Multilevel Schwarz methods. (English) Zbl 0796.65129
The author presents a solution of a system of linear algebraic equations which results from the discretization of second order elliptic equations. A class of multilevel algorithms is studied using the additive Schwarz framework. It is established that the condition number of the iteration operators are bounded independently of the mesh sizes and the number of levels. Numerical experiments are performed for illustration.
Reviewer: P.K.Mahanti (Ranchi)
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
numerical experiments; multilevel Schwarz methods; second order elliptic equations; multilevel algorithm; condition numberReferences:
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