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A direction preserving discretization for computing phase-space densities

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

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David Chappell

Jonathan J. Crofts

Assistant Professor in Applied Mathematics

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Professor of Applied Mathematics


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.


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.

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
Keywords Applied Mathematics; Computational Mathematics
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