Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | Shihua Gong，Chinese University of Hong Kong (Shenzhen)
| | Inviter: | | Title:
| Convergence of Restricted Additive Schwarz method with impedance transmission conditions for discretized Helmholtz problems | Time & Venue:
| 2021.12.22 19:30-21:00 腾讯会议：98873715026 | Abstract:
| 点击链接入会，或添加至会议列表：
https://meeting.tencent.com/dm/jOtuYVFJlHeR
The Restricted Additive Schwarz method with impedance transmission conditions, also known as the Optimised Restricted Additive Schwarz (ORAS) method, is a simple overlapping one-level parallel domain decomposition method. It is implemented in PETSc and FreeFEM++ and has been successfully used as an iterative solver and a preconditioner for wave propagation problems. However, there remains limited rigorous convergence analysis of this method. This talk will revisit some background of the Helmholtz equation and some standard convergence theory for the iterative methods. Then I will present a novel convergence analysis for ORAS based on "power contractivity". The analysis starts by showing that ORAS is an unconventional finite element approximation of a classical parallel iterative Schwarz method, formulated at the PDE (non-discrete) level. This non-discrete Schwarz method was recently analyzed in [Gong, Gander, Graham, Lafontaine, Spence, arXiv 2106.05218]. Using a novel weighted finite-element error estimate for Helmholtz problems, we show that ORAS inherits the convergence properties of the Schwarz method, independent of polynomial order.
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