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arXiv · 2407.04364

Robust Multiscale Methods for Helmholtz equations in high contrast heterogeneous media

Xingguang Jin·Changqing Ye·Eric T. Chung
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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.

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Xingguang Jin, Changqing Ye, Eric T. Chung. 2024-07-05. Robust Multiscale Methods for Helmholtz equations in high contrast heterogeneous media. https://arxiv.org/abs/2407.04364

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