Janis Bajars
Improved approximation of phase-space densities on triangulated domains using discrete flow mapping with p-refinement
Bajars, Janis; Chappell, David; Hartmann, Timo; Tanner, Gregor
Authors
David Chappell
Timo Hartmann
GREGOR TANNER GREGOR.TANNER@NOTTINGHAM.AC.UK
Professor of Applied Mathematics
Abstract
We consider the approximation of the phase-space flow of a dynamical system on a triangulated surface using an approach known as Discrete Flow Mapping. Such flows are of interest throughout statistical mechanics, but the focus here is on flows arising from ray tracing approximations of linear wave equations. An orthogonal polynomial basis approximation of the phase-space density is applied in both the position and direction coordinates, in contrast with previous studies where piecewise constant functions have typically been applied for the spatial approximation. In order to improve the tractability of an orthogonal polynomial approximation in both phase-space coordinates, we propose a careful strategy for computing the propagation operator. For the favourable case of a Legendre polynomial basis we show that the integrals in the definition of the propagation operator may be evaluated analytically with respect to position and via a spectrally convergent quadrature rule for the direction coordinate. A generally applicable spectral quadrature scheme for integration with respect to both coordinates is also detailed for completeness. Finally, we provide numerical results that motivate the use of p-refinement in the orthogonal polynomial basis.
Citation
Bajars, J., Chappell, D., Hartmann, T., & Tanner, G. (2017). Improved approximation of phase-space densities on triangulated domains using discrete flow mapping with p-refinement. Journal of Scientific Computing, 72(3), https://doi.org/10.1007/s10915-017-0397-8
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 18, 2017 |
Online Publication Date | Mar 4, 2017 |
Publication Date | Sep 30, 2017 |
Deposit Date | Sep 21, 2017 |
Publicly Available Date | Mar 29, 2024 |
Journal | Journal of Scientific Computing |
Print ISSN | 0885-7474 |
Electronic ISSN | 1573-7691 |
Publisher | Springer Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 72 |
Issue | 3 |
DOI | https://doi.org/10.1007/s10915-017-0397-8 |
Keywords | High frequency wave asymptotics, Ray tracing, Frobenius–Perron operator, Liouville equation, Geometrical optics, Vibro-acoustics |
Public URL | https://nottingham-repository.worktribe.com/output/885506 |
Publisher URL | https://link.springer.com/article/10.1007%2Fs10915-017-0397-8 |
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
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