A high-order tangential basis algorithm for electromagnetic scattering by curved surfaces
Journal of Computational Physics
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
SIAM Journal on Scientific Computing
Numerical Estimation of Coercivity Constants for Boundary Integral Operators in Acoustic Scattering
SIAM Journal on Numerical Analysis
Wavenumber-Explicit $hp$-BEM for High Frequency Scattering
SIAM Journal on Numerical Analysis
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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We propose a new robust method for the computation of scattering of high-frequency acoustic plane waves by smooth convex objects in 2D. We formulate this problem by the direct boundary integral method, using the classical combined potential approach. By exploiting the known asymptotics of the solution, we devise particular expansions, valid in various zones of the boundary, which express the solution of the integral equation as a product of explicit oscillatory functions and more slowly varying unknown amplitudes. The amplitudes are approximated by polynomials (of minimum degree d) in each zone using a Galerkin scheme. We prove that the underlying bilinear form is continuous in L 2, with a continuity constant that grows mildly in the wavenumber k. We also show that the bilinear form is uniformly L 2-coercive, independent of k, for all k sufficiently large. (The latter result depends on rather delicate Fourier analysis and is restricted in 2D to circular domains, but it also applies to spheres in higher dimensions.) Using these results and the asymptotic expansion of the solution, we prove superalgebraic convergence of our numerical method as d → ∞ for fixed k. We also prove that, as k → ∞, d has to increase only very modestly to maintain a fixed error bound (d ∼ k 1/9 is a typical behaviour). Numerical experiments show that the method suffers minimal loss of accuracy as k →∞, for a fixed number of degrees of freedom. Numerical solutions with a relative error of about 10−5 are obtained on domains of size $$\mathcal{O}(1)$$ for k up to 800 using about 60 degrees of freedom.