Design And Implementation Of Out-of-core Parallel Solution Of Linear Equations

Because of the large-scale system of linear equations having widespread applications in some fiels such as chemical engineering,weather forecast and numerical methods and so on,the research on its solution has been a hot topic.With the rapid development of science and technology,the amount of data that people need to deal with is the rapid growth.Computer hardware has a rapid development in recent years,but memory capacity usually can not meet the storage needs of a large amount of data calculation.Now,various types of parallel processing system has become the mainstream computing environment of scientific research or solving the problem of signification scale.In order to adapt to the new computing environment,pursuit the solving of higher speed and greater capacity,cluster system is widely used in scientific research and application because it is a parallel processor system with good cost-effective.Therefore the research and design of parallel solution of the larger linear equations in the cluster environment have an important significance of theoretical and practical.There are many methods to solving linear equations,because the symmetry of coefficient matrix which solves linear equations in this paper,so the method of cholesky decomposition has been used to solve linear equations.This article carefully researches and analysises the Serial and Parallel Algorithms of linear equations based on the cluster system, the content including:(1) To achieve the cholesky decomposition algorithms of serial and parallel in core to solve linear equations in MPI environment.(2) Analysis cholesky decomposition algorithm of serial and parallel in core,then given the problems and optimization.(3) We proposed a parallel method of out-of-core prefetching algorithm based on parallel method in core.The method not only sove the problem of small memory capacity,but also shorten the speed gap between I/O and CPU effectively and improved the efficiency of cholesky decomposition.(4) We proposed a parallel method of data reuse based on out-of-core parallel algorithms. The algorithm reduced the time of I/O operation and achieved reasonable schedule and efficient access to out-of-core array by the data remaining in memory which has been read into memory now and still be used in next time. This article built a parallel computing platform based on Linux and constructed MPI environment of parallel programming.At the same time,test the algorithm of out-of-core prefetching and data reuse on Linux platform, then analysis the performance of experimental results.The results show that this algorithm can run cholesky decomposition program of large-scale linear equations on cluster in a small memory.