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

## TL;DR

This paper presents a wavelet-based multiscale finite element method for efficiently solving high-frequency Helmholtz problems in perforated domains, demonstrating convergence and effectiveness through numerical tests.

## Contribution

It introduces a novel wavelet-based edge multiscale finite element method tailored for Helmholtz problems in perforated domains, allowing for large wavenumbers and providing proven convergence.

## Key findings

- O(H) convergence under certain conditions
- Effective for high wavenumbers in perforated domains
- Validated by extensive 2D numerical experiments

## 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 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.