NDLI: A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Huybrechs, Daan Vandewalle, Stefan
Copyright Year	2007
Abstract	We consider two-dimensional scattering problems, formulated as an integral equation defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency scattering problems necessitates a large number of unknowns in classical boundary element methods. In addition, the corresponding discretization matrix of the integral equation is dense. We formulate a boundary element method with basis functions that incorporate the asymptotic behavior of the solution at high frequencies. The method exhibits the effectiveness of asymptotic methods at high frequencies with only few unknowns, but retains accuracy for lower frequencies. New in our approach is that we combine this hybrid method with very effective quadrature rules for oscillatory integrals. As a result, we obtain a sparse discretization matrix for the oscillatory problem. Moreover, numerical experiments indicate that the accuracy of the solution actually increases with increasing frequency. The sparse discretization applies to problems where the phase of the solution can be predicted a priori, for example in the case of smooth and convex scatterers.
Starting Page	2305
Ending Page	2328
Page Count	24
File Format	PDF
ISSN	10648275
DOI	10.1137/060651525
e-ISSN	10957197
Issue Number	6
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-10-05
Access Restriction	Subscribed
Subject Keyword	integral equations Numerical integration high-frequency scattering oscillatory integrals steepest descent Asymptotic approximations, asymptotic expansions Fredholm integral equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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