A super-convergence analysis of the Poisson solver with Octree grids and irregular domains

Jeongho Kim, Chohong Min, Byungjoon Lee

Research output: Contribution to journalArticlepeer-review

Abstract

Resolving the difficulty of T-junctions in Octree grids, Losasso et al. [9] introduced an ingenious Poisson solver with rectangular domains and Neumann boundary conditions. Its numerical solution was empirically observed [9] to be second order convergent and its numerical gradient was rigorously proved [8] to be one and a half order convergent, which is the so-called super-convergence. This article is devoted to extending the Poisson solver and its supporting proof from rectangular to irregular domains. The generalized Whitney decomposition [12] efficiently generates octree grids for irregular domains imposing the finest resolution near the boundary of domain. Combined with the Heaviside treatment [17,4], the Poisson solver is extended to irregular domains and a novel and rigorous analysis shows that the aforementioned super-convergence still holds true.

Original languageEnglish
Article number112212
JournalJournal of Computational Physics
Volume488
DOIs
StatePublished - 1 Sep 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

  • Hodge decomposition
  • Irregular domain
  • Octree
  • Poisson equation
  • Super-convergence

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