An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics

R.A.M. van Gestel; M.J.H. Anthonissen; J.H.M. ten Thije Boonkkamp; W.L. IJzerman

doi:10.1007/978-3-031-20432-6_20

An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics

R.A.M. van Gestel (Corresponding author), M.J.H. Anthonissen, J.H.M. ten Thije Boonkkamp, W.L. IJzerman

Computational Illumination Optics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Liouville’s equation describes light propagation through an optical system. It governs the evolution of an energy distribution on phase space. This distribution is discontinuous across optical interfaces. The discontinuous Galerkin spectral element method is employed to solve Liouville’s equation. At optical interfaces the laws of optics describe non-local boundary conditions for the energy distribution, which leads to a non-trivial coupling of elements at optical interfaces. A method has been developed to deal with these non-local boundary conditions in a way that ensures that the discontinuous Galerkin spectral element method conserves energy. A numerical experiment validates that the method obeys energy conservation. A comparison to the more traditional quasi-Monte Carlo ray tracing is made, showing significant speed-ups in favour of the discontinuous Galerkin spectral element method.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1
Subtitle of host publication	Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021
Editors	Jens M. Melenk, Ilaria Perugia, Joachim Schöberl, Christoph Schwab
Place of Publication	Cham
Publisher	Springer
Pages	323-335
Number of pages	13
ISBN (Electronic)	978-3-031-20432-6
ISBN (Print)	978-3-031-20431-9, 978-3-031-20434-0
DOIs	https://doi.org/10.1007/978-3-031-20432-6_20
Publication status	Published - 29 Nov 2022
Event	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021 - Vienna, Austria Duration: 12 Jul 2021 → 16 Jul 2021

Publication series

Name	Lecture Notes in Computational Science and Engineering (LNCSE)
Volume	137
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021
Country/Territory	Austria
City	Vienna
Period	12/07/21 → 16/07/21

Funding

This work is part of the research programme NWO-TTW Perspectief with project number P15-36, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.1007/978-3-031-20432-6_20

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van Gestel, R. A. M., Anthonissen, M. J. H., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2022). An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics. In J. M. Melenk, I. Perugia, J. Schöberl, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1: Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021 (pp. 323-335). (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 137). Springer. https://doi.org/10.1007/978-3-031-20432-6_20

van Gestel, R.A.M. ; Anthonissen, M.J.H. ; ten Thije Boonkkamp, J.H.M. et al. / An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1: Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021. editor / Jens M. Melenk ; Ilaria Perugia ; Joachim Schöberl ; Christoph Schwab. Cham : Springer, 2022. pp. 323-335 (Lecture Notes in Computational Science and Engineering (LNCSE)).

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abstract = "Liouville{\textquoteright}s equation describes light propagation through an optical system. It governs the evolution of an energy distribution on phase space. This distribution is discontinuous across optical interfaces. The discontinuous Galerkin spectral element method is employed to solve Liouville{\textquoteright}s equation. At optical interfaces the laws of optics describe non-local boundary conditions for the energy distribution, which leads to a non-trivial coupling of elements at optical interfaces. A method has been developed to deal with these non-local boundary conditions in a way that ensures that the discontinuous Galerkin spectral element method conserves energy. A numerical experiment validates that the method obeys energy conservation. A comparison to the more traditional quasi-Monte Carlo ray tracing is made, showing significant speed-ups in favour of the discontinuous Galerkin spectral element method.",

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van Gestel, RAM, Anthonissen, MJH , ten Thije Boonkkamp, JHM & IJzerman, WL 2022, An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics. in JM Melenk, I Perugia, J Schöberl & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1: Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021. Lecture Notes in Computational Science and Engineering (LNCSE), vol. 137, Springer, Cham, pp. 323-335, 13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021, Vienna, Austria, 12/07/21. https://doi.org/10.1007/978-3-031-20432-6_20

An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics. / van Gestel, R.A.M. (Corresponding author); Anthonissen, M.J.H.; ten Thije Boonkkamp, J.H.M. et al.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1: Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021. ed. / Jens M. Melenk; Ilaria Perugia; Joachim Schöberl; Christoph Schwab. Cham: Springer, 2022. p. 323-335 (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 137).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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van Gestel RAM, Anthonissen MJH , ten Thije Boonkkamp JHM , IJzerman WL. An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics. In Melenk JM, Perugia I, Schöberl J, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1: Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021. Cham: Springer. 2022. p. 323-335. (Lecture Notes in Computational Science and Engineering (LNCSE)). doi: 10.1007/978-3-031-20432-6_20

An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics

Abstract

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