arXiv subjects

Yaniv Brick

Publications and source records attributed to Yaniv Brick.

3 recordsLinked to original sources

arXiv2026

Well-conditioned Electric Field Surface Integral Equations using Reflective Generalized Sources

This work uses the generalized source approach to develop a class of well-conditioned integral operators that are free of internal resonance, without the need for combined formulations. The Generalized source integral equations (GSIEs) kernels are obtained by augmenting the conventional electric field integral equation (EFIE) kernel with auxiliary contributions to enhance the rank deficiency of the corresponding moment matrix blocks. This paper presents the first investigation of the spectra of GSIE operators for auxiliary kernels produced by internal scattering convex shields. Using closed-form expressions for concentric circular scatterers and shields, it is shown that, with shield parameters that are suitable for enhanced compressibility, the transverse magnetic (TM)- and transverse electric (TE)-GSIE operators are free of internal proper and quasi-resonances. The auxiliary components are shown to be compact perturbations of their EFIE counterparts. Hence these GSIESs inherit their dense-discretization breakdown, which remains curable via Calder\'on-type preconditioning. The mechanisms that govern the high-frequency breakdown are shown to be influenced by the auxiliary component, leading, in some cases, to greater resilience. These observations are shown to remain valid for moment matrices and GSIEs designed with non-circular stencil shields. For both GSIE-dual and Yukawa-kernel preconditioners, the formulations exhibit favorable spectral properties while maintaining their compressibility. This makes the formulations attractive for the design of fast iterative solvers. The results on the two-dimensional shield-based operators provide a foundation for extending the approach to three-dimensional problems and to auxiliary kernels with broader geometric applicability.

math.NA↗

arXiv2026

Spatial Degrees of Freedom and Channel Strength for Antenna Systems

The number of spatial degrees of freedom (NDoF) and channel strength in antenna systems are examined within a geometric framework. Starting from a correlation-operator representation of the channel between transmitter and receiver regions, we analyze the associated eigenspectrum and relate the NDoF to its spectral transition (corner). We compare the spectrum-based effective NDoF and effective rank metrics, clarifying their behavior for both idealized and realistic eigenvalue distributions. In parallel, we develop geometry-based asymptotic estimates in terms of mutual shadow (view) measures and coupling strength. Specifically, we show that while the projected length or area predicts the number of usable modes in two- and three-dimensional settings, the coupling strength determines the average eigenvalue level. Canonical configurations of parallel lines and regions are used to derive closed-form asymptotic expressions for the effective NDoF, revealing significant deviations from the spectral corner in closely spaced configurations. The results illustrate that these are physically grounded. The proposed theory and techniques are computationally efficient and form a toolbox for estimating the modal richness in near-field channels, with implications for array design, inverse problems, and high-capacity communication systems.

eess.SP↗

arXiv2026

Interpreting Moment Matrix Blocks Spectra using Mutual Shadow Area

The mutual shadow area of pairs of surface regions is used for guiding the study of the spectral components and rank of their wave interaction, as captured by the corresponding moment matrix blocks. It is demonstrated that the mutual shadow area provides an asymptotically accurate predictor of the location of the singular value curve knee. This predicted knee index is shown to partition the interacting parts of the range and domain of blocks into two subspaces that can be associated with different wave phenomena: an "aperture" subspace of dimension that scales with the subdomains area (or length in 2-D) and a remainder "diffraction" subspace of dimension that scales much slower with the electrical length, depending on the geometric configuration. For interactions between open surface domains typical for the common hierarchical partitioning in most fast solvers, the latter can be attributed to the domain edges visible by its interacting counterpart. For interactions in 3-D with a small aspect angles between the source and observers, the diffraction subspace dimension is dominant in determining the rank until fairly large electrical lengths are reached. This explains the delayed asymptotic scaling of ranks and impressive fast solver performance observed in recent literature for seemingly arbitrary scatterers with no special geometric characteristics. In the extreme cases of "endfire" reduced dimensionality interactions, where the shadow area vanishes, the diffraction governs also the asymptotic rank, which translates to superior asymptotic solver performance.

math.NA↗