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.

翻译：本文提出约束能量最小化广义多尺度有限元方法（CEM-GMsFEM）来求解异质介质中的亥姆霍兹方程。这一新颖的多尺度方法专门用于克服与污染效应、高对比系数及算子埃尔米特性缺失相关的问题。我们在若干既定假设和分辨率条件下，建立了该方法的inf-sup稳定性并给出了先验误差估计。数值实验验证了理论结果，进一步表明该多尺度技术能有效捕捉相关物理现象。