Computational multiscale methods for first-order wave equation using mixed CEM-GMsFEM
arXiv:1909.08215 · doi:10.1016/j.jcp.2020.109359
Abstract
In this paper, we consider a pressure-velocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method provides a flexible framework to construct crucial multiscale basis functions for approximating the pressure and velocity. These basis functions are constructed by solving a class of local auxiliary optimization problems over the eigenspaces that contain local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. The first-order convergence of the proposed method is proved and illustrated by several numerical tests.
arXiv comment18 pages, 5 figures, proof of Theorem 4.2 modified
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