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Fast Localization of Eigenfunctions via Smoothed Potentials

Publication ,  Journal Article
Lu, J; Murphey, C; Steinerberger, S
Published in: Journal of Scientific Computing
January 1, 2022

We study the problem of predicting highly localized low-lying eigenfunctions (- Δ + V) ϕ= λϕ in bounded domains Ω ⊂ Rd for rapidly varying potentials V. Filoche and Mayboroda introduced the function 1/u, where (- Δ + V) u= 1 , as a suitable regularization of V from whose minima one can predict the location of eigenfunctions with high accuracy. We proposed a fast method that produces a landscapes that is exceedingly similar, can be used for the same purposes and can be computed very efficiently: the computation time on an n× n grid, for example, is merely O(n2log n) , the cost of two FFTs.

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Published In

Journal of Scientific Computing

DOI

EISSN

1573-7691

ISSN

0885-7474

Publication Date

January 1, 2022

Volume

90

Issue

1

Related Subject Headings

  • Applied Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Lu, J., Murphey, C., & Steinerberger, S. (2022). Fast Localization of Eigenfunctions via Smoothed Potentials. Journal of Scientific Computing, 90(1). https://doi.org/10.1007/s10915-021-01682-x
Lu, J., C. Murphey, and S. Steinerberger. “Fast Localization of Eigenfunctions via Smoothed Potentials.” Journal of Scientific Computing 90, no. 1 (January 1, 2022). https://doi.org/10.1007/s10915-021-01682-x.
Lu J, Murphey C, Steinerberger S. Fast Localization of Eigenfunctions via Smoothed Potentials. Journal of Scientific Computing. 2022 Jan 1;90(1).
Lu, J., et al. “Fast Localization of Eigenfunctions via Smoothed Potentials.” Journal of Scientific Computing, vol. 90, no. 1, Jan. 2022. Scopus, doi:10.1007/s10915-021-01682-x.
Lu J, Murphey C, Steinerberger S. Fast Localization of Eigenfunctions via Smoothed Potentials. Journal of Scientific Computing. 2022 Jan 1;90(1).
Journal cover image

Published In

Journal of Scientific Computing

DOI

EISSN

1573-7691

ISSN

0885-7474

Publication Date

January 1, 2022

Volume

90

Issue

1

Related Subject Headings

  • Applied Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics