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

Ebeida, Mohamed Salah

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:: Ebeida, Mohamed Salah

Issue Date:: 2019-05-28

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

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G - PHYSICS G06 - COMPUTING G06K - RECOGNITION OF DATA
G06K9/6286 - {Linear, e.g. hyperplane}
G06K9/6276 - {based on distances to closest patterns, e.g. nearest neighbour classification}
G06K9/6224 - {based on graph theory, e.g. Minimum Spanning Trees [MST], graph cuts, spectral clustering techniques

G - PHYSICS G06 - COMPUTING G06F - ELECTRIC DIGITAL DATA PROCESSING
G06F30/20 - Design optimisation, verification or simulation
G06F2111/10 - Numerical modelling

G - PHYSICS G06 - COMPUTING G06T - IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
G06T17/20 - Finite element generation, e.g. wire-frame surface description, {tesselation}

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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.

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                    Ebeida, Mohamed Salah. Generating an implicit voronoi mesh to decompose a domain of arbitrarily many dimensions.  United States.

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                    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.

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@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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Works referenced in this record:

Forming a model of a subsurface region
patent, August 2014

Calvert, Craig S.; Benson, Gregory S.; Wu, Xiaohui
US Patent Document 8,818,780
URL: http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=8818780

Method for constructing a fracture network grid from a Voronoi diagram
patent, August 2015

Khvoenkova, Nina; Delorme, Matthieu
US Patent Document 9,103,194
URL: http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=9103194

Method for generating a hex-dominant mesh of a geometrically complex basin
patent, March 2014

Ran, Longmin; Benali, Abdallah; Borouchaki, Houman
US Patent Document 8,674,984
URL: http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=8674984

Generation of constrained Voronoi grid in a plane
patent, July 2012

Branets, Larisa V.; Wu, Xiaohui; Verma, Santosh K.
US Patent Document 8,212,814
URL: http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=8212814

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

Abstract

Citation Formats

Forming a model of a subsurface region patent, August 2014

Method for constructing a fracture network grid from a Voronoi diagram patent, August 2015

Method for generating a hex-dominant mesh of a geometrically complex basin patent, March 2014

Generation of constrained Voronoi grid in a plane patent, July 2012

Forming a model of a subsurface region
patent, August 2014

Method for constructing a fracture network grid from a Voronoi diagram
patent, August 2015

Method for generating a hex-dominant mesh of a geometrically complex basin
patent, March 2014

Generation of constrained Voronoi grid in a plane
patent, July 2012