PolySolve

This library contains a cross-platform Eigen wrapper for many different external linear solvers including (but not limited to):

• CHOLMOD
• Hypre
• AMGCL
• Pardiso

Example Usage

const std::string solver_name = "Hypre"
auto solver = LinearSolver::create(solver_name, "");

// Configuration parameters like iteration or accuracy for iterative solvers
// solver->setParameters(params);

// System sparse matrix
Eigen::SparseMatrix<double> A;

// Right-hand side
Eigen::VectorXd b;

// Solution
Eigen::VectorXd x(b.size());

solver->analyzePattern(A, A.rows());
solver->factorize(A);
solver->solve(b, x);

You can use LinearSolver::availableSolvers() to obtain the list of available solvers.

Parameters

Polysolve uses a JSON file to provide parameters to the individual solvers. The following template can be used as a starting point, and a more detailed explanation of the parameters is below.

{
    "Eigen::LeastSquaresConjugateGradient": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Eigen::DGMRES": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Eigen::ConjugateGradient": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Eigen::BiCGSTAB": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Eigen::GMRES": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Eigen::MINRES": {
        "max_iter": 1000,
        "tolerance": 1e-6
    },
    "Pardiso": {
        "mtype": -1
    },
    "Hypre": {
        "max_iter": 1000,
        "pre_max_iter": 1000,
        "tolerance": 1e-6
    },
    "AMGCL": {
        "precond": {
            "relax": {
                "degree": 16,
                "type": "chebyshev",
                "power_iters": 100,
                "higher": 2,
                "lower": 0.008333333333,
                "scale": true
            },
            "class": "amg",
            "max_levels": 6,
            "direct_coarse": false,
            "ncycle": 2,
            "coarsening": {
                "type": "smoothed_aggregation",
                "estimate_spectral_radius": true,
                "relax": 1,
                "aggr": {
                    "eps_strong": 0
                }
            }
        },
        "solver": {
            "tol": 1e-10,
            "maxiter": 1000,
            "type": "cg"
        }
    }
}

Iterative solvers (AMGCL, Eigen Internal Solvers, HYPRE)

• max_iter controls the solver’s iterations, default 1000
• conv_tol, tolerance controls the convergence tolerance, default 1e-10

Hypre Only

• pre_max_iter, number of pre iterations, default 1

AMGCL Only

The default parameters of the AMGCL solver are:

{
    "precond": {
        "relax": {
            "degree": 16,
            "type": "chebyshev",
            "power_iters": 100,
            "higher": 2,
            "lower": 0.008333333333,
            "scale": true
        },
        "class": "amg",
        "max_levels": 6,
        "direct_coarse": false,
        "ncycle": 2,
        "coarsening": {
            "type": "smoothed_aggregation",
            "estimate_spectral_radius": true,
            "relax": 1,
            "aggr": {
                "eps_strong": 0
            }
        }
    },
    "solver": {
        "tol": 1e-10,
        "maxiter": 1000,
        "type": "cg"
    }
}

For a more details and options refer to the AMGCL documentation.

Pardiso

mtype, sets the matrix type, default 11

mtype	Description
1	real and structurally symmetric
2	real and symmetric positive definite
-2	real and symmetric indefinite
3	complex and structurally symmetric
4	complex and Hermitian positive definite
-4	complex and Hermitian indefinite
6	complex and symmetric
11	real and nonsymmetric
13	complex and nonsymmetric

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Last update: 2023-10-03