کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4642680 | 1341352 | 2007 | 12 صفحه PDF | دانلود رایگان |
In this paper we present an error analysis for a high-order accurate combined Dirichlet-to-Neumann (DtN) map/finite element (FE) algorithm for solving two-dimensional exterior scattering problems. We advocate the use of an exact DtN (or Steklov–Poincaré) map at an artificial boundary exterior to the scatterer to truncate the unbounded computational region. The advantage of using an exact DtN map is that it provides a transparent condition which does not reflect scattered waves unphysically. Our algorithm allows for the specification of quite general artificial boundaries which are perturbations of a circle. To compute the DtN map on such a geometry we utilize a boundary perturbation method based upon recent theoretical work concerning the analyticity of the DtN map. We also present some preliminary work concerning the preconditioning of the resulting system of linear equations, including numerical experiments.
Journal: Journal of Computational and Applied Mathematics - Volume 204, Issue 2, 15 July 2007, Pages 493–504