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PolySolve

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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
Last update: 2023-10-03