRegionsString() );
    string_array const & solidMechanicsTargetRegionNames =
      this->solidMechanicsSolver()->template getReference< string_array >( PhysicsSolverBase::viewKeyStruct::targetRegionsString() );
    string_array const & flowTargetRegionNames =
      this->flowSolver()->template getReference< string_array >( PhysicsSolverBase::viewKeyStruct::targetRegionsString() );
    for( size_t i = 0; i < poromechanicsTargetRegionNames.size(); ++i )
    {
      GEOS_THROW_IF( std::find( solidMechanicsTargetRegionNames.begin(), solidMechanicsTargetRegionNames.end(),
                                poromechanicsTargetRegionNames[i] )
                     == solidMechanicsTargetRegionNames.end(),
                     GEOS_FMT( "{} {}: region {} must be a target region of {}",
                               this->getCatalogName(), this->getDataContext(), poromechanicsTargetRegionNames[i],
                               this->solidMechanicsSolver()->getDataContext() ),
                     InputError );
      GEOS_THROW_IF( std::find( flowTargetRegionNames.begin(), flowTargetRegionNames.end(), poromechanicsTargetRegionNames[i] )
                     == flowTargetRegionNames.end(),
                     GEOS_FMT( "{} {}: region `{}` must be a target region of `{}`",
                               this->getCatalogName(), this->getDataContext(), poromechanicsTargetRegionNames[i], this->flowSolver()->getDataContext() ),
                     InputError );
    }
  }
 
  template< typename TYPE_LIST,
            typename KERNEL_WRAPPER,
            typename ... PARAMS >
  real64 assemblyLaunch( MeshLevel & mesh,
                         DofManager const & dofManager,
                         string_array const & regionNames,
                         string const & materialNamesString,
                         CRSMatrixView< real64, globalIndex const > const & localMatrix,
                         arrayView1d< real64 > const & localRhs,
                         real64 const dt,
                         PARAMS && ... params )
  {
    GEOS_MARK_FUNCTION;
 
    NodeManager const & nodeManager = mesh.getNodeManager();
 
    string const dofKey = dofManager.getKey( fields::solidMechanics::totalDisplacement::key() );
    arrayView1d< globalIndex const > const & dofNumber = nodeManager.getReference< globalIndex_array >( dofKey );
 
    real64 const gravityVectorData[3] = LVARRAY_TENSOROPS_INIT_LOCAL_3( this->gravityVector() );
 
    KERNEL_WRAPPER kernelWrapper( dofNumber,
                                  dofManager.rankOffset(),
                                  localMatrix,
                                  localRhs,
                                  dt,
                                  gravityVectorData,
                                  std::forward< PARAMS >( params )... );
 
    return finiteElement::
             regionBasedKernelApplication< parallelDevicePolicy< >,
                                           TYPE_LIST >( mesh,
                                                        regionNames,
                                                        this->solidMechanicsSolver()->getDiscretizationName(),
                                                        materialNamesString,
                                                        kernelWrapper );
  }
 
  /* Implementation of Nonlinear Acceleration (Aitken) of averageMeanTotalStressIncrement */
 
  void recordAverageMeanTotalStressIncrement( DomainPartition & domain,
                                              array1d< real64 > & averageMeanTotalStressIncrement )
  {
    averageMeanTotalStressIncrement.resize( 0 );
    this->forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
                                                                       MeshLevel & mesh,
                                                                       string_array const & regionNames )
    {
      mesh.getElemManager().forElementSubRegions< CellElementSubRegion >( regionNames, [&]( localIndex const,
                                                                                            auto & subRegion )
      {
        // get the solid model (to access stress increment)
        string const & solidName =
          subRegion.template getReference< string >( viewKeyStruct::porousMaterialNamesString() );
        constitutive::CoupledSolidBase & solid =
          this->template getConstitutiveModel< constitutive::CoupledSolidBase >( subRegion, solidName );
 
        arrayView1d< const real64 > const & averageMeanTotalStressIncrement_k = solid.getAverageMeanTotalStressIncrement_k();
        for( localIndex k = 0; k < localIndex( averageMeanTotalStressIncrement_k.size()); k++ )
        {
          averageMeanTotalStressIncrement.emplace_back( averageMeanTotalStressIncrement_k[k] );
        }
      } );
    } );
  }
 
