OOF2: The Manual

`Preconditioner`
	6.5.1. Base RegisteredClasses

Name

Preconditioner — Preconditioners for efficient solution of matrix equations.

Subclasses

Subclasses are listed as they appear in the GUI and (in parentheses) as they appear in scripts.

ILU (ILUPreconditioner) -- Incomplete LU-factorization
IC (ICPreconditioner) -- Incomplete Cholesky preconditioner. Appropriate only for meshes with symmetric, positive definite stiffness matrices.
Jacobi (JacobiPreconditioner) -- A light-weight preconditioner, that simply inverts the diagonal part of the matrix.
Null (UnPreconditioner) -- Be bold (or foolhardy) and attempt to solve the mesh without a preconditioner

Description

Preconditioning is a technique for speeding the convergence of iterative matrix solvers by replacing a given matrix problem with an easier one. The preconditioner parameter for the iterative linear solvers is an object of the Preconditioner class.

Simply put, preconditioning a linear matrix equation, Ax=b, means finding some matrix, M, which is close to the inverse of A and is easy to compute. Then instead of solving Ax=b, solve (MA)x=Mb. Since MA is nearly the unit matrix, this equation is relatively easy to solve.

In practice, preconditioning a large sparse system is an imprecise science. Different precondioners work better for different kinds of problems. The best way of choosing one is to experiment and see which works best. The reference pages for the various Preconditioner subclasses give some guidance, where possible.


`OutputDestination`		`ProfileX`