Type
ArticleAuthors
Cecka, CrisDarve, Eric
Date
2013-01Permanent link to this record
http://hdl.handle.net/10754/598360
Metadata
Show full item recordAbstract
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.Citation
Cecka C, Darve E (2013) Fourier-Based Fast Multipole Method for the Helmholtz Equation. SIAM Journal on Scientific Computing 35: A79–A103. Available: http://dx.doi.org/10.1137/11085774X.Sponsors
This research was supported by the U.S. Army Research Laboratory, through the Army HighPerformance Computing Research Center, Cooperative Agreement W911NF-07-0027, the StanfordSchool of Engineering, and the King Abdullah University of Science and Technology.ae974a485f413a2113503eed53cd6c53
10.1137/11085774X