# Talk

Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

## Generalized FEMs based on locally optimal spectral approximations for Helmholtz equation with heterogeneous coefficient

Talk by Dr. Chupeng Ma

Date: 10.11.21  Time: 16.15 - 17.15  Room: ETH HG E 1.2

In this talk, I will present generalized FEMs with optimal local approximation spaces for solving Helmholtz equation with heterogeneous coefficient and high wavenumber. The optimal local approximation spaces are constructed by eigenvectors of local eigenvalue problems involving a partition of unity function defined on generalized harmonic spaces. Nearly exponential convergent and wavenumber explicit local approximation errors are derived both at the continuous and fully discrete level. The method can be viewed as an extension of Trefftz methods to Helmholtz equation with heterogeneous coefficients. This is a joint work with Robert Scheichl.