A multiresolution method for solving the Poisson equation using high order regularization

Mads Mølholm Hejlesen, Jens Honore Walther

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We present a novel high order multiresolution Poisson solver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poisson solver produces convergence rates that correspond to the regularization order of the derived Green's functions.
Original languageEnglish
JournalJournal of Computational Physics
Volume326
Pages (from-to)188-196
ISSN0021-9991
DOIs
Publication statusPublished - 2016

Keywords

  • Green's function solution
  • Particle–mesh methods
  • Regularization methods
  • The Poisson equation

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