Full-FAS multigrid grid generation algorithms

Abstract

This paper deals with the aim of coupling multigrid generation of boundary-fitted grids with an effective full multigrid technique. For the last years we have been developing the generation of structured grids by the definition of specific elliptic systems and the application of multigrid computation to their solution. In this paper we present a Full-FAS multigrid algorithm for the generation of curvilinear coordinate systems on physical domains. We adopt standard central differencing for the approximation of the nonlinear generating 2D and 3D systems, full approximation storage (FAS) algorithms to solve the resulting discrete equations and Full multigrid computation to obtain a better initial guess for the already developed multigrid algorithms. In the paper we introduce the elliptic grid generation models, the multigrid computation and the full multigrid algorithm, based on the nested iteration technique. Then we detail the multigrid components, and therefore the available forms, of the basic Full-FAS algorithm and we comment numerical results with the help of figures.