Advanced three-dimensional electromagnetic modeling using a nested
integral equation approach
Most of the existing three-dimensional (3-D) electromagnetic (EM)
modeling solvers based on the integral equation (IE) method exploit fast
Fourier transform (FFT) to accelerate the matrix-vector multiplications.
This in turn requires a laterally-uniform discretization of the modeling
domain. However, there is often a need for multi-scale modeling and
inversion, for instance, to properly account for the effects of
non-uniform distant structures, and at the same time, to accurately
model the effects from local anomalies. In such scenarios, the usage of
laterally-uniform grids leads to excessive computational loads, both in
terms of memory and time. To alleviate this problem, we developed an
efficient 3-D EM modeling tool based on a multi-nested IE approach.
Within this approach the IE modeling is first performed at a large
domain and on a (laterally-uniform) coarse grid, and then the results
are refined in the region of interest by performing modeling at a
smaller domain and on a (laterally-uniform) denser grid. At the latter
stage, the modeling results obtained at the previous stage are
exploited. The lateral uniformity of the grids at each stage allows us
to keep using the FFT, and thus attain the remarkable performance of the
developed tool. An important novelty of the paper is a development of a
“rim domain” concept which further improves the efficiency of the
multi-nested IE approach.