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Title of article :
A collocation method for high-frequency scattering by convex polygons
Author/Authors :
Arden، نويسنده , , S. and Chandler-Wilde، نويسنده , , S.N. and Langdon، نويسنده , , S.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2007
Pages :
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Abstract :
We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.
Keywords :
collocation method , High-frequency scattering , Oscillatory integrals
Journal title :
Journal of Computational and Applied Mathematics
Serial Year :
Link To Document :