ImplicitRateAndStateKernels.hpp

/*
 * ------------------------------------------------------------------------------------------------------------
 * 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) 2018-2024 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_INDUCEDSEISMICITY_KERNELS_IMPLICITRATEANDSTATEKERNELS_HPP_
#define GEOS_PHYSICSSOLVERS_INDUCEDSEISMICITY_KERNELS_IMPLICITRATEANDSTATEKERNELS_HPP_
 
#include "RateAndStateKernelsBase.hpp"
#include "denseLinearAlgebra/denseLASolvers.hpp"
 
namespace geos
{
 
namespace rateAndStateKernels
{
 
template< typename FRICTION_LAW_TYPE >
class ImplicitFixedStressRateAndStateKernel
{
public:
 
  ImplicitFixedStressRateAndStateKernel( SurfaceElementSubRegion & subRegion,
                                         FRICTION_LAW_TYPE const & frictionLaw,
                                         real64 const shearImpedance ):
    m_slipRate( subRegion.getField< fields::rateAndState::slipRate >() ),
    m_stateVariable( subRegion.getField< fields::rateAndState::stateVariable >() ),
    m_stateVariable_n( subRegion.getField< fields::rateAndState::stateVariable_n >() ),
    m_slipRate_n( subRegion.getField< fields::rateAndState::slipRate_n >() ),
    m_normalTraction( subRegion.getField< fields::rateAndState::normalTraction >() ),
    m_shearTraction( subRegion.getField< fields::rateAndState::shearTraction >() ),
    m_slipVelocity( subRegion.getField< fields::rateAndState::slipVelocity >() ),
    m_shearImpedance( shearImpedance ),
    m_frictionLaw( frictionLaw.createKernelUpdates()  )
  {}
 
  struct StackVariables
  {
public:
 
    StackVariables( ) = default;
 
    real64 jacobian[2][2]{};
 
    real64 rhs[2]{};
 
  };
 
  GEOS_HOST_DEVICE
  void setup( localIndex const k,
              real64 const dt,
              StackVariables & stack ) const
  {
    real64 const normalTraction = m_normalTraction[k];
    real64 const shearTractionMagnitude = LvArray::tensorOps::l2Norm< 2 >( m_shearTraction[k] );
 
    // Eq 1: Scalar force balance for slipRate and shear traction magnitude
    stack.rhs[0] = shearTractionMagnitude - m_shearImpedance * m_slipRate[k]
                   - normalTraction * m_frictionLaw.frictionCoefficient( k, m_slipRate[k], m_stateVariable[k] );
    real64 const dFriction[2] = { -normalTraction * m_frictionLaw.dFrictionCoefficient_dStateVariable( k, m_slipRate[k], m_stateVariable[k] ),
                                  -m_shearImpedance - normalTraction * m_frictionLaw.dFrictionCoefficient_dSlipRate( k, m_slipRate[k], m_stateVariable[k] ) };
 
    // Eq 2: slip law
    stack.rhs[1] = (m_stateVariable[k] - m_stateVariable_n[k]) / dt - m_frictionLaw.stateEvolution( k, m_slipRate[k], m_stateVariable[k] );
    real64 const dStateEvolutionLaw[2] = { 1.0 / dt - m_frictionLaw.dStateEvolution_dStateVariable( k, m_slipRate[k], m_stateVariable[k] ),
                                           -m_frictionLaw.dStateEvolution_dSlipRate( k, m_slipRate[k], m_stateVariable[k] ) };
 
    // Assemble Jacobian matrix
    stack.jacobian[0][0] = dFriction[0];          // derivative of Eq 1 w.r.t. stateVariable
    stack.jacobian[0][1] = dFriction[1];          // derivative of Eq 1 w.r.t. slipRate
    stack.jacobian[1][0] = dStateEvolutionLaw[0]; // derivative of Eq 2 w.r.t. stateVariable
    stack.jacobian[1][1] = dStateEvolutionLaw[1]; // derivative of Eq 2 w.r.t. slipRate
  }
 
  GEOS_HOST_DEVICE
  void solve( localIndex const k,
              StackVariables & stack ) const
  {
    real64 solution[2] = {0.0, 0.0};
    LvArray::tensorOps::scale< 2 >( stack.rhs, -1.0 );
    denseLinearAlgebra::solve< 2 >( stack.jacobian, stack.rhs, solution );
 
