TY - JOUR

T1 - Direct Solution of Scattering Problems Using Generalized Source Integral Equations

AU - Sharshevsky, Arkadi

AU - Brick, Yaniv

AU - Boag, Amir

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2020/7

Y1 - 2020/7

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 - 10.1109/TAP.2020.2975549

DO - 10.1109/TAP.2020.2975549

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AN - SCOPUS:85088021158

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 -