Fast directional algorithms for the Helmholtz kernel

Authors:
Björn Engquist;Lexing Ying
Affiliations:
Department of Mathematics, University of Texas, Austin, TX 78712, USA;Department of Mathematics, University of Texas, Austin, TX 78712, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 9
Cited 0

A fast algorithm for particle simulations

Journal of Computational Physics
Sparse approximation for solving integral equations with oscillatory kernels

SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
A fast adaptive multipole algorithm in three dimensions

Journal of Computational Physics
A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications

Journal of Computational Physics
Fast and Efficient Algorithms in Computational Electromagnetics

Fast and Efficient Algorithms in Computational Electromagnetics
An elementary proof of a theorem of Johnson and Lindenstrauss

Random Structures & Algorithms
Dimensionality Reductions That Preserve Volumes and Distance to Affine Spaces, and Their Algorithmic Applications

RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
A wideband fast multipole method for the Helmholtz equation in three dimensions

Journal of Computational Physics
Fast Directional Multilevel Algorithms for Oscillatory Kernels

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	7.29

Visualization

Abstract

This paper presents a new directional multilevel algorithm for solving N-body or N-point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius r 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 O(1/r) and is at a distance which is at least O(r^2) 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 O(NlogN) computational complexity for any given accuracy when the points are sampled from a two-dimensional surface.