Reza Gholami, Jamiu Babatunde Mojolagbe, Anton Menshov, Farhad Sheikh Hosseini Lori, and Vladimir Okhmatovski
R. Gholami, J. B. Mojolagbe, A. Menshov, F. Sheikh Hosseini Lori, and V. Okhmatovski, “H-matrix arithmetic for fast direct and iterative method of moment solution of surface-volume-surface EFIE for 3-D radiation problems,” Progress Electromagn. Research B, vol. 82, pp. 189–210, Dec. 2018.
Publication year: 2018

Full text of this paper is freely available at Progress In Electromagnetics Research website.

Abstract

Hierarchical (H-) matrix based fast direct and iterative algorithms are presented for acceleration of the Method of Moment (MoM) solution of the Surface-Volume-Surface Electric Field
Integral Equation (SVS-EFIE) formulated for scattering and radiation problems on homogeneous dielectric objects. As the SVS-EFIE features the product of the integral operator mapping the tangential equivalent electric current on the surface of the scatterer to the volume polarization current and the integral operator mapping the volume polarization current to the tangential component of the scattered electric field, its MoM discretization produces the product of non-square matrices. Formation of the non-square H-matrices for the MoM discretized integral operators is described. The algorithms for arithmetics pertinent to the product of the non-square H-matrices are explained. The memory and CPU time complexity scaling of the required H-matrix operations are analyzed in details and verified numerically. The numerical validation of the proposed algorithm is provided for both the low-loss dielectric objects as well as for the high-loss biological tissues found in the bioelectromagnetics applications. The numerical experiments demonstrate a significant reduction of memory usage and a
considerable speedup for CPU time compared to na¨ıve MoM, thus, enabling solution of the large-scale scattering and radiation problems with the SVS-EFIE.