A robust two-level domain decomposition preconditioner for systems of PDEs. (English. Abridged French version) Zbl 1252.65201
Summary: Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the coefficients of partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples of a heterogeneous elasticity problem.
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 74B05 | Classical linear elasticity |
Keywords:
domain decomposition; generalized eigenvalue problems; convergence; numerical examples; heterogeneous elasticity problemSoftware:
FreeFem++References:
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