Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators
Spectral Theory
2024-11-26 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the convergence of two of the most widely used and intuitive approaches for computing the spectra of differential operators with quasiperiodic coefficients: the supercell method and the superspace method. In both cases, Floquet-Bloch theory for periodic operators can be used to compute approximations to the spectrum. We illustrate our results with examples of Schr\"odinger and Helmholtz operators.
Keywords
Cite
@article{arxiv.2411.15906,
title = {Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators},
author = {Bryn Davies and Clemens Thalhammer},
journal= {arXiv preprint arXiv:2411.15906},
year = {2024}
}