Domain Decomposition Using a 2- Level Correction Scheme
The PHYSICA software 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 enable 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. 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.
Unable to display preview. Download preview PDF.
- 3.Brandt, A.: Multi-level Adaptive Technique (MLAT) for Fast Numerical Solution to Boundary Value Problems. Lecture Notes in Physics, 18 (1973) 82–89Google Scholar
- 6.Croft, T.N., Pericleous, K.A., Cross, M.: PHYSICA: A Multiphysics environment for complex flow processes. Numerical Methods for Laminar and Turbulent Flow (IX/2), C. Taylor et al. (Eds), Pineridge Press, U.K. (1995)Google Scholar
- 7.Proceedings of International Conference on Domain Decomposition Methods for Science and Engineering. Vol 9, 11, and 12, DDM.Org.Google Scholar
- 8.Djambazov, G.S.: Numerical Techniques for Computational Aeroacoustics. Ph.D. Thesis, University of Greenwich (1998)Google Scholar
- 10.Frederickson, P.O., McByran, O.A.: Parallel Superconvergent Multigrid. Cornell Theory Centre Report CTC87TR12 (1987)Google Scholar
- 11.Lai, C.-H.: Non-linear Multigrid Methods for TSP Equations on the ICL DAP. Annual Research Report, Queen Mary, University of London, (1984)Google Scholar
- 12.Lai, C.-H.: Domain Decomposition Algorithms for Parallel Computers. High Performance Computing in Engineering-Volume 1: Introduction and Algorithms, H. Power and C.A. Brebbia (Eds), Computational Mechanics Publication, Southampton, (1995) 153–188Google Scholar
- 13.McCormick, S.F. Ruge, J.W.: Unigrid for Multigrid Simulation. Math. Comp., 41 (1983) 43–62Google Scholar
- 14.Naik, V.K., Ta’asan, S.: Implementation of Multigrid Methods for Solving Navier-Stokes Equations on a Multiprocessor System. ICASE Report 87-37 (1987)Google Scholar
- 15.PHYSICA on-line Menu: Three-dimensional Unstructured Mesh Multi-physics Computational Mechanics Computational Modellings. http://physica.gre.ac.uk/physica.html (1999)
- 16.Trottenberg, U., Oosterlee, C., Schuller, A.: Multigrid. Academic Press, New York (2001)Google Scholar
- 17.Introduction to Multigrid Methods. ICASE Report 95-11 (1995)Google Scholar