An Asymptotically Derived Boundary Element Method for the Helmholtz Equation
Abstract
We present an asymptotically derived boundary element method for the Helmholtz equation in exterior domains, in which the basis functions are asymptotically derived. Each basis function is the product of a smooth amplitude and an oscillatory phase factor, like the asymptotic solution. The phase factor is determined a-priori by using arguments from geometrical optics and the geometrical theory of diffraction, while the smooth amplitude is represented by high order splines. Our approach accounts for all the components of the scattered field namely the reflected, shadow forming and diffracted fields, and we demonstrate that it is substantially more accurate than an approach which accounts for the reflected field only. Two types of diffracted basis functions are presented: the first accounts for the dominant oscillatory behavior in the shadow region while the second also accounts for the decay of the amplitude there. Although the method is applicable to a variety of scatterers, we focus our attention here on scattering from smooth convex bodies in two dimensions. Our computations with a conducting circular cylinder demonstrate that the number of unknowns necessary to achieve a given accuracy with this new basis is virtually independent of the wave-number.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 24, 2004
- Accession Number
- ADA438899
Entities
People
- Eldar Giladi
- Joseph B. Keller
Organizations
- Rensselaer Polytechnic Institute