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Title: The fluid dynamic approach to equidistribution methods for grid generation and adaptation

Abstract

The equidistribution methods based on L{sub p} Monge-Kantorovich optimization [Finn and Delzanno, submitted to SISC, 2009] and on the deformation [Moser, 1965; Dacorogna and Moser, 1990, Liao and Anderson, 1992] method are analyzed primarily in the context of grid generation. It is shown that the first class of methods can be obtained from a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density, arising from a variational principle. In this context, deformation methods arise from a fluid formulation by making a specific assumption on the time evolution of the density (but with some degree of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L{sub 1} Monge-Kantorovich optimization, by making a further assumption on the momentum density. Some applications of the L{sub p} fluid dynamic formulation to imaging are also explored.

Authors:
 [1];  [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
962380
Report Number(s):
LA-UR-09-01688; LA-UR-09-1688
TRN: US200920%%136
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article
Journal Name:
SIAM Journal of Scientific Computing
Additional Journal Information:
Journal Name: SIAM Journal of Scientific Computing
Country of Publication:
United States
Language:
English
Subject:
99; MESH GENERATION; FLUID MECHANICS; DEFORMATION; CALCULATION METHODS

Citation Formats

Delzanno, Gian Luca, and Finn, John M. The fluid dynamic approach to equidistribution methods for grid generation and adaptation. United States: N. p., 2009. Web.
Delzanno, Gian Luca, & Finn, John M. The fluid dynamic approach to equidistribution methods for grid generation and adaptation. United States.
Delzanno, Gian Luca, and Finn, John M. 2009. "The fluid dynamic approach to equidistribution methods for grid generation and adaptation". United States. https://www.osti.gov/servlets/purl/962380.
@article{osti_962380,
title = {The fluid dynamic approach to equidistribution methods for grid generation and adaptation},
author = {Delzanno, Gian Luca and Finn, John M},
abstractNote = {The equidistribution methods based on L{sub p} Monge-Kantorovich optimization [Finn and Delzanno, submitted to SISC, 2009] and on the deformation [Moser, 1965; Dacorogna and Moser, 1990, Liao and Anderson, 1992] method are analyzed primarily in the context of grid generation. It is shown that the first class of methods can be obtained from a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density, arising from a variational principle. In this context, deformation methods arise from a fluid formulation by making a specific assumption on the time evolution of the density (but with some degree of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L{sub 1} Monge-Kantorovich optimization, by making a further assumption on the momentum density. Some applications of the L{sub p} fluid dynamic formulation to imaging are also explored.},
doi = {},
url = {https://www.osti.gov/biblio/962380}, journal = {SIAM Journal of Scientific Computing},
number = ,
volume = ,
place = {United States},
year = {2009},
month = {1}
}