OOF2: The Manual
Preconditioner — Preconditioners for efficient solution of matrix equations.
Subclasses are listed as they appear in the GUI and (in parentheses) as they appear in scripts.
ILUPreconditioner) -- Incomplete LU-factorization
ICPreconditioner) -- Incomplete Cholesky preconditioner. Appropriate only for meshes with symmetric, positive definite stiffness matrices.
JacobiPreconditioner) -- A light-weight preconditioner, that simply inverts the diagonal part of the matrix.
UnPreconditioner) -- Be bold (or foolhardy) and attempt to solve the mesh without a preconditioner
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
is an object of the
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.