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opm-simulators/opm/autodiff/NewtonIterationBlackoilCPR.cpp

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/*
Copyright 2014 SINTEF ICT, Applied Mathematics.
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 3 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/>.
*/
#include <config.h>
#include <opm/autodiff/DuneMatrix.hpp>
#include <opm/autodiff/NewtonIterationBlackoilCPR.hpp>
#include <opm/autodiff/CPRPreconditioner.hpp>
#include <opm/autodiff/AutoDiffHelpers.hpp>
#include <opm/core/utility/ErrorMacros.hpp>
#include <opm/core/utility/Units.hpp>
#include <opm/core/linalg/LinearSolverFactory.hpp>
#include <opm/core/utility/platform_dependent/disable_warnings.h>
#include <dune/istl/bvector.hh>
// #include <dune/istl/bcrsmatrix.hh>
#include <dune/istl/operators.hh>
#include <dune/istl/io.hh>
#include <dune/istl/owneroverlapcopy.hh>
#include <dune/istl/preconditioners.hh>
#include <dune/istl/schwarz.hh>
#include <dune/istl/solvers.hh>
#include <dune/istl/paamg/amg.hh>
#include <dune/istl/paamg/kamg.hh>
#include <dune/istl/paamg/pinfo.hh>
#include <opm/core/utility/platform_dependent/reenable_warnings.h>
namespace Opm
{
typedef AutoDiffBlock<double> ADB;
typedef ADB::V V;
typedef ADB::M M;
typedef Dune::FieldVector<double, 1 > VectorBlockType;
typedef Dune::FieldMatrix<double, 1, 1> MatrixBlockType;
typedef Dune::BCRSMatrix <MatrixBlockType> Mat;
typedef Dune::BlockVector<VectorBlockType> Vector;
namespace {
/// Eliminate a variable via Schur complement.
/// \param[in] eqs set of equations with Jacobians
/// \param[in] n index of equation/variable to eliminate.
/// \return new set of equations, one smaller than eqs.
/// Note: this method requires the eliminated variable to have the same size
/// as the equation in the corresponding position (that also will be eliminated).
/// It also required the jacobian block n of equation n to be diagonal.
std::vector<ADB> eliminateVariable(const std::vector<ADB>& eqs, const int n);
/// Recover that value of a variable previously eliminated.
/// \param[in] equation previously eliminated equation.
/// \param[in] partial_solution solution to the remainder system after elimination.
/// \param[in] n index of equation/variable that was eliminated.
/// \return solution to complete system.
V recoverVariable(const ADB& equation, const V& partial_solution, const int n);
/// Determine diagonality of a sparse matrix.
/// If there are off-diagonal elements in the sparse
/// structure, this function returns true if they are all
/// equal to zero.
/// \param[in] matrix the matrix under consideration
/// \return true if matrix is diagonal
bool isDiagonal(const M& matrix);
/// Form an elliptic system of equations.
/// \param[in] num_phases the number of fluid phases
/// \param[in] eqs the equations
/// \param[out] A the resulting full system matrix
/// \param[out] b the right hand side
/// This function will deal with the first num_phases
/// equations in eqs, and return a matrix A for the full
/// system that has a elliptic upper left corner, if possible.
void formEllipticSystem(const int num_phases,
const std::vector<ADB>& eqs,
Eigen::SparseMatrix<double, Eigen::RowMajor>& A,
V& b);
/// Create a dune-istl matrix from an Eigen matrix.
/// \param[in] matrix input Eigen::SparseMatrix
/// \return output Dune::BCRSMatrix
Mat makeIstlMatrix(const Eigen::SparseMatrix<double, Eigen::RowMajor>& matrix);
} // anonymous namespace
/// Construct a system solver.
NewtonIterationBlackoilCPR::NewtonIterationBlackoilCPR(const parameter::ParameterGroup& param)
: iterations_( 0 )
{
use_amg_ = param.getDefault("cpr_use_amg", false);
use_bicgstab_ = param.getDefault("cpr_use_bicgstab", true);
}
/// Solve the linear system Ax = b, with A being the
/// combined derivative matrix of the residual and b
/// being the residual itself.
