半经典（高频）波传播数值模拟中的平滑Wigner变换
Smoothed Wigner transforms in the numerical simulation of semiclassical (high-frequency) wave propagation
AI总结：
针对半经典波传播数值模拟难题，提出基于平滑Wigner变换的相空间方法，相比传统Wigner变换和原方程全数值解显著提高计算效率。
摘要：
众所周知，半经典（高频）问题中波传播的数值模拟面临巨大挑战。本文提出一种新的相空间方法，利用平滑Wigner变换（SWT）进行半经典波传播的数值模拟。已有大量工作使用Wigner变换（WT）研究各种波传播问题，包括线性、非线性和/或随机波的高频极限。然而，WT在数值格式的制定中存在显著困难。通过半经典线性薛定谔方程的具体实例，发现SWT方法在计算速度上（在明确定义的意义上）显著快于WT以及半经典区域中原始方程的全数值解。通过与精确解和数值解的比较来跟踪数值误差。
英文摘要：
The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for the numerical simulation of semiclassical wave propagation, making use of the smoothed Wigner Transform (SWT), is proposed. There are numerous works which use the Wigner Transform (WT) in the study of a variety of wave propagation problems including high-frequency limits for linear, nonlinear and/or random waves. The WT however is well known to present significant difficulties in the formulation of numerical schemes. Working with concrete examples for the semiclassical linear Schrodinger equation it is seen that the SWT approach is indeed significantly faster (in a well-defined sense) to work with than the WT and than full numerical solutions of the original equation in the semiclassical regime. Comparisons with exact and numerical solutions are used to keep track of numerical errors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
