Rodin::Solver namespace

Module for solving linear and nonlinear systems.

The Solver module provides linear solvers for the systems arising from finite element discretizations. Available solvers include:

CG — Conjugate Gradient (for SPD systems)
GMRES — Generalized Minimum Residual
SparseLU — Direct sparse LU factorization
UMFPack — UMFPACK direct solver

Usage:

// Iterative solver
Solver::CG(problem).solve();

// Direct solver
Solver::SparseLU(problem).solve();

Classes

template<class LinearSystem> class BiCGSTAB: Bi-conjugate gradient stabilized iterative solver.
template<class Scalar> class BiCGSTAB<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Bi-conjugate gradient stabilized solver for non-symmetric sparse systems.
template<class LinearSystem> class CG: Conjugate gradient solver for symmetric positive definite systems.
template<class Scalar> class CG<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: Conjugate gradient solver for symmetric positive definite dense systems.
template<class Scalar> class CG<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Conjugate gradient solver for symmetric positive definite sparse systems.
template<> class CG<PETSc::Math::LinearSystem>: Conjugate gradient solver for PETSc linear systems.
template<class LinearSystem> class DGMRES: Deflated generalized minimal residual iterative solver.
template<class Scalar> class DGMRES<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: DGMRES solver for dense systems.
template<class Scalar> class DGMRES<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: DGMRES solver for sparse systems.
template<class EigenSolverType, class OperatorType, class VectorType> class EigenSolver: Wrapper class for any Eigen sparse solver.
template<class LinearSystem> class GMRES: Generalized minimal residual iterative solver.
template<class Scalar> class GMRES<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: GMRES solver for dense systems.
template<class Scalar> class GMRES<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: GMRES solver for sparse systems.
template<> class GMRES<PETSc::Math::LinearSystem>: Generalized minimal residual (GMRES) solver for PETSc linear systems.
template<class LinearSystem> class HouseholderQR: Householder QR decomposition for dense matrices.
template<class Scalar> class HouseholderQR<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: A direct sparse HouseholderQR Cholesky factorizations without square root for use with Math::SparseMatrix and Math::Vector.
template<class Scalar> class IDRS<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: IDRS(s) solver for dense systems.
template<class Scalar> class IDRS<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: IDRS(s) solver for sparse systems.
template<class LinearSystem> class IDRSTABL: IDR(s)STABL iterative solver.
template<class Scalar> class IDRSTABL<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: IDRstab(l) solver for dense systems.
template<class Scalar> class IDRSTABL<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: IDRstab(l) solver for sparse systems.
class KSP: PETSc KSP (Krylov subspace) linear solver wrapper.
template<class LinearSystem> class LDLT: Robust LDLT Cholesky decomposition for dense matrices.
template<class Scalar> class LDLT<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: Robust LDLT Cholesky factorization with pivoting for dense matrices.
template<class LinearSystem> class LeastSquaresCG: Least-squares conjugate gradient solver.
template<class Scalar> class LeastSquaresCG<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: Least-squares conjugate gradient solver for dense systems.
template<class Scalar> class LeastSquaresCG<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Least-squares conjugate gradient solver for sparse systems.
template<class LinearSystem> class LinearSolverBase: Abstract base class for linear system solvers.
template<class Scalar> class MINRES<Math::LinearSystem<Math::Matrix<Scalar>, Math::Vector<Scalar>>>: MINRES solver for symmetric dense systems.
template<class Scalar> class MINRES<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: MINRES solver for symmetric sparse systems.
template<class LinearSolver> class NewtonSolver: Newton solver for state-dependent tangential problems.
template<class LinearSolver> class NewtonSolverBase: Abstract base class for Newton-type nonlinear solvers.
template<class LinearSystem> class SimplicialLDLT: Direct sparse LDLT Cholesky factorization solver.
template<class Scalar> class SimplicialLDLT<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Simplicial LDLT Cholesky factorization without square root.
template<class LinearSystem> class SimplicialLLT: Direct sparse LLT Cholesky factorization solver.
template<class Scalar> class SimplicialLLT<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Simplicial LLT Cholesky factorization for sparse SPD matrices.
class SNES: PETSc SNES (Scalable Nonlinear Equations Solvers) wrapper.
template<class LinearSystem> class SparseLU: Sparse supernodal LU factorization for general matrices.
template<class Scalar> class SparseLU<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Sparse supernodal LU factorization solver for general sparse matrices.
template<class LinearSystem> class SparseQR: Sparse QR factorization with column pivoting.
template<class Scalar> class SparseQR<Math::LinearSystem<Math::SparseMatrix<Scalar>, Math::Vector<Scalar>>>: Sparse QR factorization with numerical column pivoting.