Coulomb interactions on planar structures: Inverting the square root of the Laplacian

Zydrunas Gimbutas, Leslie Greengard, Michael Minion

Research output: Contribution to journalArticlepeer-review

Abstract

We present an adaptive fast multipole method for inverting the square root of the Laplacian in two dimensions. Solving this problem is the dominant computational cost in many applications arising in electrical engineering, geophysical fluid dynamics, and the study of thin films. It corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity. Our algorithm is direct and assumes only that the source distribution is discretized using an adaptive quad-tree. The amount of work grows linearly with the number of mesh points.

Original languageEnglish (US)
Pages (from-to)2093-2108
Number of pages16
JournalSIAM Journal on Scientific Computing
Volume22
Issue number6
DOIs
StatePublished - 2001

Keywords

  • Integral equation methods
  • Planar circuits
  • Quasi-geostrophic fluid dynamics
  • Thin films

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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