CollOfScalar EquelleRuntimeCPU::solveForUpdate(const CollOfScalar& residual) const
{
Eigen::SparseMatrix<double, Eigen::RowMajor> matr = residual.derivative()[0];
CollOfScalar::V du = CollOfScalar::V::Zero(residual.size());
Opm::time::StopWatch clock;
clock.start();
// solve(n, # nonzero values ("val"), ptr to col indices
// ("col_ind"), ptr to row locations in val array ("row_ind")
// (these two may be swapped, not sure about the naming convention
// here...), array of actual values ("val") (I guess... '*sa'...),
// rhs, solution)
Opm::LinearSolverInterface::LinearSolverReport rep
= linsolver_.solve(matr.rows(), matr.nonZeros(),
matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
residual.value().data(), du.data());
if (verbose_ > 2) {
std::cout << " solveForUpdate: Linear solver took: " << clock.secsSinceLast() << " seconds." << std::endl;
}
if (!rep.converged) {
OPM_THROW(std::runtime_error, "Linear solver convergence failure.");
}
return du;
}
CollOfScalar EquelleRuntimeCUDA::newtonSolve(const ResidualFunctor& rescomp,
const CollOfScalar& u_initialguess)
{
Opm::time::StopWatch clock;
clock.start();
// Set up Newton loop.
// Define the primary variable
CollOfScalar u = CollOfScalar(u_initialguess, true);
if (verbose_ > 2) {
output("Initial u", u);
output(" newtonSolve: norm (initial u)", twoNorm(u));
}
CollOfScalar residual = rescomp(u);
if (verbose_ > 2) {
output("Initial residual", residual);
output(" newtonSolve: norm (initial residual)", twoNorm(residual));
}
int iter = 0;
// Debugging output not specified in Equelle.
if (verbose_ > 1) {
std::cout << " newtonSolve: iter = " << iter << " (max = " << max_iter_
<< "), norm(residual) = " << twoNorm(residual)
<< " (tol = " << abs_res_tol_ << ")" << std::endl;
}
CollOfScalar du;
// Execute newton loop until residual is small or we have used too many iterations.
while ( (twoNorm(residual) > abs_res_tol_) && (iter < max_iter_) ) {
if ( solver_.getSolver() == CPU ) {
du = serialSolveForUpdate(residual);
}
else {
// Solve linear equations for du, apply update.
du = solver_.solve(residual.derivative(),
residual.value(),
verbose_);
}
// du is a constant, hence, u is still a primary variable with an identity
// matrix as its derivative.
u = u - du;
// Recompute residual.
residual = rescomp(u);
if (verbose_ > 2) {
// Debugging output not specified in Equelle.
output("u", u);
output(" newtonSolve: norm(u)", twoNorm(u));
output("residual", residual);
output(" newtonSolve: norm(residual)", twoNorm(residual));
}
++iter;
// Debugging output not specified in Equelle.