/// \param[in] residual residual object containing A and b.
/// \return the solution x
NewtonIterationBlackoilCPR::SolutionVector
NewtonIterationBlackoilCPR::computeNewtonIncrement(const LinearisedBlackoilResidual& residual) const
{
// Build the vector of equations.
const int np = residual.material_balance_eq.size();
std::vector<ADB> eqs;
eqs.reserve(np + 2);
for (int phase = 0; phase < np; ++phase) {
eqs.push_back(residual.material_balance_eq[phase]);
}
eqs.push_back(residual.well_flux_eq);
eqs.push_back(residual.well_eq);
// Eliminate the well-related unknowns, and corresponding equations.
std::vector<ADB> elim_eqs;
elim_eqs.reserve(2);
elim_eqs.push_back(eqs[np]);
eqs = eliminateVariable(eqs, np); // Eliminate well flux unknowns.
elim_eqs.push_back(eqs[np]);
eqs = eliminateVariable(eqs, np); // Eliminate well bhp unknowns.
assert(int(eqs.size()) == np);
// Scale material balance equations.
const double matbalscale[3] = { 1.1169, 1.0031, 0.0031 }; // HACK hardcoded instead of computed.
for (int phase = 0; phase < np; ++phase) {
eqs[phase] = eqs[phase] * matbalscale[phase];
}
// Add material balance equations (or other manipulations) to
// form pressure equation in top left of full system.
Eigen::SparseMatrix<double, Eigen::RowMajor> A;
V b;
formEllipticSystem(np, eqs, A, b);
// Scale pressure equation.
const double pscale = 200*unit::barsa;
const int nc = residual.material_balance_eq[0].size();
A.topRows(nc) *= pscale;
b.topRows(nc) *= pscale;
// Solve reduced system.
SolutionVector dx(SolutionVector::Zero(b.size()));
// Create ISTL matrix.
DuneMatrix istlA( A );
// Create ISTL matrix for elliptic part.
DuneMatrix istlAe( A.topLeftCorner(nc, nc) );
// Construct operator, scalar product and vectors needed.
typedef Dune::MatrixAdapter<Mat,Vector,Vector> Operator;
Operator opA(istlA);
Dune::SeqScalarProduct<Vector> sp;
// Right hand side.
Vector istlb(opA.getmat().N());
std::copy_n(b.data(), istlb.size(), istlb.begin());
// System solution
Vector x(opA.getmat().M());
x = 0.0;
// Construct preconditioner.
// typedef Dune::SeqILU0<Mat,Vector,Vector> Preconditioner;
typedef Opm::CPRPreconditioner<Mat,Vector,Vector> Preconditioner;
const double relax = 1.0;
Preconditioner precond(istlA, istlAe, relax, use_amg_, use_bicgstab_);
// Construct linear solver.
const double tolerance = 1e-3;
const int maxit = 5000;
const int verbosity = 0;
const int restart = 40;
Dune::RestartedGMResSolver<Vector> linsolve(opA, sp, precond, tolerance, restart, maxit, verbosity);
// Solve system.
Dune::InverseOperatorResult result;
linsolve.apply(x, istlb, result);
// store number of iterations
iterations_ = result.iterations;
// Check for failure of linear solver.
if (!result.converged) {
OPM_THROW(std::runtime_error, "Convergence failure for linear solver.");
}
// Copy solver output to dx.
std::copy(x.begin(), x.end(), dx.data());
// Compute full solution using the eliminated equations.
// Recovery in inverse order of elimination.
dx = recoverVariable(elim_eqs[1], dx, np);
dx = recoverVariable(elim_eqs[0], dx, np);
return dx;
}
namespace
{
std::vector<ADB> eliminateVariable(const std::vector<ADB>& eqs, const int n)
{
// Check that the variable index to eliminate is within bounds.
const int num_eq = eqs.size();
const int num_vars = eqs[0].derivative().size();
if (num_eq != num_vars) {
OPM_THROW(std::logic_error, "eliminateVariable() requires the same number of variables and equations.");
}
if (n >= num_eq) {
OPM_THROW(std::logic_error, "Trying to eliminate variable from too small set of equations.");
}
// Schur complement of (A B ; C D) wrt. D is A - B*inv(D)*C.
