Grid generation method with optimal shape parameters

We considered the grid generation problem of computation of a grid over a given domain from the knowledge of the domain boundary. A simple grid generation method based on the direct computing of grid curves was proposed. The grid curves wer constructed in u-direction and v-direction by two formulas with the shape parameters, seperately. By choosing different shape parameters, different grid curves could be obtained. Then, the choice of the optimal shape parameters were considered by solving a optimization problem. And the choice of the objective function was given by the function with geometric properties: Length Functional and Orthogonality Functional. Based on the expressions of u-directional grid curves and v-directional grid curves obtained by us, the optimal shape parameters could be obtained easily. Some numerical experiments on the examples proposed in Rogue's Gallery of Grid showed that the presented method in this paper was effective.