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Title: Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP

Abstract

The Monge-Kantorovich grid generation and adaptation scheme of is generalized from a variational principle based on L{sub 2} to a variational principle based on L{sub p}. A generalized Monge-Ampere (MA) equation is derived and its properties are discussed. Results for p > 1 are obtained and compared in terms of the quality of the resulting grid. We conclude that for the grid generation application, the formulation based on L{sub p} for p close to unity leads to serious problems associated with the boundary. Results for 1.5 {approx}< p {approx}< 2.5 are quite good, but there is a fairly narrow range around p = 2 where the results are close to optimal with respect to grid distortion. Furthermore, the Newton-Krylov methods used to solve the generalized MA equation perform best for p = 2.

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:
956413
Report Number(s):
LA-UR-09-00875; LA-UR-09-875
Journal ID: ISSN 0021-9991; JCTPAH; TRN: US201013%%151
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Name: Journal of Computational Physics; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
99; OPTIMIZATION; EQUATIONS; LANL

Citation Formats

Delzanno, G L, and Finn, J M. Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP. United States: N. p., 2009. Web.
Delzanno, G L, & Finn, J M. Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP. United States.
Delzanno, G L, and Finn, J M. 2009. "Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP". United States. https://www.osti.gov/servlets/purl/956413.
@article{osti_956413,
title = {Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP},
author = {Delzanno, G L and Finn, J M},
abstractNote = {The Monge-Kantorovich grid generation and adaptation scheme of is generalized from a variational principle based on L{sub 2} to a variational principle based on L{sub p}. A generalized Monge-Ampere (MA) equation is derived and its properties are discussed. Results for p > 1 are obtained and compared in terms of the quality of the resulting grid. We conclude that for the grid generation application, the formulation based on L{sub p} for p close to unity leads to serious problems associated with the boundary. Results for 1.5 {approx}< p {approx}< 2.5 are quite good, but there is a fairly narrow range around p = 2 where the results are close to optimal with respect to grid distortion. Furthermore, the Newton-Krylov methods used to solve the generalized MA equation perform best for p = 2.},
doi = {},
url = {https://www.osti.gov/biblio/956413}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = ,
place = {United States},
year = {2009},
month = {1}
}