Computational & Applied Math Seminar

Abstract

We introduce a new efficient algorithm for Helmholtz problems in perforated domains with the design of the scheme allowing for possibly large wavenumbers. Our method is based upon the Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) as proposed recently. For a regular coarse mesh with mesh size H, we establish O(H) quasi-optimal convergence of this algorithm under the normal resolution assumption, and with the level parameter being properly chosen that depends on the wavenumber on logrithmically. The performance of the algorithm is demonstrated by extensive numerical tests including those motivated by photonic crystals.