Fourier-Based Fast Multipole Method for the Helmholtz Equation

Cris Cecka, Eric Darve

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)A79-A103
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Jan 2013
Externally publishedYes


Dive into the research topics of 'Fourier-Based Fast Multipole Method for the Helmholtz Equation'. Together they form a unique fingerprint.

Cite this