ABSTRACT
This chapter extends one-dimensional variational grid generation to the two-dimensional planar case. Variational methods of grid generation have seen relatively little application in industry, so another goal of the chapter is to convince the reader that variational methods are a worthwhile approach to grid generation. It begins by reviewing basic ideas from the Calculus of Variations such as the concept of a functional, its first and second variation, and the Euler-Lagrange equations. The main section in the chapter describes the variational approach to grid generation. The variational approach is appealing because powerful mathematical results have long been available for variational problems in classical mechanics and more recently for problems in nonlinear elasticity. The hope is that by taking the variational approach, grid generation can be given a solid footing and made more powerful; certainly it already has been made more intuitive.
