A computational differential geometry approach to grid generation - Vladimir D. Liseikin

The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. This monograph describes in detail the eminent role played by differential geometry ingrid technology based on mapping. It demonstrates how the Beltrami operator helps to develop robust multidimensional grid generation codes, while supplying related numerical code. In particular, procedures for the construction of monitor metric tensors are given and their qualitative effect on the resulting mesh is analyzed. Reviewing concepts from Riemannian geometry, the book applies them to general grids with prescribed properties, and discusses the role of mean and of Gaussian curvature and other geometric characteristics for the Beltrami equations for grid generation. It addresses scientists and practitioners as well as graduate students from applied mathematics, physics, and engineering.