Volume 11, Issue 5
On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation

Qinghua Wu

Adv. Appl. Math. Mech., 11 (2019), pp. 1248-1262.

Published online: 2019-06

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  • Abstract

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.

  • Keywords

Oscillatory Hankel kernels, highly oscillatory integrals, Clenshaw-Curtis Filon methods, oscillatory integral equations.

  • AMS Subject Headings

65D32, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-1248, author = {}, title = {On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {1248--1262}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0173}, url = {http://global-sci.org/intro/article_detail/aamm/13209.html} }
TY - JOUR T1 - On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1248 EP - 1262 PY - 2019 DA - 2019/06 SN - 11 DO - http://dor.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 -

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.

Qinghua Wu. (2019). On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation. Advances in Applied Mathematics and Mechanics. 11 (5). 1248-1262. doi:10.4208/aamm.OA-2018-0173
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