New Parallel Group Accelerated Overrelaxation Algorithms For The Solution Of 2-D Poisson And Diffusion Equations

Finite difference method is commonly used to solve partial differential equations (PDEs) which arise from fluid mechanics and thermodynamics problem. However, the discretization of these PDEs oftenly lead to large sparse linear systems which require large amount of execution times to solve. The development in accelerated iterative techniques and parallel computing technologies can be utilized to surmount this problem. Point iterative schemes which are based on the standard five point discretization and the rotated five point discretization are commonly used to solve the Poisson equation. In addition, block or group iterative schemes where the mesh points are grouped into block have been shown to reduce the number of iterations and execution timings because the solution at the mesh points can be updated in groups or blocks instead of pointwise