一类复代数方程组的高阶PCG法  

HIGH-ORDER PCG METHOD SOLVING COMPLEX SYSTEMS

作　　者：黄朝晖[1] 雷光耀[1,2] 刘兴平[3] 

机构地区：[1]中科院应用数学研究所 [2]北京应用物理与计算数学研究所计算物理实验室,北京100088 [3]北京应用物理与计算数学研究所计算物理实验室

出　　处：《计算物理》2000年第4期401-406,共6页Chinese Journal of Computational Physics

摘　　要：对二维非线性Schr¨odinger方程离散后的复代数方程组 ,将高阶预处理技术与双CG法相结合 ,给出高阶PCG法。同时 ,将M阶复代数方程组化成 2M阶非对称实代数方程组 ,给出 0阶、1阶和 2阶近似LU分解的公式 ,并应用高阶PCG法求解。计算结果表明 ,高阶PCG法可以在0阶PCG法的基础上将计算效率提高近一倍。To solve complex systems obtained from 2D nonlinear Schrdinger equation, a method of high\|order PCG coupling with BICG has been developed. Meanwhile, the complex systems of order M can be reconstructed as the real systems of order 2M . From the theory of order matrix, the high order approximate LU decompositions are given as the preconditioners to solve the real systems. Numerical results show that the computational efficiency can be nearly doubled by the high\|order PCG method comparing with the ICCG method. [

关 键 词：复代数方程组 迭代法 高阶PCG法 薛定锷方程 

分 类 号：O411[理学—理论物理] O241.6[理学—物理]