Algebraic Multilevel Krylov Methods
| Autor: | Yogi A. Erlangga, Reinhard Nabben |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Numerical linear algebra
Partial differential equation Helmholtz equation Applied Mathematics Mathematical analysis computer.software_genre Generalized minimal residual method Computational Mathematics Algebraic equation Multigrid method Rate of convergence computer Eigenvalues and eigenvectors Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing. 31:3417-3437 |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/080731657 |
| Popis: | In [Erlangga and Nabben, SIAM J. Sci. Comput., 30 (2008), pp. 1572–1595], we developed a new type of multilevel method, called the multilevel Krylov (MK) method, to solve linear systems of equations. The basic idea of this type of method is to shift small eigenvalues that are responsible for slow convergence of Krylov methods to an a priori fixed constant. This shifting of the eigenvalues is similar to projection-type methods and is achieved via the solution of subspace or coarse level systems. Numerical results show that MK works very well for the two-dimensional (2D) Poisson and convection-diffusion equation, i.e., the convergence can be made almost independent of the grid size h and the physical parameter involved. In a follow-up paper we have used MK in the context of the preconditioned Helmholtz equation. For this problem, we show that the convergence can be made only mildly dependent on the wavenumber. Even though the coarse level system of MK is algebraically related to that of multigrid, the const... |
| Databáze: | OpenAIRE |
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