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

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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 ... continued below

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Delzanno, G L & Finn, J M January 1, 2009.

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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.

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  • Journal Name: Journal of Computational Physics

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  • Report No.: LA-UR-09-00875
  • Report No.: LA-UR-09-875
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956413
  • Archival Resource Key: ark:/67531/metadc928936

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 9, 2016, 11:37 p.m.

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Delzanno, G L & Finn, J M. Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP, article, January 1, 2009; [New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc928936/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.