Solving variational problems and partial differential equations mapping into general target manifolds.
type: Item
instance of: scholarly article
title: Solving variational problems and partial differential equations mapping into general target manifolds.
zbMATH Open document ID: 1044.65060
author: Facundo Mémoli
author: Guillermo Sapiro
author: Stanley Osher
published in: Journal of Computational Physics
publication date: 2004-03-29T00:00:00Z
full work available at URL: http://purl.umn.edu/3718
review text: A framework for solving variational problems and partial differential equations that define maps into a given generic manifold is introduced. The basic idea consists in representing the target manifold as the level-set of a higher-dimensional function and then implement the equations in the Cartesian coordinate system where this embedding function is defined. This permits to use classical numerical techniques in Cartesian grids. Extension to open surfaces and submanifolds is also possible. Examples of the applications of the framework are given by the authors (harmonic maps in liquid cristals, probability maps, chroma enhancement, general geometric mapping)
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 65M99
zbMATH DE Number: 2062898
zbMATH Keywords: variational problems
zbMATH Keywords: target manifolds
zbMATH Keywords: partial differential equations
zbMATH Keywords: geometric mapping
reviewed by: Yves Cherruault
describes a project that uses: VTK
describes a project that uses: Flujos
MaRDI profile type: Publication
OpenAlex ID: W2045311917
cites work: Transport and diffusion of material quantities on propagating interfaces via level set methods.
cites work: Variational problems and partial differential equations on implicit surfaces
cites work: Harmonic maps with defects
cites work: Heat flow of \(p\)-harmonic maps with values into spheres
cites work: Theory and applications of liquid crystals
cites work: Minimizing p-harmonic maps into spheres.
cites work: Numerical methods for the Landau--Lifshitz equation
cites work: A Report on Harmonic Maps
cites work: Another Report on Harmonic Maps
cites work: Variational problems for maps of bounded variation with values in \(S^ 1\)
cites work: Q4875410
cites work: Harmonic maps of manifolds with boundary
cites work: Singularities of harmonic maps
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: Q4531800
cites work: Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces
cites work: On the Neumann problem for the nonlinear parabolic equation of Eells- Sampson and harmonic mappings
cites work: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
cites work: A general framework for low level vision
cites work: On the evolution of harmonic mappings of Riemannian surfaces
cites work: Q3997570
cites work: Color image enhancement via chromaticity diffusion
cites work: Q4855462
cites work: Numerical Methods forp-Harmonic Flows and Applications to Image Processing
cites work: Q4375274
DOI: 10.1016/J.JCP.2003.10.007
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description: scientific article; zbMATH DE number 2062898