Fast convolution with free-space Green's functions

Felipe Vico, Leslie Greengard, Miguel Ferrando

Research output: Contribution to journalArticle

Abstract

We introduce a fast algorithm for computing volume potentials – that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Green's function by cutting off the interaction in physical space beyond the domain of interest. This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data. Moreover, the method can be interpreted as employing a Nystrom discretization of the corresponding integral operator, with matrix entries which can be obtained explicitly and rapidly. This is of use in the design of preconditioners or fast direct solvers for a variety of volume integral equations. The method proposed permits the computation of any derivative of the potential, at the cost of an additional FFT.

Original languageEnglish (US)
Pages (from-to)191-203
Number of pages13
JournalJournal of Computational Physics
Volume323
DOIs
StatePublished - Oct 15 2016

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Keywords

  • Convolution
  • FFT
  • Free space
  • Green's function
  • Volume potential

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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