Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator

2017/09/07 by Yangqingxiang Wu, Ludmil Zikatanov, Wu, Yangqingxiang +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1709.02351

openalex publication_date 2017/09/07 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly. We propose solving the related constant coefficient Helmholtz equation with Fast Fourier Transform (FFT) based on carefully designed extensions and restrictions of the equation. The proposed Fourier method, combined with proper eigensolver, results in an efficient and clear approach for computing the Stekloff eigenvalues.

Citations

• An algorithm for the machine calculation of complex Fourier series

Cited by

• The spectrum of the Steklov-Helmholtz operator

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