Accelerated numerical simulation by multigrid computation

In this paper we present recent advances in the development of multigrid methods, applied to the numerical solution of partial differential equations (PDEs). We specifically deal with algorithms for handling two different numerical simulation sub processes, assumed as performance evaluation cases: elliptic grid generation : we present the main components of non-linear multigrid algorithms for the generation of boundary-fitted grids, semi-implicit finite-difference simulation : we sketch the multigrid solution of the shallow water equations and results on computed water circulation in artificial and real basins.