Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
This work addresses the computational bottleneck of solving eigenvalue problems for the Stekloff operator, which is relevant for applications in acoustics and wave propagation, but the improvement appears incremental.
The paper introduces a Fourier-based method for efficiently computing Stekloff eigenvalues of the Helmholtz equation, using FFT with designed extensions and restrictions. The method is shown to be efficient and clear, but no concrete numerical results are provided.
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.