Spectral Element Method and Domain Decomposition for Low-Frequency Subsurface EM Simulation

Abstract

Low-frequency subsurface electromagnetic measurements are important tools for characterizing natural resources and environmental wastes. Rapid simulations of low-frequency subsurface electromagnetic measurements are still a challenge because of the large computational domain and low-frequency breakdown phenomenon. We develop an effective method to simulate these low-frequency subsurface electromagnetic measurements by using the spectral element method together with a domain decomposition method (DDM). A specific mesh has been designed based on the traveling wave nature in the air and the diffusion field nature in the underground space to greatly reduce the number of unknowns. The frequency-domain version of the Riemann solver (upwind flux) is used as an effective transmission condition to simulate the interactions between neighboring subdomains in DDM. Several numerical examples demonstrate the efficiency of the proposed approach in low-frequency subsurface electromagnetics simulations.