    // Slip rate is bracketed between [0, shear traction magnitude / shear impedance]
    // Check that the update did not end outside of the bracket.
    real64 const shearTractionMagnitude = LvArray::tensorOps::l2Norm< 2 >( m_shearTraction[k] );
    real64 const upperBound = shearTractionMagnitude / m_shearImpedance - m_slipRate[k];
    real64 const lowerBound = -m_slipRate[k];
 
    real64 scalingFactor = 1.0;
    if( solution[1] > upperBound )
    {
      scalingFactor = 0.5 * upperBound / solution[1];
    }
    else if( solution[1] < lowerBound )
    {
      scalingFactor = 0.5 * lowerBound / solution[1];
    }
 
    LvArray::tensorOps::scale< 2 >( solution, scalingFactor );
 
    // Update variables
    m_stateVariable[k]  +=  solution[0];
    m_slipRate[k]       +=  solution[1];
  }
 
  GEOS_HOST_DEVICE
  void projectSlipRate( localIndex const k ) const
  {
    real64 const frictionCoefficient = m_frictionLaw.frictionCoefficient( k, m_slipRate[k], m_stateVariable[k] );
    projectSlipRateBase( k, frictionCoefficient, m_shearImpedance, m_normalTraction, m_shearTraction, m_slipRate, m_slipVelocity );
  }
 
  GEOS_HOST_DEVICE
  void udpateVariables( localIndex const k ) const
  {
    projectSlipRate( k );
    m_stateVariable_n[k] = m_stateVariable[k];
    m_slipRate_n[k] = m_slipRate[k];
  }
 
  GEOS_HOST_DEVICE
  camp::tuple< int, real64 > checkConvergence( StackVariables const & stack,
                                               real64 const tol ) const
  {
    real64 const residualNorm = LvArray::tensorOps::l2Norm< 2 >( stack.rhs );
    int const converged = residualNorm < tol ? 1 : 0;
    camp::tuple< int, real64 > result { converged, residualNorm };
    return result;
  }
 
  GEOS_HOST_DEVICE
  void resetState( localIndex const k ) const
  {
    m_stateVariable[k] = m_stateVariable_n[k];
    m_slipRate[k] = m_slipRate_n[k];
  }
 
  template< typename POLICY >
  static real64 solveRateAndStateEquation( SurfaceElementSubRegion & subRegion,
                                           ImplicitFixedStressRateAndStateKernel & kernel,
                                           real64 dt,
                                           integer const maxNewtonIter,
                                           real64 const newtonTol )
  {
    bool converged = false;
    for( integer attempt = 0; attempt < 5; attempt++ )
    {
      if( attempt > 0 )
      {
        forAll< POLICY >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const k )
        {
          kernel.resetState( k );
        } );
      }
      GEOS_LOG_RANK_0( GEOS_FMT( "  Attempt {} ", attempt ) );
      converged = newtonSolve< POLICY >( subRegion, kernel, dt, maxNewtonIter, newtonTol );
      if( converged )
      {
        forAll< POLICY >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const k )
        {
          kernel.udpateVariables( k );
        } );
        return dt;
      }
      else
      {
        GEOS_LOG_RANK_0( GEOS_FMT( "  Attempt {} failed. Halving dt and retrying.", attempt ) );
        dt *= 0.5;
      }
    }
    if( !converged )
    {
      GEOS_ERROR( "Maximum number of attempts reached without convergence." );
    }
    return dt;
  }
 
private:
 
  arrayView1d< real64 > const m_slipRate;
 
  arrayView1d< real64 > const m_stateVariable;
 
  arrayView1d< real64 > const m_stateVariable_n;
 
  arrayView1d< real64 > const m_slipRate_n;
 
  arrayView1d< real64 > const m_normalTraction;
 
  arrayView2d< real64 > const m_shearTraction;
 
  arrayView2d< real64 > const m_slipVelocity;
 
  real64 const m_shearImpedance;
 
  typename FRICTION_LAW_TYPE::KernelWrapper m_frictionLaw;
 
};
 
} /* namespace rateAndStateKernels */
 
} /* namespace geos */
 
#endif /* GEOS_PHYSICSSOLVERS_INDUCEDSEISMICITY_KERNELS_IMPLICITRATEANDSTATEKERNELS_HPP_ */