if (verbose_ > 1) {
std::cout << " newtonSolve: iter = " << iter << " (max = " << max_iter_
<< "), norm(residual) = " << twoNorm(residual)
<< " (tol = " << abs_res_tol_ << ")" << std::endl;
}
}
if (verbose_ > 0) {
if (twoNorm(residual) > abs_res_tol_) {
std::cout << "Newton solver failed to converge in " << max_iter_ << " iterations" << std::endl;
} else {
std::cout << "Newton solver converged in " << iter << " iterations" << std::endl;
}
}
if (verbose_ > 1) {
std::cout << "Newton solver took: " << clock.secsSinceLast() << " seconds." << std::endl;
}
return CollOfScalar(u.value());
}
int main()
try
{
typedef Opm::AutoDiffBlock<double> ADB;
typedef ADB::V V;
typedef Eigen::SparseMatrix<double> S;
Opm::time::StopWatch clock;
clock.start();
const Opm::GridManager gm(3,3);//(50, 50, 10);
const UnstructuredGrid& grid = *gm.c_grid();
using namespace Opm::unit;
using namespace Opm::prefix;
// const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
// { 1000.0, 800.0 },
// { 1.0*centi*Poise, 5.0*centi*Poise },
// 0.2, 100*milli*darcy,
// grid.dimensions, grid.number_of_cells);
// const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
// { 1000.0, 1000.0 },
// { 1.0, 1.0 },
// 1.0, 1.0,
// grid.dimensions, grid.number_of_cells);
const Opm::IncompPropertiesBasic props(2, Opm::SaturationPropsBasic::Linear,
{ 1000.0, 1000.0 },
{ 1.0, 30.0 },
1.0, 1.0,
grid.dimensions, grid.number_of_cells);
V htrans(grid.cell_facepos[grid.number_of_cells]);
tpfa_htrans_compute(const_cast<UnstructuredGrid*>(&grid), props.permeability(), htrans.data());
V trans_all(grid.number_of_faces);
// tpfa_trans_compute(const_cast<UnstructuredGrid*>(&grid), htrans.data(), trans_all.data());
const int nc = grid.number_of_cells;
std::vector<int> allcells(nc);
for (int i = 0; i < nc; ++i) {
allcells[i] = i;
}
std::cerr << "Opm core " << clock.secsSinceLast() << std::endl;
// Define neighbourhood-derived operator matrices.
const Opm::HelperOps ops(grid);
const int num_internal = ops.internal_faces.size();
std::cerr << "Topology matrices " << clock.secsSinceLast() << std::endl;
typedef Opm::AutoDiffBlock<double> ADB;
typedef ADB::V V;
// q
V q(nc);
q.setZero();
q[0] = 1.0;
q[nc-1] = -1.0;
// s0 - this is explicit now
typedef Eigen::Array<double, Eigen::Dynamic, 2, Eigen::RowMajor> TwoCol;
TwoCol s0(nc, 2);
s0.leftCols<1>().setZero();
s0.rightCols<1>().setOnes();
// totmob - explicit as well
TwoCol kr(nc, 2);
props.relperm(nc, s0.data(), allcells.data(), kr.data(), 0);
const V krw = kr.leftCols<1>();
const V kro = kr.rightCols<1>();
const double* mu = props.viscosity();
const V totmob = krw/mu[0] + kro/mu[1];
// Moved down here because we need total mobility.
tpfa_eff_trans_compute(const_cast<UnstructuredGrid*>(&grid), totmob.data(),
htrans.data(), trans_all.data());
// Still explicit, and no upwinding!
V mobtransf(num_internal);
for (int fi = 0; fi < num_internal; ++fi) {
mobtransf[fi] = trans_all[ops.internal_faces[fi]];
}
std::cerr << "Property arrays " << clock.secsSinceLast() << std::endl;
// Initial pressure.
V p0(nc,1);
p0.fill(200*Opm::unit::barsa);
// First actual AD usage: defining pressure variable.
const std::vector<int> bpat = { nc };
// Could actually write { nc } instead of bpat below,
// but we prefer a named variable since we will repeat it.
const ADB p = ADB::variable(0, p0, bpat);
const ADB ngradp = ops.ngrad*p;
// We want flux = totmob*trans*(p_i - p_j) for the ij-face.
const ADB flux = mobtransf*ngradp;
const ADB residual = ops.div*flux - q;
std::cerr << "Construct AD residual " << clock.secsSinceLast() << std::endl;
// It's the residual we want to be zero. We know it's linear in p,
// so we just need a single linear solve. Since we have formulated
// ourselves with a residual and jacobian we do this with a single
// Newton step (hopefully easy to extend later):
// p = p0 - J(p0) \ R(p0)
// Where R(p0) and J(p0) are contained in residual.value() and
// residual.derived()[0].
