On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation (Advances in Applied Mathematics and Mechanics, 2019)
We compare the diagonal form fast multipole method (FMM) with the traditional boundary element method (BEM) for a boundary integral equation (BIE) with oscillatory Hankel kernels which arising in using hybrid numerical-asymptotic boundary integral method to the two-dimensional (2D) scattering of a time-harmonic acoustic incident plane wave. The diagonal form FMM is a very efficient and popular algorithm for the rapid solution of boundary value problems. However, we show that the efficiency of the diagonal form FMM is greatly reduced for this kind of BIE. Numerical examples are given to confirm the proposed results.