Adaptive grid generation from harmonic maps on Riemannian manifolds (Q809574)

A new approach to generate adaptive grids based on harmonic maps on Riemannian manifolds is presented. The method can be viewed as a generalization and extension of \textit{A. M. Winslow}'s method [J. Comput. Phys. 1(1966), 149-172 (1967; Zbl 0254.65069)]. The approach uses a single functional whose critical points are harmonic maps to accomplish the adaptive mapping. The reliability of the procedure is assured by an existence and uniqueness theorem for one-to-one maps between multidimensional multiconnected domains. Several examples demonstrating applications of the approach are provided.