Non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions

Mads Mølholm Hejlesen, Grégoire Winckelmans, Jens Honore Walther*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

In this paper, we derive the non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions using a spectral cut-off function approach to impose a minimum length scale in the homogeneous solution. The resulting non-singular Green’s functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size ) and thus cannot handle the singular Green’s function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green’s function, as this is useful in applications where the Poisson equation represents potential functions of a vector field.
Original languageEnglish
JournalApplied Mathematics Letters
Volume89
Pages (from-to)28-34
ISSN0893-9659
DOIs
Publication statusPublished - 2019

Keywords

  • Partial differential equations
  • Poisson equation
  • Green’s function
  • Unbounded domain

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