An efficient one dimensional parabolic equation solver using parallel computing

Abstract

This paper will discuss the heat equation or as known as parabolic equation by Jacobi, Gauss Seidel and Alternating Direct Implicit (ADI) methods with the implementation of parallel computing on it. The numerical method is emphasized as platform to discretize the one dimensional heat equation. The result of three types of numerical methods will be presented graphically. The parallel algorithm is used to solve the one dimensional parabolic equation. Parallel Virtual Machine (PVM) is used in support of the communication among all microprocessors of Parallel Computing System. PVM is a software system that enables a collection of heterogeneous computers to be used as coherent and flexible concurrent computational resource. The numerical results and how fast of the convergence by Jacobi, Gauss-Seidel, and ADI will be evaluated, which are the main effort of this paper in order to fabricate an efficient One Dimensional Parabolic Equation Solver (ODPES). This new well-organized ODPES technique will enhance the research and analysis procedure of many engineering and mathematic fields.