泊松方程四阶有限差分迭代算法  

Iterative Method for Solving Fourth Order Finite Difference Approximation to Poisson Equation

作　　者：刘扬[1] 高飞[1] 

机构地区：[1]武汉理工大学理学院,湖北武汉430070

出　　处：《武汉理工大学学报（信息与管理工程版）》2010年第6期873-876,共4页Journal of Wuhan University of Technology：Information & Management Engineering

基　　金：湖北省自然科学基金资助项目(2009Cbd213);武汉理工大学自主创新研究基金资助项目(2010-ia-004)

摘　　要：首先建立Poisson方程的四阶有限差分格式,然后提出求解Poisson方程的一种新Jacobi型迭代算法,新算法与经典的Jacobi方法一样具有并行性,并给出了新算法的收敛性分析。数值实验表明,新算法比经典Jacobi方法收敛快,精度高,达到同等误差精度所需迭代次数和时间均为经典Jacobi方法的50%。Fourth order finite difference approximation to Poisson equation was presented,and then a new iterative algorithm was established for solving Poisson equation.The new algorithm has the obvious property of parallelism as the classical Jacobi method.The convergence theory was discussed in detail.Numerical experiments indicat that the new algorithm has faster convergence rate and higher accuracy than Jacobi method.The iteration number and time of the new algorithm for achieving convergence criteria is only a half of the classical Jacobi method.

关 键 词：POISSON方程 有限差分 迭代法 JACOBI方法 并行性 

分 类 号：O241.82[理学—计算数学]