New theory for two-level domain-decomposition preconditioners for the high-frequency Helmholtz equation (Euan Spence, University of Bath)

15.04.2025 14:00 – 15:00

When solving self-adjoint positive-definite problems (such as Laplace’s equation) with domain-decomposition methods, coarse spaces provide global transfer of information, and are the key to parallel scalability. However, the design of practical coarse spaces for high-frequency wave problems, such as the high-frequency Helmholtz equation, is much more difficult than in the self-adjoint positive-definite case. In the last year, there have been several papers providing theory for specific coarse-spaces consisting of (pre-computed) problem-adapted basis functions. This talk will present:
1) a general theory that applies to all these previously-analysed coarse spaces, and
2) new results about piecewise-polynomial coarse spaces.

This is joint work with Jeffrey Galkowski (University College London) and Ivan Graham (University of Bath).

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre