Regularization of the barrier variational method of grid generation

A regularization of the barrier variational method for planar grid generation is proposed. The regularization provides a fast and reliable procedure for constructing nondegenerate grids through solution of a discrete minimization problem using only a prescribed cell connectivity structure and given boundary grid points. An efficient numerical method for determining the stationary points of the barrier functional up to the machine truncation error is proposed and tested, which makes it possible to examine the nonuniqueness of stationary points in a number of examples. Numerical experiments have shown that the proposed technique can be used to generate computational grids reliably without any adjustment or control parameters.