Re-parameterisation Technique in Algebraic Numerical Grid Generation via Subdivision Schemes

In this paper we discuss a strategy for reducing the computational cost of a re-parameterisation procedure to be used in algebraic numerical grid generation. The re-parameterisation phase is based on a tensor product transformation following given directions. The free parameters in the tensor product are set by solving the discretization of an elliptic differential system of small size, via an iterative scheme, thus generating a grid conforming to the boundary of a prescribed domain with orthogonal inner grid cells and with almost constant aspect ratio. The bases involved in the tensor product are refinable, i.e., they can be written as linear combination of dilate of translates of their-self. This property allows us to use few iterations of the corresponding subdivision algorithm to produce a good parameter distribution.