کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4643031 | 1341365 | 2007 | 23 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Asymptotically derived boundary elements for the Helmholtz equation in high frequencies Asymptotically derived boundary elements for the Helmholtz equation in high frequencies](/preview/png/4643031.png)
We present an asymptotically derived boundary element method for the Helmholtz equation in exterior domains. 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. This yields a high-order method in which the number of unknowns is virtually independent of the wavenumber k. 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. We show that the matrix A , associated with the discrete problem, has only O(N)O(N) significant entries as k→∞k→∞, where N is the number of basis functions. Hence it can be approximated with a matrix A^ having O(N)O(N) terms, and the relative error between A and A^ rapidly converges to zero as k→∞k→∞. Although the method is applicable to a variety of scatterers, we focus our attention here on scattering from smooth closed convex bodies in two dimensions. Computations on a circular cylinder illustrate our results.
Journal: Journal of Computational and Applied Mathematics - Volume 198, Issue 1, 1 January 2007, Pages 52–74