A moving mesh method for time-dependent problems based on Schwarz waveform relaxation. (English) Zbl 1139.65314
Langer, Ulrich (ed.) et al., Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Berlin: Springer (ISBN 978-3-540-75198-4/pbk). Lecture Notes in Computational Science and Engineering 60, 229-236 (2008).
Summary: We propose a moving mesh Schwarz waveform relaxation method. In this approach, classical Schwarz waveform relaxation is applied to the physical PDE and a moving mesh method is used to facilitate the solution on each subdomain. In this way a solution is obtained which benefits both from the domain decomposition approach and the ability to dynamically refine meshes within each subdomain. A careful comparison with previous approaches is ongoing. The benefits of such an approach are likely to be fully realized in two or more space dimensions. This is certainly the subject of current work and interest. The effects of higher order transmission conditions are also studied in this context.
For the entire collection see [Zbl 1130.65004].
For the entire collection see [Zbl 1130.65004].
MSC:
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
