TY - JOUR
T1 - On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation
AU - Wu , Qinghua
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1248
EP - 1262
PY - 2019
DA - 2019/06
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0173
UR - https://global-sci.org/intro/article_detail/aamm/13209.html
KW - Oscillatory Hankel kernels, highly oscillatory integrals, Clenshaw-Curtis  Filon methods, oscillatory integral equations.
AB - <p style="text-align: justify;">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.</p>