论文标题
用于光谱方法的频率依赖$ P $ - 适应技术
A frequency-dependent $p$-adaptive technique for spectral methods
论文作者
论文摘要
当使用光谱方法时，出现一个问题是如何确定扩展顺序，尤其是对于时间依赖的问题，其中新兴振荡可能需要调整扩展顺序。在本文中，我们提出了一种频率依赖的$ P $自适应技术，该技术根据频率指示器适应性地调整了扩展顺序。使用这种$ p $ - 自适应技术，结合最近提出的缩放和移动技术，我们能够在无界域中设计一种自适应光谱方法，可以捕获和处理扩散，对流和振荡。作为应用程序，我们使用这种自适应光谱方法在整个域中在数值上求解Schrödinger方程，并成功捕获了无穷大的溶液的振荡行为。
When using spectral methods, a question arises as how to determine the expansion order, especially for time-dependent problems in which emerging oscillations may require adjusting the expansion order. 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 the Schrödinger equation in the whole domain and successfully capture the solution's oscillatory behavior at infinity.
