A frequency-dependent p-adaptive technique for spectral methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:446

Article

Xia, Mingtao¹  Shao, Sihong^2,3  Chou, Tom¹ 

[1] UCLA, Dept Math, Los Angeles, CA 90095 USA

[2] Peking Univ, LMAM, Beijing 100871, Peoples R China

[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

关键词: Adaptive spectral method;    Schrodinger equation;    Unbounded domains;    Jacobi polynomial;    Hermite function;    Laguerre function;   

DOI  :  10.1016/j.jcp.2021.110627

来源: Elsevier

【 摘 要 】

When using spectral methods, a consistent method for tuning the expansion order is often required, especially for time-dependent problems in which oscillations emerge in the solution. In this paper, we propose a frequency-dependent p-adaptive technique that adaptively adjusts the expansion order based on a frequency indicator. Using this p-adaptive technique, combined with recently proposed scaling and moving techniques, we are able to devise an adaptive spectral method in unbounded domains that can capture and handle diffusion, advection, and oscillations. As an application, we use this adaptive spectral method to numerically solve Schrodinger's equation in an unbounded domain and successfully capture the solution's oscillatory behavior at infinity. (C) 2021 The Authors. Published by Elsevier Inc.

【 授权许可】

Free