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H -Matrix Arithmetic for Fast Direct and Iterative Method of Moment Solution of Surface-Volume-Surface EFIE for 3-D Radiation Problems

By Reza Gholami, Jamiu Mojolagbe, Anton Menshov, Farhad Sheikh Hosseini Lori, and Vladimir I. Okhmatovski
Progress In Electromagnetics Research B, Vol. 82, 189-210, 2018


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 lowloss dielectric objects as well as for the high-loss biological tissues found in the bioelectromagnetics applications. The numerical experiments demonstrate a signi cant reduction of memory usage and a considerable speedup for CPU time compared to nave MoM, thus, enabling solution of the large-scale scattering and radiation problems with the SVS-EFIE.


Reza Gholami, Jamiu Mojolagbe, Anton Menshov, Farhad Sheikh Hosseini Lori, and Vladimir I. Okhmatovski, "H -Matrix Arithmetic for Fast Direct and Iterative Method of Moment Solution of Surface-Volume-Surface EFIE for 3-D Radiation Problems," Progress In Electromagnetics Research B, Vol. 82, 189-210, 2018.


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