双调和方程Schwarz区域分解算法的Fourier分析  

Fourier Analysis on Schwarz Domain Decomposition Methods for the Biharmonic Equation

作　　者：尚月强[1,2] 何银年[1] 

机构地区：[1]西安交通大学理学院,西安710049 [2]贵州师范大学数学与计算机科学学院,贵阳550001

出　　处：《应用数学和力学》2009年第9期1100-1106,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10671154);国家基础研究基金资助项目(2005CB321703);贵州省科学技术基金资助项目(2008(2123))

摘　　要：Schwarz方法是一类重要的区域分解算法.以Fourier变换作为分析工具,推导了经典Schwarz交替迭代法和加性Schwarz迭代法用于求解双调和方程的误差传播阵及其谱半径的准确表达式,不但从新的角度更简洁地证明了Schwarz交替迭代法和加性Schwarz迭代法的收敛性,还刻画了其收敛速度,以及收敛速度随子区域的重叠程度变化而变化的情况.所得结果不依赖于任何未知常数,不受具体离散方法的影响,同时表明经典Schwarz交替迭代法具有比加性Schwarz方法快1倍的收敛速度.Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform tool, the error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation were deduced. It not only concisely proves the convergence of the Schwarz methods from a new point of view, but also provides detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, show that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

关 键 词：区域分解算法 Schwarz方法 FOURIER变换 双调和方程 

分 类 号：O241.82[理学—计算数学]