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

Abstract

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:

Powell, Devon; Abel, Tom

• Search DOE PAGES for author "Abel, Tom"
• Search DOE PAGES for ORCID "0000-0002-5969-1251"

Publication Date:

Tue Sep 01 00:00:00 EDT 2015

Research Org.:

SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC); Stanford SGF

OSTI Identifier:

1228391

Alternate Identifier(s):

OSTI ID: 1183695

Report Number(s):

SLAC-PUB-16295
Journal ID: ISSN 0021-9991; S0021999115003563; PII: S0021999115003563

Grant/Contract Number:  

AC02-76SF00515; DE-AC02-76SF00515

Resource Type:

Published Article

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Name: Journal of Computational Physics Journal Volume: 297 Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; ASTRO, COMP, GRQC