Computational high frequency wave diffraction by a corner via the Liouville equation and geometric theory of diffraction
type: Item
instance of: scholarly article
title: Computational high frequency wave diffraction by a corner via the Liouville equation and geometric theory of diffraction
zbMATH Open document ID: 1217.78033
author: Dongsheng Yin
author: Shi Jin
published in: Kinetic and Related Models
publication date: 2011-03-23T00:00:00Z
review text: This paper deals with a numerical scheme to approximate the high frequency wave equation in two-dimension. In the first part of the paper under review there are reviewed geometric optics approximations by the Wigner transform for the wave equation. Next, the authors present the behavior of waves at a corner based on the geometric theory of diffraction, and provide the conditions that account for reflections at the boundary of the corner and diffractions at the vertex of the corner. These conditions are built into the numerical flux in the two space dimension. There are also studied the positivity and \(l^\infty\) stability of the numerical scheme. Numerical examples are given in the final section of this paper in order to validate the model and to verify the accuracy of the scheme against the full simulation based on the original wave equation.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 78M20
zbMATH DE Number: 5869607
zbMATH Keywords: geometrical theory of diffraction
zbMATH Keywords: Liouville equation
zbMATH Keywords: high frequency wave
MaRDI profile type: Publication
full work available at URL: krm.2011.4.295
OpenAlex ID: W2139350823
DOI: 10.3934/KRM.2011.4.295
description: scientific article; zbMATH DE number 5869607