Meshes Generated by Elliptic Equations

In this paper, a new method to determine the source terms (P and Q) of Poisson equations for grid generation is presented with which the resulting interior grid point distribution is controlled entirely by a priori selection of the grid point distribution along the boundaries of the region, and in particular, the transverse lines may be constrained to be orthogonal to the boundary. For a simply connected region, the source terms (P and Q) are computed from the Dirichlet boundary values, and multiply connected regions are treated by segmentation into simply connected sub regions. Comparison with Thomas's method, the disadvantage of assumption of boundary lines being locally straight is overcome, and a high quality grid can be generated.