A Higher Order Hybrid SIE/FEM/SEM Method for the Flexible Electromagnetic Simulation in Layered Medium

A novel hybrid method is developed for the flexible and accurate electromagnetic simulation of penetrable objects in a layered medium (LM). In this method, the original complex simulation domain is first divided into several subdomains, following the spirit of divide-and-conquer. Each subdomain is then meshed and solved independently, where nonconformal mesh is inevitable. The Riemann type transmission condition is utilized at the interfaces of each subdomain to correctly exchange information so that the solutions of all subdomains converge rapidly to the real solution of the original problem. More specifically, in our method, the surface integral equation (SIE) combined with the LM Green’s functions (LMGFs) is adopted for the boundary subdomain, while the finite-element method (FEM) and the spectral element method (SEM) are employed for all the other interior dielectric subdomains. The SIE with LMGFs truncates the simulation domain tightly within the object itself, which drastically decreases the number of unknowns. The interior subdomains are modeled by either FEM or SEM, depending on the geometry and material property of each subdomain. To further enhance the simulation capability, higher order approaches are adopted for all the subdomain solvers in this hybrid method. Several numerical examples are demonstrated, where a high convergence and accuracy of this method is observed. This paper will serve as an efficient and flexible simulation tool for the applications of geophysical exploration.