Maxwell Eigensolvers with Overlapping Schwarz Methods - ICBS 2024

Explore a 51-minute lecture on Maxwell Eigensolvers using Overlapping Schwarz Methods presented by Xuejun Xu at ICBS2024. Delve into the long-standing open problem of condition number bounds for overlapping domain decomposition methods in $\bf{H}(\bf{{\rm curl}};\Omega)$ spaces. Learn how the speaker proves that $C(1+\frac{H}{\delta})$ is indeed the best bound, improving upon the previously established $C(1+\frac{H^2}{\delta^2})$. Discover a novel two-level preconditioned Helmholtz subspace iterative (PHSI) method for solving algebraic eigenvalue problems arising from edge element approximation of Maxwell eigenvalue problems. Understand how this method effectively computes simple, multiple, and clustered eigenpairs, advancing the field of computational electromagnetics.