Parallel Mesh Refinement Without Communication

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.437-448, September 19-22 2004

MESHING
RESEARCH
CORNER

13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Sandia National Laboratories
Livermore, CA, U.S.A.
[pppebay,dcthomp]@ca.sandia.gov

Abstract
This paper presents a technique for the adaptive refinement of tetrahedral meshes. What makes it unique is that no neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges present 26 = 64 possible subdivision combinations. The challenge is to triangulate the new vertices (i.e., the original vertices plus some subset of the edge midpoints) in a way that neighboring tetrahedra always generate the same triangles on their shared boundary. A geometric solution based on geometric properties (edge lengths) was developed previously, but did not account for geometric degeneracies (edges of equal length). This paper provides a solution that works in all cases.

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