Adaptive Parallel Algorithm Of Large Linear Equations

It is key technology to solve large linear system of equations in numerical analysis of engineering filed.As the improvement of compute precision and engineer scale,the produced linear system of equations became larger and larger,and the speed of the computer became quicker and quicker.How to solve large linear system of equations in a faster and better way is became a projecting problem.For the reason of expensive price of traditional high-performance computer and the restrict of the western countries,only a few research school have the traditional high-performance Computers.As Many projects have no capability to do large numerical analysis,the schedule and the quality will be infected.As the improving and increasing network technology,cluster became one of main technology of high property computer gradually.And due to the low price,the flexible structure,the quick compute speed and the convenient programming,the cluster has been the hotspot.Now the algorithm based parallel linear system of equations are more,but because of prodigious differences of matrix type,matrix scale and cluster capability,there has a large problem in the popularizing of research production,that is to get perfect high-performance algorithm need to program in every computing,and due to the restrict ability of engineering programming person,which is they can not write high-performance algorithm and do a mass of labs,the schedule and the quality will be deeply infected.Aim at the two points above,this article includes the research of matrix type and the corresponding algorithm and also the Adaptive parallel algorithm of large linear system of equations.In the hope of actualizing the Adaptive parallel algorithm,we build a cluster composed of 15 computers and also a parallel algorithms library based a PETSC software engineering.In this article,we do two labs based Adaptive parallel algorithm and the results tell that the Adaptive parallel algorithm can select the optimum algorithm from algorithm library and can compute the optimum nodes by the user's preferences,so consequently to improve the universal property of parallel solver of linear system of equations and lower the difficulty of numerical analysis.