离散流映射：三角曲面上的相空间密度传输
Discrete flow mapping: transport of phase space densities on triangulated surfaces
AI总结：
提出离散流映射方法，用于在三角曲面上高效求解由哈密顿向量场驱动的相空间密度传输方程，并应用于结构动力学中的振动声学响应计算。
摘要：
高频线性波场的能量分布通常通过流或传输方程建模，其射线动力学由相空间中的哈密顿向量场给出。应用出现在水下声学、室内声学、振动声学、地震学、电磁学和量子力学中。基于一般守恒定律的相关流问题被用于天气预报或分子动力学模拟等。这些流方程的解通常是大尺度、复杂且高维的，给数值近似方法带来了巨大挑战。本文提出了一种高效且广泛适用的方法，称为离散流映射，用于在三角曲面上求解此类问题。给出了一个结构动力学应用——确定铸铝汽车车身部件的振动声学响应。
英文摘要：
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented.
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。
