Wavelet-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains
Shubin Fu, Guanglian Li, Richard V. Craster, Sébastien R. L. Guenneau · Multiscale Modeling and Simulation · 2021
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 as proposed recently in [S. Fu, E. Chung, and G. Li, J. Comput. Phys., 396 (2019), pp. 228--242]. For a regular coarse mesh with mesh size $H$, we establish $\mathcal{O}(H)$ convergence of this algorithm under the resolution assumption 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.