High-frequency asymptotic acceleration of the fast multipole method
Article first published online: 7 DEC 2012
Copyright 1996 by the American Geophysical Union.
Volume 31, Issue 5, pages 1199–1206, September-October 1996
How to Cite
1996), High-frequency asymptotic acceleration of the fast multipole method, Radio Sci., 31(5), 1199–1206, doi:10.1029/96RS01785., and (
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 11 JUN 1996
- Manuscript Received: 17 AUG 1995
The plane wave translation operator of the fast multipole method (FMM) is evaluated asymptotically in the high-frequency limit. This operator relates the plane wave components of a source region to a plane wave expansion for the radiated fields over a region away from the source. The asymptotic evaluation exploits the source-to-receiver directivity of the operator, leading to terms analogous to the geometrical optics (GO) and diffracted fields in the uniform theory of diffraction. Most importantly, the GO term identifies a “lit” region which may be used to define a windowing function for filtering out weak plane wave translations in the “shadow” region. The reduction in plane waves lowers the operational count of the FMM from O(N3/2) to O(N4/3) without increasing the complexity of the implementation.