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Title: An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as “physically conservative voxelization.” At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara [48], who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also addressmore » practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.« less
Authors:
 [1] ;  [1]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Report Number(s):
SLAC-PUB-16295
Journal ID: ISSN 0021-9991
Grant/Contract Number:
AC02-76SF00515; DE-AC02-76SF00515
Type:
Published Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 297; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC); Stanford SGF
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; ASTRO, COMP, GRQC
OSTI Identifier:
1228391
Alternate Identifier(s):
OSTI ID: 1183695