Resolving the Gibbs phenomenon via a discontinuous basis in a mode solver for open optical systems

DOI10.1016/j.jcp.2020.110004OpenAlexW3031329135MaRDI QIDQ2120022

Yonatan Sivan, Parry Y. Chen

Publication date: 31 March 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.12346

zbMATH Keywords

Gibbs phenomenonexponential convergenceopen systemsmodal expansionstep discontinuitydiscontinuous basis

Mathematics Subject Classification ID

Harmonic analysis in one variable (42Axx) General topics in optics and electromagnetic theory (78Axx) Numerical methods in Fourier analysis (65Txx)

Uses Software

• disproots

Cites Work

• Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
• Reconstruction of piecewise smooth functions from non-uniform grid point data
• On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
• Towards the resolution of the Gibbs phenomena.
• Robust location of optical fiber modes via the argument principle method
• An efficient solver for the generalized normal modes of non-uniform open optical resonators
• Fourier spectral simulations and Gegenbauer reconstructions for electromagnetic waves in the presence of a metal nanoparticle
• On the Gibbs Phenomenon and Its Resolution
• On a high order numerical method for functions with singularities
• A Review of David Gottlieb’s Work on the Resolution of the Gibbs Phenomenon
• A Padé-based algorithm for overcoming the Gibbs phenomenon
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