On Direction Preserving Discretizations for Computing Phase-Space Densities

TL;DR

This paper compares two Petrov-Galerkin discretizations for phase-space boundary integral models of wave energy densities, focusing on how well they preserve directional information across complex domains.

Contribution

It introduces and compares piecewise constant and linear test functions for discretizing wave energy transport, highlighting their impact on direction preservation.

Findings

Piecewise linear functions better preserve directionality.

Discretization choice affects accuracy of wave energy modeling.

Method improves modeling in multi-component domains.

Abstract

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.