Numerical solution of elliptic partial differential equations on parallel systems

The numerical solution of two-dimensional, linear and non-linear elliptic partial differential equations (PDEs) using two parallel algorithms namely Lawrie Sameh and domain decomposition has been computed on three parallel architectures. The PDEs considered here, describe the diffusion of a pollutant released from a constant source, variable source and a point source. In addition, an example with diffusion and chemical removal modelled by a non-linear PDE and three-dimensional diffusion equation is given. The parallel algorithms have been implemented on three-different systems (i) SUNFIRE (ii) IBM and (iii) PARAM. The scalability analysis has been done to analyze the performance of both the algorithms on all three parallel systems.