  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.
