<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Mingtao Xia</style></author><author><style face="normal" font="default" size="100%">Sihong Shao</style></author><author><style face="normal" font="default" size="100%">Tom Chou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A frequency-dependent p-adaptive technique for spectral methods</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Computational Physics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.jcp.2021.110627</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">446</style></volume><pages><style face="normal" font="default" size="100%">110627</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">


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 Schrödinger’s equation in an unbounded domain and successfully capture the solution’s oscillatory behavior at infinity. 


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