Uniform Asymptotic Theory of Edge Diffraction

Algorithm of Diffraction for Standing Tree based on the Uniform Geometrical Theory of Diffraction

Manuscript received September 11, 2011 * Corresponding author; E-mail: [email protected] Abstract— The diffraction fields and the shadow of standing tree diffraction are solved by using polygons to approximately take the place and approximation as approximate substitutes of for the circle. The algorithm model of ray path tracing is computed by tracing the ray path on standing tree. Considering el...

Diffraction Theory

Uniform Global Asymptotic Stability of Differential Inclusions

Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not ne...

Implementation of the Uniform Theory of Diffraction in the Phased Beam Tracing Method

The phased beam tracing method (PBTM), which introduces the phase information into the geometrical acoustic technique, has a definite advantage in simulating the interference of waves at medium frequencies in an enclosed space. Generally, the diffraction effect cannot be included due to the straight propagation of triangular beams. However, the diffraction should be considered in, particularly,...

Uniform Asymptotic Expansions of Multiple Scattering Iterations

Although every implementation of a recent high frequency multiple scattering solver has displayed a frequency independent operation count, its numerical analysis yet remains as a challenging open problem. This is, in part, due to the absence of detailed information on the uniform asymptotic expansions of multiple scattering iterations. Here we address precisely this issue for a collection of co...