Domain decomposition for 3D electromagnetic modeling

Abstract

Using the staggered grid full domain 3D modeling schemes of various accuracies have been developed. This study focuses on the second order finite difference method with the 13-point rule for meshes extending into the air. Tests with Krylov space iterative solvers indicate that the restarted Bi-CG Stablised method offers the best convergence for our problems. Because the air and the conductive earth have distinctive physical properties which greatly broaden the spectra of the whole matrix system, the whole mesh with both domains in one system either converges very slowly or fails to converge completely. However, the matrix systems for each domain have much smaller condition numbers. To overcome instability caused by the inclusion of the air in the mesh a domain decomposition method are experimented. Tests show that the adaptive iteration amongst the subdomains converges exponentially, which implies that large models can be solved by using the domain decomposition method.