Domain Decomposition Using a 2-Level Correction Scheme R.H. Marsden, T.N. Croft, and C.-H. Lai School of Computing and Mathematical Sciences, University of Greenwich, Greenwich, London SE10 9LS, U.K. {R.H.Marsden, T.N.Croft, C.H.Lai}@gre.ac.uk http://cms1.gre.ac.uk Abstract. The PHYSICA software was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynam- ics (CFD) and Computational Solid Mechanics (CSM) and Computa- tional Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to enable the modelling of complex geome- tries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multi- grid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. This papers attempts to address two major issues of this iterative solver, including parallelisation of multigrid methods and their applications to time dependent multiscale problems. 1 Introduction The PHYSCIA software [6][15] was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM) and Computational Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to en- able the modelling of complex geometries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multigrid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. There are two major issues in this fast iterative solver. First, multigrid methods are usually very difficult to parallelise and the performance of the resulting algorithms are machine dependent. Early work in parallelisation of multigrid methods include Barkai and Brandt [2], Chan [5], Frederickson [10], Naik [14], etc. Methods developed by these authors con- cerned the load balancing between processors and the full use of all co-existing coarse level meshes in order to fit into the parallelism requirement. This paper intends to address these issues with particular attention being paid to linear and nonlinear diffusion type of problems in a distributed computing environment. The method is then extended to time-dependent and multiscale problems. P.M.A. Sloot et al. (Eds.): ICCS 2002, LNCS 2330, pp. 480-489, 2002.  Springer-Verlag Berlin Heidelberg 2002