// This is applied to all 2x2 block submatrices.
// We require that D is diagonal.
const M& D = eqs[n].derivative()[n];
if (!isDiagonal(D)) {
// std::cout << "++++++++++++++++++++++++++++++++++++++++++++\n"
// << D
// << "++++++++++++++++++++++++++++++++++++++++++++\n" << std::endl;
std::cerr << "WARNING (ignored): Cannot do Schur complement with respect to non-diagonal block." << std::endl;
//OPM_THROW(std::logic_error, "Cannot do Schur complement with respect to non-diagonal block.");
}
V diag = D.diagonal();
Eigen::DiagonalMatrix<double, Eigen::Dynamic> invD = (1.0 / diag).matrix().asDiagonal();
std::vector<V> vals(num_eq); // Number n will remain empty.
std::vector<std::vector<M>> jacs(num_eq); // Number n will remain empty.
for (int eq = 0; eq < num_eq; ++eq) {
if (eq == n) {
continue;
}
jacs[eq].reserve(num_eq - 1);
const M& B = eqs[eq].derivative()[n];
for (int var = 0; var < num_eq; ++var) {
if (var == n) {
continue;
}
// Create new jacobians.
M schur_jac = eqs[eq].derivative()[var] - B * (invD * eqs[n].derivative()[var]);
jacs[eq].push_back(schur_jac);
}
// Update right hand side.
vals[eq] = eqs[eq].value().matrix() - B * (invD * eqs[n].value().matrix());
}
// Create return value.
std::vector<ADB> retval;
retval.reserve(num_eq - 1);
for (int eq = 0; eq < num_eq; ++eq) {
if (eq == n) {
continue;
}
retval.push_back(ADB::function(vals[eq], jacs[eq]));
}
return retval;
}
V recoverVariable(const ADB& equation, const V& partial_solution, const int n)
{
// The equation to solve for the unknown y (to be recovered) is
// Cx + Dy = b
// y = inv(D) (b - Cx)
// where D is the eliminated block, C is the jacobian of
// the eliminated equation with respect to the
// non-eliminated unknowms, b is the right-hand side of
// the eliminated equation, and x is the partial solution
// of the non-eliminated unknowns.
// We require that D is diagonal.
// Find inv(D).
const M& D = equation.derivative()[n];
if (!isDiagonal(D)) {
std::cerr << "WARNING (ignored): Cannot do Schur complement with respect to non-diagonal block." << std::endl;
//OPM_THROW(std::logic_error, "Cannot do Schur complement with respect to non-diagonal block.");
}
V diag = D.diagonal();
Eigen::DiagonalMatrix<double, Eigen::Dynamic> invD = (1.0 / diag).matrix().asDiagonal();
// Build C.
std::vector<M> C_jacs = equation.derivative();
C_jacs.erase(C_jacs.begin() + n);
ADB eq_coll = collapseJacs(ADB::function(equation.value(), C_jacs));
const M& C = eq_coll.derivative()[0];
// Compute value of eliminated variable.
V elim_var = invD * (equation.value().matrix() - C * partial_solution.matrix());
// Find the relevant sizes to use when reconstructing the full solution.
const int nelim = equation.size();
const int npart = partial_solution.size();
assert(C.cols() == npart);
const int full_size = nelim + npart;
int start = 0;
for (int i = 0; i < n; ++i) {
start += equation.derivative()[i].cols();
}
assert(start < full_size);
// Reconstruct complete solution vector.
V sol(full_size);
std::copy_n(partial_solution.data(), start, sol.data());
std::copy_n(elim_var.data(), nelim, sol.data() + start);
std::copy_n(partial_solution.data() + start, npart - start, sol.data() + start + nelim);
return sol;
}
bool isDiagonal(const M& matr)
{
M matrix = matr;
matrix.makeCompressed();
for (int k = 0; k < matrix.outerSize(); ++k) {
for (M::InnerIterator it(matrix, k); it; ++it) {
if (it.col() != it.row()) {
// Off-diagonal element.
if (it.value() != 0.0) {
// Nonzero off-diagonal element.
