Solving variational problems and partial differential equations mapping into general target manifolds.
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)
scientific article; zbMATH DE number 2062898
scientific article