A smooth partition of unity finite element method for vortex particle regularization

Matthias Kirchhart, Shinnosuke Obi

Research output: Contribution to journalArticle

Abstract

We present a new class of C-smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations of particle fields, i.e., finite sums of weighted Dirac deltas. In order to use the spaces on general domains, we propose a fictitious domain formulation, together with a new high-order accurate stabilization. Stability, convergence, and conservation properties of the scheme are established. Numerical experiments confirm the analysis and show that the Cartesian grid-size σ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods.

Original languageEnglish
Pages (from-to)A2345-A2364
JournalSIAM Journal on Scientific Computing
Volume39
Issue number5
DOIs
Publication statusPublished - 2017 Jan 1

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Keywords

  • Biot-Savart law
  • Fictitious domains
  • Particle method
  • Partition of unity finite element method
  • Smooth shape functions
  • Vortex method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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