// std::cout << "off-diag: " << it.row() << ' ' << it.col() << std::endl;
return false;
}
}
}
}
return true;
}
/// Form an elliptic system of equations.
/// \param[in] num_phases the number of fluid phases
/// \param[in] eqs the equations
/// \param[out] A the resulting full system matrix
/// \param[out] b the right hand side
/// This function will deal with the first num_phases
/// equations in eqs, and return a matrix A for the full
/// system that has a elliptic upper left corner, if possible.
void formEllipticSystem(const int num_phases,
const std::vector<ADB>& eqs_in,
Eigen::SparseMatrix<double, Eigen::RowMajor>& A,
V& b)
{
if (num_phases != 3) {
OPM_THROW(std::logic_error, "formEllipticSystem() requires 3 phases.");
}
// A concession to MRST, to obtain more similar behaviour:
// swap the first two equations, so that oil is first, then water.
auto eqs = eqs_in;
std::swap(eqs[0], eqs[1]);
// Characterize the material balance equations.
const int n = eqs[0].size();
const double ratio_limit = 0.01;
typedef Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> Block;
// The l1 block indicates if the equation for a given cell and phase is
// sufficiently strong on the diagonal.
Block l1 = Block::Zero(n, num_phases);
for (int phase = 0; phase < num_phases; ++phase) {
const M& J = eqs[phase].derivative()[0];
V dj = J.diagonal().cwiseAbs();
V sod = V::Zero(n);
for (int elem = 0; elem < n; ++elem) {
sod(elem) = J.col(elem).cwiseAbs().sum() - dj(elem);
}
l1.col(phase) = (dj/sod > ratio_limit).cast<double>();
}
// By default, replace first equation with sum of all phase equations.
// Build helper vectors.
V l21 = V::Zero(n);
V l22 = V::Ones(n);
V l31 = V::Zero(n);
V l33 = V::Ones(n);
// If the first phase diagonal is not strong enough, we need further treatment.
// Then the first equation will be the sum of the remaining equations,
// and we swap the first equation into one of their slots.
for (int elem = 0; elem < n; ++elem) {
if (!l1(elem, 0)) {
const double l12x = l1(elem, 1);
const double l13x = l1(elem, 2);
const bool allzero = (l12x + l13x == 0);
if (allzero) {
l1(elem, 0) = 1;
} else {
if (l12x >= l13x) {
l21(elem) = 1;
l22(elem) = 0;
} else {
l31(elem) = 1;
l33(elem) = 0;
}
}
}
}
// Construct the sparse matrix L that does the swaps and sums.
Span i1(n, 1, 0);
Span i2(n, 1, n);
Span i3(n, 1, 2*n);
std::vector< Eigen::Triplet<double> > t;
t.reserve(7*n);
for (int ii = 0; ii < n; ++ii) {
t.emplace_back(i1[ii], i1[ii], l1(ii));
t.emplace_back(i1[ii], i2[ii], l1(ii+n));
t.emplace_back(i1[ii], i3[ii], l1(ii+2*n));
t.emplace_back(i2[ii], i1[ii], l21(ii));
t.emplace_back(i2[ii], i2[ii], l22(ii));
t.emplace_back(i3[ii], i1[ii], l31(ii));
t.emplace_back(i3[ii], i3[ii], l33(ii));
}
M L(3*n, 3*n);
L.setFromTriplets(t.begin(), t.end());
// Combine in single block.
ADB total_residual = eqs[0];
for (int phase = 1; phase < num_phases; ++phase) {
total_residual = vertcat(total_residual, eqs[phase]);
}
total_residual = collapseJacs(total_residual);
// Create output as product of L with equations.
A = L * total_residual.derivative()[0];
b = L * total_residual.value().matrix();
}
} // anonymous namespace
} // namespace Opm
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