A Generalized Source Integral Equation for Homogeneous Penetrable Scatterers
Abstract
The generalized source integral equation (GSIE)approach is extended to enhance the compressibility of moment matrices for essentially-convex homogeneous penetrable scatterers. In the proposed indirect surface integral equation (SIE) formulation, the scattered field representations use a single distribution of generalized sources that radiate only weakly into the scatterer. A separate distribution of conventional sources is used for representing the interior fields. The wave interactions between surface subdomains via the generalized kernel are of a reduced effective dimensionality. The corresponding exterior integral operator moment matrix blocks exhibit enhanced rank deficiency. For lossy scatterers, this secures the low-rank (LR) compressibility of hierarchical matrix structures for the full system. For scatterers in a much slower background medium, significant savings with very delayed asymptotic scaling of the costs can be achieved. The GSIE is formulated for the transverse magnetic (TM) scattering problem. It is validated for representative examples and its superior compressibility is demonstrated.
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BibTeX
@misc{diner2026generalized,
title = {{A Generalized Source Integral Equation for Homogeneous Penetrable Scatterers}},
author = {Boris Diner and Yaniv Brick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02223},
eprint = {2610.02223},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02223},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Generalized Source Integral Equation for Homogeneous Penetrable Scatterers
AU - Boris Diner
AU - Yaniv Brick
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02223
UR - https://arxiv.org/abs/2610.02223
AB - The generalized source integral equation (GSIE)approach is extended to enhance the compressibility of moment matrices for essentially-convex homogeneous penetrable scatterers. In the proposed indirect surface integral equation (SIE) formulation, the scattered field representations use a single distribution of generalized sources that radiate only weakly into the scatterer. A separate distribution of conventional sources is used for representing the interior fields. The wave interactions between surface subdomains via the generalized kernel are of a reduced effective dimensionality. The corresponding exterior integral operator moment matrix blocks exhibit enhanced rank deficiency. For lossy scatterers, this secures the low-rank (LR) compressibility of hierarchical matrix structures for the full system. For scatterers in a much slower background medium, significant savings with very delayed asymptotic scaling of the costs can be achieved. The GSIE is formulated for the transverse magnetic (TM) scattering problem. It is validated for representative examples and its superior compressibility is demonstrated.
ER -