Non-manifold boundary element methods
Vortrag von Dr. Martin Averseng
Datum: 25.09.24 Zeit: 16.30 - 18.00 Raum: ETH HG G 19.2
The Boundary Element Method (BEM) is a discretization technique commonly employed for the accurate and rapid numerical solution of constant-coefficient second-order partial differential equations (PDEs) in the complement of an obstacle, e.g., electromagnetic scattering problems. The BEM exploits the fundamental solution of the PDE to reduce the number of unknowns compared to the Finite Element Method for the same level of error. However, it is a non-local method and thus leads to full linear systems. For this reason, the BEM linear systems are often solved iteratively, and good preconditioners often turn out to be a key ingredient to ensure a fast resolution. In this talk, we present the motivation and the practical and mathematical challenges for extending the BEM to geometric settings involving non-manifold boundaries. We will first summarize the recent advances in the mathematical formalization of this problem. We will then present a particular preconditioning technique for "multi-screen" obstacles based on substructuring (domain decomposition). This work is in collaboration with Xavier Claeys and Ralf Hiptmair.