  void applyAcceleratedAverageMeanTotalStressIncrement( DomainPartition & domain,
                                                        array1d< real64 > & averageMeanTotalStressIncrement )
  {
    integer i = 0;
    this->forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
                                                                       MeshLevel & mesh,
                                                                       string_array const & regionNames )
    {
      mesh.getElemManager().forElementSubRegions< CellElementSubRegion >( regionNames, [&]( localIndex const,
                                                                                            auto & subRegion )
      {
        // get the solid model (to access stress increment)
        string const & solidName = subRegion.template getReference< string >( viewKeyStruct::porousMaterialNamesString() );
        constitutive::CoupledSolidBase & solid =
          this->template getConstitutiveModel< constitutive::CoupledSolidBase >( subRegion, solidName );
        auto & porosityModel = dynamic_cast< constitutive::BiotPorosity const & >( solid.getBasePorosityModel());
        arrayView1d< real64 > const & averageMeanTotalStressIncrement_k = solid.getAverageMeanTotalStressIncrement_k();
        for( localIndex k = 0; k < localIndex( averageMeanTotalStressIncrement_k.size()); k++ )
        {
          porosityModel.updateAverageMeanTotalStressIncrement( k, averageMeanTotalStressIncrement[i] );
          i++;
        }
      } );
    } );
  }
 
  real64 computeAitkenRelaxationFactor( array1d< real64 > const & s0,
                                        array1d< real64 > const & s1,
                                        array1d< real64 > const & s1_tilde,
                                        array1d< real64 > const & s2_tilde,
                                        real64 const omega0 )
  {
    array1d< real64 > r1 = axpy( s1_tilde, s0, -1.0 );
    array1d< real64 > r2 = axpy( s2_tilde, s1, -1.0 );
 
    // diff = r2 - r1
    array1d< real64 > diff = axpy( r2, r1, -1.0 );
 
    real64 const denom = dot( diff, diff );
    real64 const numer = dot( r1, diff );
 
    real64 omega1 = 1.0;
    if( !isZero( denom ))
    {
      omega1 = -1.0 * omega0 * numer / denom;
    }
    return omega1;
  }
 
  array1d< real64 > computeUpdate( array1d< real64 > const & s1,
                                   array1d< real64 > const & s2_tilde,
                                   real64 const omega1 )
  {
    return axpy( scale( s1, 1.0 - omega1 ),
                 scale( s2_tilde, omega1 ),
                 1.0 );
  }
 
  void startSequentialIteration( integer const & iter,
                                 DomainPartition & domain ) override
  {
    if( this->getNonlinearSolverParameters().m_nonlinearAccelerationType == NonlinearSolverParameters::NonlinearAccelerationType::Aitken )
    {
      if( iter == 0 )
      {
        recordAverageMeanTotalStressIncrement( domain, m_s1 );
      }
      else
      {
        m_s0 = m_s1;
        m_s1 = m_s2;
        m_s1_tilde = m_s2_tilde;
        m_omega0 = m_omega1;
      }
    }
  }
 
  void finishSequentialIteration( integer const & iter,
                                  DomainPartition & domain ) override
  {
    if( this->getNonlinearSolverParameters().m_nonlinearAccelerationType == NonlinearSolverParameters::NonlinearAccelerationType::Aitken )
    {
      if( iter == 0 )
      {
        m_s2 = m_s2_tilde;
        m_omega1 = 1.0;
      }
      else
      {
        m_omega1 = computeAitkenRelaxationFactor( m_s0, m_s1, m_s1_tilde, m_s2_tilde, m_omega0 );
        m_s2 = computeUpdate( m_s1, m_s2_tilde, m_omega1 );
        applyAcceleratedAverageMeanTotalStressIncrement( domain, m_s2 );
      }
    }
  }
 
  virtual void mapSolutionBetweenSolvers( DomainPartition & domain, integer const solverType ) override
  {
    GEOS_MARK_FUNCTION;
 
    if( solverType == static_cast< integer >( SolverType::Flow ) )
    {
      updateBulkDensity( domain );
    }
 
    if( solverType == static_cast< integer >( SolverType::SolidMechanics )
        && !m_performStressInitialization ) // do not update during poromechanics initialization
    {
      // compute the average of the mean total stress increment over quadrature points
      averageMeanTotalStressIncrement( domain );
 
      this->template forDiscretizationOnMeshTargets<>( domain.getMeshBodies(), [&]( string const &,
                                                                                    MeshLevel & mesh,
                                                                                    string_array const & regionNames )
      {
 
        mesh.getElemManager().forElementSubRegions< CellElementSubRegion >( regionNames, [&]( localIndex const,
                                                                                              auto & subRegion )
        {
          // update the porosity after a change in displacement (after mechanics solve)
          // or a change in pressure/temperature (after a flow solve)
          flowSolver()->updatePorosityAndPermeability( subRegion );
          // update bulk density to reflect porosity change into mechanics
          updateBulkDensity( subRegion );
        } );
      } );
    }
 
