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Title: Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions

Abstract

Described herein are technologies pertaining to generating a Voronoi mesh for an enclosed domain of arbitrarily many dimensions. An implicit Voronoi mesh is received that comprises locations of seeds in the domain. Neighbors of a seed are identified by extending a segment from the seed to the boundary of the domain and performing successive hyperplane trimming of the segment to identify a point on the facet of the Voronoi cell of the seed. A vertex of the cell can be identified by successively extending and trimming one or more additional spokes to identify points on a facet of the cell that are constrained to lie in a (d−n) space, where d is a number of dimensions of the domain and n is a number of iterations. A numerical simulation is performed based on the Voronoi mesh to generate simulation results in applications including surrogate modeling, global optimization, calibration, dimension reduction.

Inventors:
Issue Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1568404
Patent Number(s):
10304243
Application Number:
15/634,750
Assignee:
National Technology & Engineering Solutions of Sandia, LLC (Albuquerque, NM)
Patent Classifications (CPCs):
G - PHYSICS G06 - COMPUTING G06K - RECOGNITION OF DATA
G - PHYSICS G06 - COMPUTING G06F - ELECTRIC DIGITAL DATA PROCESSING
DOE Contract Number:  
NA0003525
Resource Type:
Patent
Resource Relation:
Patent File Date: 06/27/2017
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Ebeida, Mohamed Salah. Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions. United States: N. p., 2019. Web.
Ebeida, Mohamed Salah. Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions. United States.
Ebeida, Mohamed Salah. Tue . "Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions". United States. https://www.osti.gov/servlets/purl/1568404.
@article{osti_1568404,
title = {Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions},
author = {Ebeida, Mohamed Salah},
abstractNote = {Described herein are technologies pertaining to generating a Voronoi mesh for an enclosed domain of arbitrarily many dimensions. An implicit Voronoi mesh is received that comprises locations of seeds in the domain. Neighbors of a seed are identified by extending a segment from the seed to the boundary of the domain and performing successive hyperplane trimming of the segment to identify a point on the facet of the Voronoi cell of the seed. A vertex of the cell can be identified by successively extending and trimming one or more additional spokes to identify points on a facet of the cell that are constrained to lie in a (d−n) space, where d is a number of dimensions of the domain and n is a number of iterations. A numerical simulation is performed based on the Voronoi mesh to generate simulation results in applications including surrogate modeling, global optimization, calibration, dimension reduction.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {5}
}

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