双曲方程基于分离算子的交替方向差分算法  

THE ALTERNATING-DIRECTION PARALLEL DIFFERENCE ALGORITHM BASED ON OPERATOR SPLITTING TECHNIQUE FOR HYPERBOLIC EQUATION

作　　者：张琎[1] 王震[2] 

机构地区：[1]济南大学信息科学与工程学院,济南250022 [2]山东科技大学信息科学与工程学院,山东青岛266510

出　　处：《数值计算与计算机应用》2011年第3期159-164,共6页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(60573065);济南大学科研基金项目(XKY0821)

摘　　要：因为在自然科学领域有着广泛的应用,双曲型方程组的数值求解一直是研究的热点.本文中,为求解一类非线性二阶双曲型方程,将方程中的非线性椭圆微分算子分解为线性部分和非线性部分,对线性部分用隐格式逼近,对非线性部分用显格式逼近,这种方法可以把非线性间题转化成每一时间层只有右端项不同的线性方程组,计算简单且计算格式绝对稳定;交替方向格式可以把多维间题转化成一维问题,x,y两个方向的迭代矩阵均为三对角矩阵,结构相同,易于编程并行计算.最后通过数值实验表明结果符合理论分析.Numerical solution for hyperbolic systems has always been a hot problem because of its wide applications in the field of natural science. In this paper, nonlinear elliptic differential operator can be decomposed as linear item and nonlinear item for solving a class of nonlinear second order hyperbolic systems. The former is approximated by the implicit scheme and the latter is approximated by the explicit scheme. The method can turn nonlinear problems to the similar linear system with different right-hand side at each time step, while we have similar triple diagonal matrix on left-hand, it is easy to compute and the scheme is absolutely stable. The Alternating-Direction Schemes can turn multi-dimensional problem into one- dimensional problem and Iterative matrix of x, y are triple diagonal matrices which have same structure, so they are easy to program for parallel computing. At last some numerical results are presented to prove theory analysis.

关 键 词：分离算子 交替方向 并行差分 三对角矩阵 

分 类 号：O175.27[理学—数学]