    // needed to perform nonlinear acceleration
    if( solverType == static_cast< integer >( SolverType::SolidMechanics ) &&
        this->getNonlinearSolverParameters().m_nonlinearAccelerationType== NonlinearSolverParameters::NonlinearAccelerationType::Aitken )
    {
      recordAverageMeanTotalStressIncrement( domain, m_s2_tilde );
    }
  }
 
  void averageMeanTotalStressIncrement( DomainPartition & domain )
  {
    this->template forDiscretizationOnMeshTargets<>( domain.getMeshBodies(), [&]( string const &,
                                                                                  MeshLevel & mesh,
                                                                                  string_array const & regionNames )
    {
      mesh.getElemManager().forElementSubRegions< CellElementSubRegion >( regionNames, [&]( localIndex const,
                                                                                            auto & subRegion )
      {
        // get the solid model (to access stress increment)
        string const & solidName = subRegion.template getReference< string >( viewKeyStruct::porousMaterialNamesString() );
        constitutive::CoupledSolidBase & solid =
          this->template getConstitutiveModel< constitutive::CoupledSolidBase >( subRegion, solidName );
 
        arrayView2d< real64 const > const meanTotalStressIncrement_k = solid.getMeanTotalStressIncrement_k();
        arrayView1d< real64 > const averageMeanTotalStressIncrement_k = solid.getAverageMeanTotalStressIncrement_k();
 
        finiteElement::FiniteElementBase & subRegionFE =
          subRegion.template getReference< finiteElement::FiniteElementBase >( solidMechanicsSolver()->getDiscretizationName() );
 
        // determine the finite element type
        finiteElement::FiniteElementDispatchHandler< BASE_FE_TYPES >::
        dispatch3D( subRegionFE, [&] ( auto const finiteElement )
        {
          using FE_TYPE = decltype( finiteElement );
 
          // call the factory and launch the kernel
          AverageOverQuadraturePoints1DKernelFactory::
            createAndLaunch< CellElementSubRegion,
                             FE_TYPE,
                             parallelDevicePolicy<> >( mesh.getNodeManager(),
                                                       mesh.getEdgeManager(),
                                                       mesh.getFaceManager(),
                                                       subRegion,
                                                       finiteElement,
                                                       meanTotalStressIncrement_k,
                                                       averageMeanTotalStressIncrement_k );
        } );
      } );
    } );
  }
 
  virtual void setMGRStrategy() = 0;
 
  virtual void updateBulkDensity( ElementSubRegionBase & subRegion ) = 0;
 
  virtual string getFlowDofKey() const = 0;
 
  virtual void validateNonlinearAcceleration() override
  {
    if( MpiWrapper::commSize( MPI_COMM_GEOS ) > 1 )
    {
      GEOS_ERROR( "Nonlinear acceleration is not implemented for MPI runs" );
    }
  }
 
  integer m_isThermal;
 
  bool m_performStressInitialization;
 
  stabilization::StabilizationType m_stabilizationType;
 
  string_array m_stabilizationRegionNames;
 
  real64 m_stabilizationMultiplier;
 
  array1d< real64 > m_s0; // Accelerated averageMeanTotalStresIncrement @ outer iteration v ( two iterations ago )
  array1d< real64 > m_s1; // Accelerated averageMeanTotalStresIncrement @ outer iteration v + 1 ( previous iteration )
  array1d< real64 > m_s1_tilde; // Unaccelerated averageMeanTotalStresIncrement @ outer iteration v + 1 ( previous iteration )
  array1d< real64 > m_s2; // Accelerated averageMeanTotalStresIncrement @ outer iteration v + 2 ( current iteration )
  array1d< real64 > m_s2_tilde; // Unaccelerated averageMeanTotalStresIncrement @ outer iteration v + 1 ( current iteration )
  real64 m_omega0; // Old Aitken relaxation factor
  real64 m_omega1; // New Aitken relaxation factor
 
};
 
} /* namespace geos */
 
#endif //GEOS_PHYSICSSOLVERS_MULTIPHYSICS_POROMECHANICSSOLVER_HPP_