Domain decomposition based on the spectral element method for frequency-domain computational elastodynamics

We propose a domain decomposition method based on the spectral element method (DDM-SEM) for elastic wave computation in frequency domain. It combines the high accuracy of the spectral element method and the high degree of parallelism of a domain decomposition technique, which makes this method suitable for accurate and efficient simulations of large scale problems in elastodynamics. In the DDM-SEM, the original large-scale problem is divided into a number of well designed subdomains. We use the spectral element method independently for each subdomain, and the neighboring subdomains are connected by a frequency-domain version of Riemann transmission condition (RTC) for elastic waves. For the proposed method, we can employ the non-conforming meshes and different interpolation orders in different subdomains to maximize the efficiency. By separating the internal and boundary unknowns of each subdomain, an efficient and naturally parallelizable block LDU direct solver is developed to solve the final system matrix. Numerical experiments verify its accuracy and efficiency, and show that the proposed DDM-SEM can be a promising numerical tool for accurately and effectively solving large and multi-scale problems of elastic waves. It is potentially valuable for the frequency domain seismic inversion where multiple source illuminations are required.