Abstract
We study a new algorithm to compute harmonic maps from a domain of R 3 into S 2. The novelty of this algorithm is that the renormalization step speeds up the convergence. We also apply it to the evolution problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bethuel, F., Coron, J.M., Ghidaglia, J.M., and Soyeur, A. () “Heat flows and relaxed energies for harmonic maps, Nonlinear diffusion equations and their equilibrium states”, Gregymog, Birkhauser.
Brezis, H., Coron, J.M., and Lieb, E. (1986) “Harmonic maps with defects”, Comm. Math. Phys. 107, pp. 649–705.
Cohen, R., Hardt, R., Kinderlehrer, D., Lin, S.Y. and Luskin, M; (1987) “Minimum energy configurations for liquid crystals: computational results”, IMA vol. 5, Springer.
Dean, E., Glowinski, R. and Li, C.H. (1988) “Applications of operator splitting methods to the numerical solution of nonlinear problems in continuum mechanics and physics”, Mathematics Applied to Science, Academic Press.
Gulliver, R. (1988) “Harmonic mappings, symmetry and computer graphics”, Preprint CMA-R-52-88.
Fortin, M., and Glowinski, R. (1982) “Méthodes de lagrangien augmenté”, Méthodes Mathématiques de l’Informatique, vol. 9, Dunod.
Hardt, R., and Kinderlehrer, D. (1987) “Mathematical questions of liquid crystals theory. Theory and Applications of Liquid Crystals”, IMA Vol. 5, Springer.
Lin, S.Y. (1987), Thesis, University of Minnesota.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Alouges, F. (1991). An Energy-Decreasing Algorithm for Harmonic Map. In: Coron, JM., Ghidaglia, JM., Hélein, F. (eds) Nematics. NATO ASI Series, vol 332. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3428-6_1
Download citation
DOI: https://doi.org/10.1007/978-94-011-3428-6_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5516-1
Online ISBN: 978-94-011-3428-6
eBook Packages: Springer Book Archive