Work

Spurious-mode-free finite element method for scattering resonances in transmission problems

Year: 2026

Type: preprint

Abstract: Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from spurious modes. In this paper, we propose a spurious-mode-free method for computing scattering resonances in transmission problems. The unbounded domain is truncated using a Dirichlet-to-Neumann (DtN) map. The resonances are formulated as eigenvalues of a holomorphic Fredholm operator function, which is discretized by the finite element method. The spectrum indicator method is then used to compute the eigenvalues of the nonlinear matrix eigenvalue problems. We establish optimal order convergence and present extensive examples that demonstrate the effectiveness of the proposed method. The results are consistent with existing theoretical findings in the literature and offer new insights that may inform further theoretical developments.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.14539

Authors: Gong, Bo, Sun, Jiguang

Institutions: Beijing University of Technology, Michigan Technological University

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: Novel Finite Element Methods for Nonlinear Eigenvalue Problems - A Holomorphic Operator-Valued Function Approach, G985558949

OpenAlex ID: W7154682048

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