Preconditioning Indefinite Discretization Matrices.
Please always quote using this URN: urn:nbn:de:0297-zib-81
- The finite element discretization of many elliptic boundary value problems leads to linear systems with positive definite and symmetric coefficient matrices. Many efficient preconditioners are known for these systems. We show that these preconditioning matrices can be used also for the linear systems arising from boundary value problems which are potentially indefinite due to lower order terms in the partial differential equation. Our main tool is a careful algebraic analysis of the condition numbers and the spectra of perturbed matrices which are preconditioned by the same matrices as in the unperturbed case. {\bf Keywords: }Preconditioned conjugate gradient methods, finite elements. {\bf Subject Classification: } AMS(MOS):65F10, 65N20, 65N30.
| Author: | Harry Yserentant |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | finite elements; preconditioned conjugate gradient methods |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22] |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems | |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
| Date of first Publication: | 1987/09/23 |
| Series (Serial Number): | ZIB-Report (SC-87-06) |
| ZIB-Reportnumber: | SC-87-06 |
| Published in: | Appeared in: Numer. Mathematik 54, p. 719-734 (1988) |
