ABSTRACT
Concepts from tensor analysis are introduced in this chapter to assist in transforming hosted equations and set the stage for the advanced treatment of variational grid generation. Although the definitions and relationships hold in quite general settings, only the planar and volume cases are specifically considered since they are relevant to grid generation. The power of the definitions and relationships given in the chapter is illustrated in this subsection by inverting the physical-space Laplacian operator to derive the Winslow planar grid-generation operator. The basic objects in a grid generator such as scalar, vector, and tensor functions are related through the familiar gradient, divergence, and curl operators and through some nonclassical extensions thereof. The definitions are also relevant to the transformation of the hosted equations. A large number of relationships can be derived from the basic definitions; an attempt has been made to give only the most useful ones.
