Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains

Shubin Fu (1) , Guanglian Li (2) , Richard Craster (3, 2) , Sebastien Guenneau (4, 3)

1 Department of mathematics, Chinese University of Hong Kong
2 Department of Mathematics [Imperial College London]
3 Abraham de Moivre
4 EPSILON - EPSILON

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 in [14]. For a regular coarse mesh with mesh size H, we establish O(H) convergence of this algorithm under the resolution assumption, and with the level parameter being sufficiently large. The performance of the algorithm is demonstrated by extensive 2-dimensional numerical tests including those motivated by photonic crystals.

Domaines: Optique [physics.optics]

Shubin Fu, Guanglian Li, Richard Craster, Sebastien Guenneau. Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains. 2020. ⟨hal-03091949⟩