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Spectral/Spectral Element Method for the Transmission Eigenvalue Problem in Complex Geometric Configurations
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DOI：10.1007/s10915-026-03419-0.png)
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Abstract
En 中文
In this paper, we introduce a spectral/spectral element method based on domain mapping to solve the transmission eigenvalue problem on a class of complex geometries. Initially, for configurations that contain sector-shaped regions, we employ a domain mapping technique to transform the original problem into a standard two-dimensional fourth-order coupled system with singular variable coefficients on a rectangular domain. Subsequently, we derive a crucial and fundamental pole condition, introduce a class of non-uniformly weighted Sobolev spaces alongside their corresponding approximation spaces, and establish a Legendre spectral approximation for the mapped equation, furnishing theoretical error estimates for the numerical eigenvalues and their associated eigenfunctions. Moreover, for configurations incorporating regular polygonal and L-shaped domains, we propose a spectral element method grounded in a second-order mixed formulation, and substantiate the algorithm’s effectiveness and spectral accuracy through extensive numerical examples.
Keywords:
Transmission eigenvalue problem
Spectral/ spectral element method
Error analysis
Complex geometric configurations
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3.3
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652
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9.6K
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