Ray flow methods provide efficient tools for modelling wave energy transport in complex systems at high-frequencies. We compare two Petrov-Galerkin discretizations of a phase-space boundary integral model for stationary wave energy densities in two-dimensional domains. The directional dependence is approximated using a finite set of directions oriented into the domain from the boundary. The propagation direction can be preserved across multi-component domains when the directions within the local set for a given region of the boundary are taken as a subset of a global direction set. In this work we compare the use of piecewise constant and piecewise linear test functions, which physically corresponds to the interpolation scheme used when the transport is in a direction not belonging to the finite global set.

翻译：射线流方法为高频复杂系统中波动能量输运的建模提供了高效工具。我们比较了二维区域内静态波动能量密度相空间边界积分模型的两种Petrov-Galerkin离散格式。方向依赖性通过从边界定向进入域内的有限方向集进行近似。当局部方向集（针对边界给定区域）作为全局方向集的子集时，多组分域中的传播方向可以得到保持。本研究比较了分段常数与分段线性检验函数的使用，这两种函数在物理上对应于输运方向不属于有限全局集时的插值方案。