Fast Directional Computation of High Frequency Boundary Integrals via Local FFTs

Abstract: 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.