On the Quasi-Random Choice Method for the Liouville Equation of Geometrical Optics with Discontinuous Wave Speed
Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 6 : pp. 573–591
Abstract
We study the quasi-random choice method (QRCM) for the Liouville equation of geometrical optics with discontinuous local wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discontinuities, and measure-valued solutions. The so-called QRCM is a random choice method based on quasi-random sampling (a deterministic alternative to random sampling). The method not only is viscosity-free but also provides faster convergence rate. Therefore, it is appealing for the problem under study which is indeed a Hamiltonian flow. Our analysis and computational results show that the QRCM 1) is almost first-order accurate even with the aforementioned discontinuities; 2) gives sharp resolutions for all discontinuities encountered in the problem; and 3) for measure-valued solutions, does not need the level set decomposition for finite difference/volume methods with numerical viscosities.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1309-m3592
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 6 : pp. 573–591
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Liouville equation High frequency wave Interface Measure-valued solution Random choice method Quasi-random sequence.