A direction preserving discretization for computing phase-space densities

Chappell, David; Crofts, Jonathan J.; Richter, Martin; Tanner, Gregor

Abstract

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.

Citation

Chappell, D., Crofts, J. J., Richter, M., & Tanner, G. (2021). A direction preserving discretization for computing phase-space densities. SIAM Journal on Scientific Computing, 43(4), B884-B906. https://doi.org/10.1137/20M1352041

• Journal Article Type: Article
• Acceptance Date: Mar 24, 2021
• Online Publication Date: Jul 13, 2021
• Publication Date: 2021
• Deposit Date: Jan 10, 2022
• Publicly Available Date: Jan 12, 2022
• Journal: SIAM Journal on Scientific Computing
• Print ISSN: 1064-8275
• Electronic ISSN: 1095-7197
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 4
• Pages: B884-B906
• DOI: https://doi.org/10.1137/20M1352041
• Keywords: Applied Mathematics; Computational Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/7219549
• Publisher URL: https://epubs.siam.org/toc/sjoce3/43/4