Abstract:We present a Fourier--Galerkin asymptotic framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we apply a Fourier--Galerkin discretization to derive an explicit finite-dimensional effective matrix whose kernel characterizes the resonant frequencies. In the subwavelength regime, we obtain asymptotic expansions of this matrix in terms of $\omega$ and the material contrast, identifying the leading-order operators and their kernel structure.
This reduction transforms the resonance problem into a low-dimensional nonlinear eigenvalue problem, avoiding large-scale discretizations and global root-search procedures. The entries of the effective matrix are explicitly computable and admit fast evaluation using FFT-based quadrature. The resulting approach provides an efficient and robust computational framework for resonances in general smooth geometries.
From: Jinghao Cao [view email]
[v1]
Fri, 22 May 2026 05:50:11 UTC (1,318 KB)
[v2]
Wed, 3 Jun 2026 19:53:01 UTC (1,324 KB)
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