Name
Abstract | ||
|---|---|---|
We present a new coarse space correction for the iterative Neumann-Neumann method. We describe the method for general elliptic partial differential equations and perform the analysis for the case of the Poisson and screened Poisson equation (sometimes also called the positive definite Helmholtz equation). We prove that the new two-level Neumann-Neumann method converges after one iteration, at both the continuous and discrete levels, which means the new coarse space is optimal in the sense of best possible, and it makes the two-level method a direct solver. In two and three space dimensions, the new coarse space is too high dimensional in practice, and we introduce a spectral approximation, which transforms a divergent iterative Neumann-Neumann method into a convergent one. We also identify what the optimized choice of coarse space functions is in the approximation. Our new coarse space thus also addresses convergence or robustness problems of the underlying domain decomposition iteration, similarly to the new coarse spaces GenEO, SHEM, and ACMS, which were designed to treat different convergence difficulties of the underlying domain decomposition method, namely the presence of high contrast media. Several numerical experiments are carried out to demonstrate the performance of this new coarse space correction, also including decompositions with cross points. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/20M1316317 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
domain decomposition methods, elliptic problems, Neumann-Neumann methods | Journal | 42 |
Issue | ISSN | Citations |
6 | 1064-8275 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Faycal Chaouqui | 1 | 0 | 0.34 |
| Martin J. Gander | 2 | 467 | 51.08 |
| Kévin Santugini-Repiquet | 3 | 0 | 0.34 |