Seminars on Numerical Algorithms, Analyses, and Applications: Multiscale model reduction based on locally optimal spectral approximations for heterogeneous wave equations

Speaker：Chupeng Ma (Great Bay University)

Time：2026-8-21 15:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

In this talk, I will present a generalized finite element method with optimal local approximation spaces for solving heterogeneous Helmholtz and Maxwell equations. The local spaces are built from selected eigenvectors of carefully designed local eigenvalue problems posed on local solution spaces. Local exponential convergence rates are established for the method at both continuous and discrete levels. The multiscale method is further formulated as a two-level restricted additive Schwarz (RAS) preconditioner for solving discretized PDEs. Numerical results are provided to confirm the theoretical analysis and to validate the proposed methods.