Publications [#360558] of Jianfeng Lu

Papers Published

1. Lu, J; Murphey, C; Steinerberger, S, Fast Localization of Eigenfunctions via Smoothed Potentials, Journal of Scientific Computing, vol. 90 no. 1 (January, 2022) [doi]
   (last updated on 2024/04/18)

   Abstract:
   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.