AILU for Helmholtz problems: A new preconditioner based on an analytic factorization. (English. Abridged French version) Zbl 0960.65054
Summary: We investigate a new type of preconditioner which is based on the analytic factorization of the operator into two parabolic factors. Approximate analytic factorizations lead to new block ILU preconditioners. We analyze the preconditioner at the continuous level where it is possible to optimize its performance. Numerical experiments illustrate the effectiveness of the new approach.
MSC:
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
