Mathematical aspects of variational grid generation II

摘要

Variational grid generation techniques are now used to produce grids suitable for solving numerical partial differential equations in irregular geometries. In this paper the existence and uniqueness of solutions of the volume and smoothness problems that are used in variational grid generation are studied. An analysis of the Euler-Lagrange (EL) equations near the identity shows that the volume problem is difficult. These variational problems use a reference grid to specify the properties of the desired grid. Replication of reference grid properties is analyzed. Examples are given that show the effectiveness of the reference grid concept.