Fast Directional Computation of High Frequency Boundary Integrals via Local FFTs

8 years 6 days ago

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The boundary integral method is an eﬃcient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the boundary. This paper presents a new fast algorithm for this task in two dimensions. This algorithm is built on top of directional low-rank approximations of the scattering kernel and uses oscillatory Chebyshev interpolation and local FFTs to achieve quasi-linear complexity. The algorithm is simple, fast, and kernel-independent. Numerical results are provided to demonstrate the eﬀectiveness of the proposed algorithm. Key words. boundary integral method, scattering, high frequency waves, directional algorithm, low-rank approximation, Chebyshev interpolation, fast Fourier transforms AMS subject classiﬁcations. 65N38, 65R20, 78A45 DOI. 10.1137/140985123

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