TY - JOUR
T1 - Direct Solution of Scattering Problems Using Generalized Source Integral Equations
AU - Sharshevsky, Arkadi
AU - Brick, Yaniv
AU - Boag, Amir
N1 - Funding Information: Manuscript received October 7, 2019; revised February 4, 2020; accepted February 6, 2020. Date of publication February 27, 2020; date of current version July 7, 2020. This work was supported in part by the Israel Science Foundation (ISF) under Grant 1081/12 and Grant 677/18. (Corresponding author: Yaniv Brick.) Arkadi Sharshevsky and Amir Boag are with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: arkadish123@gmail.com; boag@eng.tau.ac.il). Publisher Copyright: © 1963-2012 IEEE.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - A class of inherently compressible integral equation formulations for problems of scattering by impenetrable objects, which makes use of generalized directional sources, is presented. The new formulation effectively reduces the problem's dimensionality and, thus, allows for efficient low-rank compression of moment matrices' off-diagonal blocks. When the formulation is used with a hierarchical matrix compression and factorization algorithm, a fast direct solver is obtained. The computational bottlenecks introduced by the proposed generalized formulation, in both the matrix-fill and matrix compression stages, are alleviated by using nonuniform sampling-based techniques. These techniques are described in detail for one choice of generalized sources, which use absorbing equivalent source shields, and can be extended to other shield types. The formulation's properties and limitations are studied and its enhanced compressibility is used for the development of a fast direct solver.
AB - A class of inherently compressible integral equation formulations for problems of scattering by impenetrable objects, which makes use of generalized directional sources, is presented. The new formulation effectively reduces the problem's dimensionality and, thus, allows for efficient low-rank compression of moment matrices' off-diagonal blocks. When the formulation is used with a hierarchical matrix compression and factorization algorithm, a fast direct solver is obtained. The computational bottlenecks introduced by the proposed generalized formulation, in both the matrix-fill and matrix compression stages, are alleviated by using nonuniform sampling-based techniques. These techniques are described in detail for one choice of generalized sources, which use absorbing equivalent source shields, and can be extended to other shield types. The formulation's properties and limitations are studied and its enhanced compressibility is used for the development of a fast direct solver.
KW - Direct solvers
KW - electromagnetic scattering
KW - fast solvers
KW - integral equations
KW - moment method
UR - http://www.scopus.com/inward/record.url?scp=85088021158&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/TAP.2020.2975549
DO - https://doi.org/10.1109/TAP.2020.2975549
M3 - Article
SN - 0018-926X
VL - 68
SP - 5512
EP - 5523
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 7
M1 - 9016355
ER -