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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-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 languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021
EditorsJens M. Melenk, Joachim Schöberl, Ilaria Perugia, Christoph Schwab
PublisherSpringer
Pages323-335
Number of pages13
ISBN (Print)9783031204319
DOIs
Publication statusPublished - 2023
Event13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021 - Vienna, Austria
Duration: 12 Jul 202116 Jul 2021

Publication series

NameLecture Notes in Computational Science and Engineering
Volume137
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021
Country/TerritoryAustria
CityVienna
Period12/07/2116/07/21

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Fingerprint

Dive into the research topics of 'An Energy-Preserving High Order Method for Liouville’s Equation of Geometrical Optics'. Together they form a unique fingerprint.

Cite this