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. (SNLNM), 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}
}