An integration scheme for electromagnetic scattering using plane wave edge elements
Advances in Engineering Software
High frequency scattering by convex curvilinear polygons
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Local solutions to high-frequency 2D scattering problems
Journal of Computational Physics
A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions
Journal of Computational Physics
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
Journal of Computational and Applied Mathematics
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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.