#if HAVE_SUITESPARSE_UMFPACK_H
typedef Eigen::UmfPackLU<S> LinSolver;
#else
typedef Eigen::BiCGSTAB<S> LinSolver;
#endif // HAVE_SUITESPARSE_UMFPACK_H
LinSolver solver;
S pmatr;
residual.derivative()[0].toSparse(pmatr);
pmatr.coeffRef(0,0) *= 2.0;
pmatr.makeCompressed();
solver.compute(pmatr);
if (solver.info() != Eigen::Success) {
std::cerr << "Pressure/flow Jacobian decomposition error\n";
return EXIT_FAILURE;
}
// const Eigen::VectorXd dp = solver.solve(residual.value().matrix());
ADB::V residual_v = residual.value();
const V dp = solver.solve(residual_v.matrix()).array();
if (solver.info() != Eigen::Success) {
std::cerr << "Pressure/flow solve failure\n";
return EXIT_FAILURE;
}
const V p1 = p0 - dp;
std::cerr << "Solve " << clock.secsSinceLast() << std::endl;
// std::cout << p1 << std::endl;
// ------ Transport solve ------
// Now we'll try to do a transport step as well.
// Residual formula is
// R_w = s_w - s_w^0 + dt/pv * (div v_w)
// where
// v_w = f_w v
// and f_w is (for now) based on averaged mobilities, not upwind.
double res_norm = 1e100;
const V sw0 = s0.leftCols<1>();
// V sw1 = sw0;
V sw1 = 0.5*V::Ones(nc,1);
const V ndp = (ops.ngrad * p1.matrix()).array();
const V dflux = mobtransf * ndp;
const Opm::UpwindSelector<double> upwind(grid, ops, dflux);
const V pv = Eigen::Map<const V>(props.porosity(), nc, 1)
* Eigen::Map<const V>(grid.cell_volumes, nc, 1);
const double dt = 0.0005;
const V dtpv = dt/pv;
const V qneg = q.min(V::Zero(nc,1));
const V qpos = q.max(V::Zero(nc,1));
std::cout.setf(std::ios::scientific);
std::cout.precision(16);
int it = 0;
do {
const ADB sw = ADB::variable(0, sw1, bpat);
const std::vector<ADB> pmobc = phaseMobility<ADB>(props, allcells, sw.value());
const std::vector<ADB> pmobf = upwind.select(pmobc);
const ADB fw_cell = fluxFunc(pmobc);
const ADB fw_face = fluxFunc(pmobf);
const ADB flux1 = fw_face * dflux;
const ADB qtr_ad = qpos + fw_cell*qneg;
const ADB transport_residual = sw - sw0 + dtpv*(ops.div*flux1 - qtr_ad);
res_norm = transport_residual.value().matrix().norm();
std::cout << "res_norm[" << it << "] = "
<< res_norm << std::endl;
S smatr;
transport_residual.derivative()[0].toSparse(smatr);
smatr.makeCompressed();
solver.compute(smatr);
if (solver.info() != Eigen::Success) {
std::cerr << "Transport Jacobian decomposition error\n";
return EXIT_FAILURE;
}
ADB::V transport_residual_v = transport_residual.value();
const V ds = solver.solve(transport_residual_v.matrix()).array();
if (solver.info() != Eigen::Success) {
std::cerr << "Transport solve failure\n";
return EXIT_FAILURE;
}
sw1 = sw.value() - ds;
std::cerr << "Solve for s[" << it << "]: "
<< clock.secsSinceLast() << '\n';
sw1 = sw1.min(V::Ones(nc,1)).max(V::Zero(nc,1));
it += 1;
} while (res_norm > 1e-7);
std::cout << "Saturation solution:\n"
<< "function s1 = solution\n"
<< "s1 = [\n" << sw1 << "\n];\n";
}
catch (const std::exception &e) {
std::cerr << "Program threw an exception: " << e.what() << "\n";
throw;
}