Design And Implementation Of Parallel Solution Of Linear Equations On Cluster System

Because of large-scale system of linear equations in oil deposit simulation,chemical engineering,domain and such ordinary differential equation boundary value problem widespread applications,its solution's researching has been a hot topic.Along with computer hardware's rapidly development in recent years,people's researching of the large-scale system of linear equations in order to adapt the new computation environment research never came to a stop. Parallel processing system becomes the mainstream computation environment in many scientific projects or the scientific research, such as industry and scientific research mostly have chosen to sloving the linear equations's solution on the parallel machine system,The cluster system is the most excellent parallel processing platform, then the researching and designing of the large-scale linear equation's parallel solution method under the cluster system has the very important theory and the practical significance.With the science and technology development rapidly, the system of linear equations scale unceasing to increase along with it, this is also getting the request of computer hardware higher and higher,This article mainly carried studied and realizes based on the system of linear equations parallel algorithm on the cluster system, the content included:(1) Has realized MPI and OpenMP the multi-granularity mix programming solution system of linear equations's Gauss algorithm.(2) As a result of server's particularity, which experiment test order with other procedure sharing processor memory, therefore the cluster system's memory insufficiency or steady frequently,In order to solve the large-scale system of linear equation under this situation, this article according to the classics Gauss algorithm to propose the divi-gauss algorithm, obtains the empirical datum on the Altix3700 server.(3) In the part of the solution of triangle equation, the algorithm has presentd according to the improvement of row-scanning algorithm according to the thought of the file-division , then it has guaranteed the procedure smooth movement.Because of using the thought of file-division, this algorithm realizes large-scale linear equations's roll-in and solves when the memory is in insufficient or not steady situation, the experimental result has confirmed the algorithm validity.The parallel computing platform has built based on the Linux Altix3700 server, and under this platform MPI and the OpenMP parallel programming environment were constructed, The divi-gauss algorithm which proposed in this article carries on the test in this platform, and analysis its performance, the experimental result indicated that the algorithm designed in this article can run large-scale system of linear Gauss equations's very well on the small memory server to solve the procedure.