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Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

Negi, YK and Balakrishnan, N and Rao, SM (2021) Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers. In: Applied Computational Electromagnetics Society Journal, 36 (10). pp. 1301-1311.

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Official URL: https://doi.org/10.13052/2021.ACES.J.361006


This paper presents a new fast power series solution method to solve the Hierarchal Method of Moment (MoM) matrix for a large complex, perfectly electric conducting (PEC) 3D structures. The proposed power series solution converges in just two (2) iterations which is faster than the conventional fast solver-based iterative solution. The method is purely algebraic in nature and, as such applicable to existing conventional methods. The method uses regular fast solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast Multipole Method Algorithm (MLFMA). In the proposed method, we use the scaling of the symmetric near-field matrix to develop a diagonally dominant overall matrix to enable a power series solution. Left and right block scaling coefficients are required for scaling near-field blocks to diagonal blocks using Schur's complement method. However, only the right-hand scaling coefficients are computed for symmetric near-field matrix leading to saving of computation time and memory. Due to symmetric property, the left side-block scaling coefficients are just the transpose of the right-scaling blocks. Next, the near-field blocks are replaced by scaled near-field diagonal blocks. Now the scaled near-field blocks in combination with far-field and scaling coefficients are subjected to power series solution terminating after only two terms. As all the operations are performed on the near-field blocks, the complexity of scaling coefficient computation is retained as O(N). The power series solution only involves the matrix-vector product of the far-field, scaling coefficients blocks, and inverse of scaled near-field blocks. Hence, the solution cost remains O(NlogN). Several numerical results are presented to validate the efficiency and robustness of the proposed numerical method. © ACES

Item Type: Journal Article
Publication: Applied Computational Electromagnetics Society Journal
Publisher: Applied Computational Electromagnetics Society (ACES)
Additional Information: The copyright for this article belongs to Applied Computational Electromagnetics Society (ACES)
Keywords: Electric conductance; Integral equations; Inverse problems; Iterative methods; Matrix algebra; Numerical methods, Adaptive cross approximation; Hierarchal matrix; matrix; Method of moment; Near fields; Power series; Power series solutions; Scaling coefficients; Scalings, Method of moments
Department/Centre: Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Date Deposited: 17 May 2022 09:00
Last Modified: 17 May 2022 09:00
URI: https://eprints.iisc.ac.in/id/eprint/71699

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