Robust Multiscale Methods for Helmholtz equations in high contrast heterogeneous media
Numerical Analysis
2024-07-09 v2 Numerical Analysis
Abstract
In this paper, we provide the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to solve Helmholtz equations in heterogeneous medium. This novel multiscale method is specifically designed to overcome problems related to pollution effect, high-contrast coefficients, and the loss of hermiticity of operators. We establish the inf-sup stability and give an a priori error estimate for this method under a number of established assumptions and resolution conditions. The theoretical results are validated by a set of numerical tests, which further show that the multiscale technique can effectively capture pertinent physical phenomena.
Cite
@article{arxiv.2407.04364,
title = {Robust Multiscale Methods for Helmholtz equations in high contrast heterogeneous media},
author = {Xingguang Jin and Changqing Ye and Eric T. Chung},
journal= {arXiv preprint arXiv:2407.04364},
year = {2024}
}