Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods
| Autor: | Reinhard Nabben, J.M. Tang, Cornelis Vuik, Yogi A. Erlangga |
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| Rok vydání: | 2009 |
| Předmět: |
Positive-definite matrix
Multigrid Deflation Mathematics::Numerical Analysis Theoretical Computer Science Two-level PCG methods Multigrid method Robustness (computer science) Applied mathematics Domain decomposition Coefficient matrix Engineering(all) Eigenvalues and eigenvectors Two-level preconditioning Mathematics Conjugate gradients Numerical Analysis Two-grid schemes Preconditioner SPD matrices Applied Mathematics Linear system General Engineering Domain decomposition methods Computer Science::Numerical Analysis Algebra Computational Mathematics Computational Theory and Mathematics Software |
| Zdroj: | Journal of Scientific Computing, 39 (3), 2009 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-009-9272-6 |
| Popis: | For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type preconditioners to get rid of the effect of both small and large eigenvalues of the coefficient matrix. In the literature, various two-level PCG methods are known, coming from the fields of deflation, domain decomposition and multigrid. Even though these two-level methods differ a lot in their specific components, it can be shown that from an abstract point of view they are closely related to each other. We investigate their equivalences, robustness, spectral and convergence properties, by accounting for their implementation, the effect of roundoff errors and their sensitivity to inexact coarse solves, severe termination criteria and perturbed starting vectors. |
| Databáze: | OpenAIRE |
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