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Fast directional algorithms for the Helmholtz kernel
- Source :
-
Journal of Computational & Applied Mathematics . Jul2010, Vol. 234 Issue 6, p1851-1859. 9p. - Publication Year :
- 2010
-
Abstract
- Abstract: This paper presents a new directional multilevel algorithm for solving -body or -point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of and is at a distance which is at least away from the ball. Based on this representation, our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy. Our algorithm is proved to have an optimal computational complexity for any given accuracy when the points are sampled from a two-dimensional surface. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 234
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 50392259
- Full Text :
- https://doi.org/10.1016/j.cam.2009.08.036