Abstract
Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. 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 in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property.
| Original language | English |
|---|---|
| Pages (from-to) | n/a |
| Number of pages | 30 |
| Journal | Numerische Mathematik |
| Volume | n/a |
| Issue number | n/a |
| Early online date | 15 Aug 2013 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords
- coarse spaces
- overlapping Schwarz method
- two-level methods
- generalized eigenvectors
- large coefficient variation
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Spillane, N., Dolean Maini, V., Hauret, P., Nataf, F., Pechstein, C., & Scheichl, R. (2013). Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. Numerische Mathematik, n/a(n/a), n/a. https://doi.org/10.1007/s00211-013-0576-y