loading page

Advanced three-dimensional electromagnetic modeling using a nested integral equation approach
  • Chaojian Chen,
  • Mikhail Kruglyakov,
  • Alexey Kuvshinov
Chaojian Chen
ETH Zurich

Corresponding Author:[email protected]

Author Profile
Mikhail Kruglyakov
ETH Zürich
Author Profile
Alexey Kuvshinov
ETH Zürich
Author Profile


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.