Abstract

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve this for any mesh composed of simplex elements, and deal.II contains a serial algorithm for constructing a consistent orientation of any quadrilateral mesh of an orientable manifold. The core contribution of this paper is the extension of this algorithm for distributed memory parallel computers, which facilitates its seamless application as part of a parallel simulation system. Furthermore, our analysis establishes a link between the well-known Union-Find algorithm and the construction of a consistent orientation of a quadrilateral mesh. As a result, existing work on the parallelization of the Union-Find algorithm can be easily adapted to construct further parallel algorithms for mesh orientations.

Keywords

  1. finite element assembly
  2. parallel algorithm
  3. quadrilateral mesh
  4. Firedrake
  5. ARCHER

MSC codes

  1. 68W10
  2. 68W15

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: S48 - S61
ISSN (online): 1095-7197

History

Submitted: 13 May 2015
Accepted: 18 December 2015
Published online: 27 October 2016

Keywords

  1. finite element assembly
  2. parallel algorithm
  3. quadrilateral mesh
  4. Firedrake
  5. ARCHER

MSC codes

  1. 68W10
  2. 68W15

Authors

Affiliations

Funding Information

The Grantham Institute
Natural Environment Research Council http://dx.doi.org/10.13039/501100000270 : NE/K006789/1, NE/K008951/1

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