Meshes optimized for discrete exterior calculus (DEC).

Technical Report · Fri Dec 01 04:00:00 EST 2017

DOI:https://doi.org/10.2172/1414659· OSTI ID:1414659

Mousley, Sarah C. ^[1]; Deakin, Michael ^[2]; Knupp, Patrick ^[2]; Mitchell, Scott A. ^[2]

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1. Univ. of Illinois, Urbana-Champaign, IL (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 1414659
• Report Number(s): SAND--2017-13575R; 659546
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING