Summary of Sparse Linear Solvers Available In PETSc¶

Preconditioners¶

	Algorithm	Associated Type	Matrix Types	External Packages	Parallel	Complex
Generic	Jacobi	`PCJACOBI`	`MATAIJ`, `MATBAIJ`, `MATSBAIJ`, `MATDENSE`	—	X	X
	Point Block Jacobi	`PCPBJACOBI`	`MATAIJ`, `MATBAIJ`, `MATSBAIJ`, `MATKAIJ`, `MATMPISELL`, `MATIS`	—	X	X
	Block Jacobi	`PCBJACOBI`	`MATAIJ`, `MATBAIJ`, `MATSBAIJ`	—	X	X
	SOR	`PCSOR`	`MATAIJ`, `MATSEQDENSE`, `MATSEQSBAIJ`	—		X
	Point Block SOR		`MATSEQBAIJ` (only for `bs` = 2,3,4,5)	—		X
	Additive Schwarz	`PCASM`	`MATAIJ`, `MATBAIJ`, `MATSBAIJ`	—	X	X
	Deflation	`PCDEFLATION`	All	—	X	X
Incomplete	ILU	`PCILU`	`MATSEQAIJ`, `MATSEQBAIJ`	—		X
	ILU with drop tolerance	`PCILU`	`MATSEQAIJ`	SuperLU Sequential ILU solver		X
		`PCILU`	`MATAIJ`	Euclid/hypre (`PCHYPRE`)	X
	ICholesky	`PCICC`	`MATSEQAIJ`, `MATSEQBAIJ`, `MATSEQSBAIJ`	—		X
Matrix Free	Infrastructure	`PCSHELL`	All	—	X	X
Multigrid	Infrastructure	`PCMG`	All	—	X	X
	Geometric		All	—	X	X
	Smoothed Aggregation	`PCGAMG`	`MATAIJ`	—	X	X
	Structured Geometric	`PCPFMG`	`MATHYPRESTRUCT`	hypre	X
	Classical Algebraic	`PCHYPRE`, `PCML`	`MATAIJ`	BoomerAMG/hypre, ML/Trilinos	X
	Domain Decomposition	`PCHPDDM`	`MATAIJ`, `MATBAIJ`, `MATSBAIJ`, `MATIS`	HPDDM	X	X
Physics-based Splitting	Relaxation & Schur Complement	`PCFIELDSPLIT`	`MATAIJ`, `MATBAIJ`, `MATNEST`	—	X	X
	Least Squares Commutator	`PCLSC`	`MATSCHURCOMPLEMENT`	—	X	X
Approximate Inverse	AIV	`PCHYPRE`, `PCSPAI`	`MATAIJ`	Parasails/hypre, SPAI	X
Substructuring	Balancing Neumann-Neumann	`PCNN`	`MATIS`	—	X	X
	Balancing Domain Decomposition	`PCBDDC`	`MATIS`	—	X	X

	Algorithm	Associated Type	Matrix Types	External Packages	Parallel	Complex
Direct LU	LU	`PCLU`	`MATSEQAIJ`, `MATSEQBAIJ`	—		X
			`MATSEQAIJ`	MATLAB		X
			`MATAIJ`	PaStiX	X	X
			`MATAIJ`	SuperLU	X	X
			`MATAIJ`, `MATBAIJ`	MUMPS	X	X
			`MATSEQAIJ`	ESSL
			`MATSEQAIJ`	UMPFPACK (SuiteSparse)		X
			`MATSEQAIJ`	KLU (SuiteSparse)		X
			`MATSEQAIJ`	LUSOL
			`MATSEQAIJ`, `MATSEQBAIJ`	MKL Pardiso		X
			`MATMPIAIJ`, `MATMPIBAIJ`	MKL CPardiso	X	X
			`MATDENSE`	Elemental	X	X
Direct Cholesky	Cholesky	`PCCHOLESKY`	`MATSEQAIJ`, `MATSEQSBAIJ`	—		X
			`MATSBAIJ`	PaStiX	X	X
			`MATSBAIJ`	MUMPS	X	X
			`MATSEQAIJ`, `MATSEQSBAIJ`	CHOLMOD (SuiteSparse)		X
			`MATDENSE`	Elemental	X	X
			`MATSEQSBAIJ`	MKL Pardiso
			`MATMPIAIJ`, `MATMPIBAIJ`	MKL CPardiso	X
Direct QR	QR		MATLAB	MATLAB
	XXt and XYt		`MATAIJ`	—	X

Algorithm	Associated Type	External Packages	Parallel	Complex
Richardson	`KSPRICHARDSON`	—	X	X
Chebyshev	`KSPCHEBYSHEV`	—	X	X
GMRES	`KSPGMRES`	—	X	X
Flexible GMRES	`KSPFGMRES`	—	X	X
LGMRES	`KSPLGMRES`	—	X	X
Conjugate Gradient	`KSPCG`	—	X	X
Conjugate Gradient Squared	`KSPCGS`	—	X	X
Conjugate Gradient for Least Squares	`KSPCGLS`	—	X	X
Conjugate Gradient on Normal Equations	`KSPCGNE`	—	X	X
Bi-Conjugate Gradient	`KSPBICG`	—	X	X
Stabilized Bi-Conjugate Gradient	`KSPBCGS`	—	X	X
Transpose-free QMR	`KSPTFQMR`	—	X	X
Conjugate Residual	`KSPCR`	—	X	X
Generalized Conjugate Residual	`KSPGCR`	—	X	X
Generalized Conjugate Residual (with inner normalization and deflated restarts)	`KSPHPDDM`	HPDDM	X	X
Minimum Residual	`KSPMINRES`	—	X	X
LSQR	`KSPLSQR`	—	X	X
SYMMLQ	`KSPSYMMLQ`	—	X	X