Available Solvers

Table of Contents

• Mixing Native and PETSc Solvers
• Basic Solvers and Preconditioners
  • Jacobi Iteration
  • LU Factorization
  • Block Jacobi
  • Additive Schwarz
• Krylov Solvers
  • Conjugate Gradient
  • Generalized Minimum Residual Method

This page outlines the solvers that are currently available through Open FUSION Toolkit solver objects. Additional solvers may be used through backend implementations, but only internally controlled and supported solvers are outlined here.

Mixing Native and PETSc Solvers

Solver interfaces have been designed to allow mixing of native and PETSc methods. Most native solvers are written with generic API calls for linear algebra and as a result can be used when either backend is used for vectors and matrices. There are many cases however where the PETSc implementation of a particular solver/preconditioner is more optimal for its matrices and vectors. Additionally, there are some methods, ex. direct methods, which are only available through PETSc. The oft_petsc_pre_solver class is provided to allow using PETSc solvers as preconditioners for native solvers. This class acts as a wrapper around the PETSc solver, allowing it to be called using the standard solver calling sequence.

Basic Solvers and Preconditioners

Jacobi Iteration

Jacobi iterations solves a system of linear equations by iterating on the method

\[ x^{n+1} = x^n + D^{-1}(A*x^n - y) \]

where \( D \) is a matrix of only the diagonal elements of \( A \). Functionality is provided through either a general native interface oft_diag_scale and an optimized PETSc interface oft_petsc_diagprecond.

XML Spec: <pre type="jacobi">

LU Factorization

This method is supported through both the native and PETSc backends through oft_lusolver and oft_petsc_direct_solver for a full solver or oft_petsc_luprecond as a PETSc preconditioner.

Warning

The native solver currently only supports local solves (ie as a sub-solver to Block Jacobi)

XML Spec: <solver type="lu">

Group	Description	Type	List
package	Solver package to use {super, superd, mumps}	str	No

PETSc only options

Group	Description	Type	List
type	Inverse type {lu, ilu}	str	No

Block Jacobi

This method is supported through both the native and PETSc backends through oft_bjprecond and oft_petsc_asprecond.

XML Spec: <pre type="block_jacobi">

Group	Description	Type	List
nlocal	Number of local blocks (-1 for field based)	int	Yes
groups	Group index for each field in multi-field vector [n]	int	Yes
boverlap	Overlap boundary rows (native only)	bool	false

Additive Schwarz

This method is currently only supported with the PETSc backend through oft_petsc_asprecond as a preconditioner.

XML Spec: <pre type="add_schwarz">

Group	Description	Type	List
nlocal	Number of local blocks (-1 for field based)	int	Yes
overlap	Overlap size	int	Yes

Krylov Solvers

Conjugate Gradient

This method is provided through both the native and PETSc backends through oft_cg_solver and oft_petsc_cg_solver.

XML Spec: <solver type="cg">

Group	Description	Type	List
atol	Absolute convergence tolerance	real	Yes
rtol	Relative convergence tolerance	real	Yes
its	Iteration limit	int	Yes

Generalized Minimum Residual Method

This method is provided through both the native and PETSc backends through oft_gmres_solver and oft_petsc_gmres_solver.

XML Spec: <solver type="gmres">

Group	Description	Type	List
atol	Absolute convergence tolerance	real	Yes
rtol	Relative convergence tolerance	real	Yes
its	Iteration limit	int	Yes
nrit	Restart size	int	Yes