A Tensor Product B-Spline Method for Numerical Grid Generation

Abstract

We present a numerical grid generation method in which the Cartesian coordinate functions are expanded in tensor product B-spline basis functions and collocation is used to solve the elliptic grid generation equations. The efficiency of the method derives from the fact that the smoothness of the basis functions is exploited to compute fine grids in the physical domain over a coarse set of knots in the computational domain. We formulate the tensor product B-spline method, investigate its computational complexity and compare its performance to the finite difference method for several 2D grids. We show that for comparable grids the computational cost of the tensor product B-spline method is less than the cost of the finite difference method.