Open access
Datum
2000-11Typ
- Report
ETH Bibliographie
yes
Altmetrics
Abstract
Sparse approximate inverses are considered as smoothers for multigrid. They are based on the SPAI-Algorithm (Grote and Huckle, 1997), which constructs a sparse approximate inverse M of a matrix A by minimizing I -MA in the Frobenius norm. This yields a new hierarchy of smoothers: SPAI-0, SPAI-1, SPAI$(\varepsilon)$. Advantages of SPAI smoothers over classical smoothers are inherent parallelism, possible local adaptivity and improved robustness. The simplest smoother, SPAI-0, is based on a diagonal matrix M. It is shown to satisfy the smoothing property for symmetric positive definite problems. Numerical experiments show that SPAI-0 smoothing is usually preferable to damped Jacobi smoothing. In more difficult situations, where the simpler SPAI-0 and SPAI-1 smoothers are not adequate, the SPAI$(\varepsilon)$ smoother provides a natural procedure for improvement where needed. Numerical examples illustrate the usefulness of SPAI smoothing. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-a-004289411Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SAM Research ReportBand
Verlag
Seminar for Applied Mathematics, ETH ZurichOrganisationseinheit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
ETH Bibliographie
yes
Altmetrics