Direct Solution of Scattering Problems Using Generalized Source Integral Equations

Arkadi Sharshevsky*, Yaniv Brick, Amir Boag

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number9016355
Pages (from-to)5512-5523
Number of pages12
JournalIEEE Transactions on Antennas and Propagation
Issue number7
StatePublished - Jul 2020


FundersFunder number
Israel Science Foundation677/18, 1081/12


    • Direct solvers
    • electromagnetic scattering
    • fast solvers
    • integral equations
    • moment method


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