OOF2: The Manual
Preconditioner |
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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.
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Incomplete Cholesky (
ICPreconditioner) — Incomplete Cholesky factorization with dual thresholding. -
Incomplete LUT (
ILUTPreconditioner) — Incomplete LU-factorization with dual thresholding. -
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.
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