An efficient high-order multiscale finite element method for frequency-domain elastic wave modeling

Solving the frequency-domain elastic wave equation in highly heterogeneous and complex media is computationally challenging. Conventional methods for solving the elastic wave Helmholtz equation usually lead to a large-dimensional linear system that is difficult to solve without specialized and sophisticated techniques. Based on the multiscale finite element theory, we develop a novel method to solve the frequency-domain elastic wave equation in complex media. The key feature of our method is employing high-order multiscale basis functions defined by solving local linear problems to achieve model reduction, which eventually leads to a linear system with significantly reduced dimensions. Solving this reduced linear system therefore results in obvious computational time reduction. We use three 2D examples to verify the accuracy and efficiency of our high-order multiscale finite element method for solving the Helmholtz equation in complex isotropic and anisotropic elastic media. The results show that our new method can approximate the fine-scale reference solution on the coarse mesh with high accuracy and significantly reduced computational time at the linear system solving stage.