SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page B884-B906, January 2021.
Ray flow methods are an efficient tool to estimate vibro-acoustic or electromagnetic energy transport in complex domains at high-frequencies. Here, a Petrov--Galerkin discretization of a phase-space boundary integral equation for transporting wave energy densities on two-dimensional surfaces is proposed. The directional dependence of the energy density is approximated at each point on the boundary in terms of a finite local set of directions propagating into the domain. The direction of propagation can be preserved for transport across multicomponent domains when the directions within the local set are inherited from a global direction set. The range of applicability and computational cost of the method will be explored through a series of numerical experiments, including wave problems from both acoustics and elasticity in both single and multicomponent domains. The domain geometries considered range from both regular and irregular polygons to curved surfaces, including a cast aluminium shock tower from a Range Rover car.

中文翻译：

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用于计算相空间密度的保向离散化

SIAM 科学计算杂志，第 43 卷，第 4 期，第 B884-B906 页，2021 年 1 月。
射线流方法是估计复杂域中高频振动声或电磁能量传输的有效工具。在这里，提出了用于在二维表面上传输波能量密度的相空间边界积分方程的 Petrov--Galerkin 离散化。根据传播到域中的有限局部方向集，在边界上的每个点处近似能量密度的方向依赖性。当本地集中的方向从全局方向集继承时，可以保留传播方向以用于跨多分量域的传输。将通过一系列数值实验探索该方法的适用范围和计算成本，包括单分量和多分量域中声学和弹性的波问题。考虑的域几何形状范围从规则和不规则多边形到曲面，包括来自 Range Rover 汽车的铸铝减震塔。