A Cost-effective Ilu Preconditioner for Weather Simulation

To date, the most efficient solver used in the weather sciences for the resolution of linear system in numerical weather prediction is the generalized minimal residual method called GMRES. However, difficulties still appear in matrix resolution when the GMRES iterative method is used without an appropriate preconditioner. For improving the computation speed in numerically solving weather equations, we investigate the use of Incomplete LU(ILU) factorization preconditioner. This is a fast algorithm for solving large scale linear equations. Some strategies for choosing the level of fill and threshold are described in this paper. As an example, we use the GMRES iterative algorithm to solve the finite difference equations of shallow equations and analyze the results that are obtained in preconditioned and un-preconditioned, respectively. It is shown that the computation speed is greatly improved by using ILU factorization preconditioner for the linear system. In addition, this preconditioning algorithm is simple and parallelizable. Therefore, the algorithm is potential in the applications of weather e-