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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. Thu . "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}
}