Commun. Comput. Phys.,
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Volume 4.


Computation of High Frequency Wave Diffraction by a Half Plane via the Liouville Equation and Geometric Theory of Diffraction

Shi Jin 1, Dongsheng Yin 2*

1 Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.

Received 2 April 2008; Accepted (in revised version) 17 July 2008
Available online 31 July 2008

Abstract

We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction (GTD) to simulate the high frequency linear waves diffracted by a half plane. We first introduce a condition, based on the GTD theory, at the vertex of the half plane to account for the diffractions, and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville equation. Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.

AMS subject classifications: 35L05, 65M06, 78A05, 78A45

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Key words: High frequency waves, Liouville equation, geometric theory of diffraction, geometric optics.

*Corresponding author.
Email: jin@math.wisc.edu (S. Jin), dyin@math.tsinghua.edu.cn (D. Yin)
 

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