| A mathematical framework is developed for the solution of problems arising in geometric design, and as a result, a collection of analytical tools is obtained and applied to multidimensional boundary conforming structured grid generation.;The starting point is a finite dimensional Riemannian manifold on which coordinate invariant integral functionals are constructed. The functionals are defined either in terms of tensor fields or as mappings on manifolds. Particular choices of tensor fields lead to variational problems in surface design, and choices of mappings lead to harmonic maps and minimal maps. Grid structures are designed utilizing the invariants of the metric and curvature tensors. Grid orthogonality is achieved by incorporating a compatibility condition, derived from the Gaussian curvature, into the grid generation equations. Grids on model test regions as well as several realistic geometries encountered in the aerospace and petroleum industries are presented. |
