SOLVERS FOR SYSTEMS OF LARGE SPARSE LINEAR AND NONLINEAR EQUATIONS BASED ON MULTI-GPUS  

基于多GPU的大型线性和非线性方程组的求解(英文)

作　　者：刘沙[1] 钟诚文[1,2] 陈效鹏[3] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室 [2]西北工业大学高性能计算中心 [3]西北工业大学力学与土木工程学院

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2011年第3期300-308,共9页南京航空航天大学学报（英文版）

摘　　要：Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.在处理工程问题时,常常需要对线性或非线性方程组进行求解。对于实际应用中经常遇到的大型方程组进行求解则需要相当长的时间。使用图形处理器(GPU)代替传统的CPU,将多块GPU通过操作系统进行协调,并将PBi-CGstab方法和Inexact Newton方法进行适合多GPU并行的改造以此作为多GPU求解器的核心算法,加速求解大型线性和非线性方程组。本文的多GPU求解器在成倍扩展了单GPU求解器允许的计算规模的同时取得了令人满意的加速比。

关 键 词：general purpose graphic process unit（GPGPU） compute unified device architecture（CUDA） system of linear equations system of nonlinear equations Inexact Newton method bi-conjugate gradient stable（Bi-CGstab）method 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]