Variational method of triangulating surfaces and domains in three- dimensional space (Q795487)

This paper describes some general ideal which can be used for automatic triangulation of multidimensional domains in the finite element method. The algorithm consists in constructing the diffeomorphism for which there exists a sufficiently simple numerical method yielding the quasi-uniform splitting of the domain (this property, however, is not proved by the authors). The procedure is elegant but somewhat costly. For example, the standard 3-dimensional cube is mapped onto the curved cube at three following steps: 1) Mapping of the edges, which is done by solving the one-dimensional nonlinear Poisson equation by some iterative method; 2) Mapping of the square faces by solving the two-dimensional nonlinear Poisson equation; 3) Mapping of the interior of the cube by solving the three-dimensional Laplace-equation.