| 基于三维对流扩散方程四阶紧致差分格式的预条件迭代法 |
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| 引用本文： | 袁冬芳,庄昕,葛永斌.基于三维对流扩散方程四阶紧致差分格式的预条件迭代法[J].宁夏大学学报(自然科学版),2012,33(1):1-5. |
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| 作者姓名： | 袁冬芳 庄昕 葛永斌 |
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| 作者单位： | 宁夏大学应用数学与力学研究所,宁夏银川,750021 |
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| 基金项目： | 国家自然科学基金资助项目(11061025);教育部科学技术研究重点项目(210239);霍英东教育基金会高等院校青年教师基金资助项目(121105);宁夏自然科学基金资助项目(NZ0937) |
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| 摘 要： | 针对三维对流扩散方程，采用四阶紧致差分格式和预条件迭代法进行数值实验，利用带填补数的不完全LU分解（ILUT（τ，s））做预处理器，FGMRES（20）做迭代加速器对离散所得方程组进行求解．验证了四阶紧致差分格式的计算精度，通过比较预条件迭代法与高斯一赛德尔迭代法以及超松弛迭代法的迭代次数和CPU时间，充分显示了预条件迭代法的高速求解特性．
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| 关 键 词： | 三维对流扩散方程 四阶紧致格式 迭代法 预条件技术 不完全LU分解 |
Preconditioned Iterative Methods Based on the Fourth-order Compact Scheme of the 3D Convection-diffusion Equation |
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| Yuan Dongfang
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Zhuang Xin
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Ge Yongbin.Preconditioned Iterative Methods Based on the Fourth-order Compact Scheme of the 3D Convection-diffusion Equation[J].Journal of Ningxia University(Natural Science Edition),2012,33(1):1-5. |
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| Authors: | Yuan Dongfang Zhuang Xin Ge Yongbin |
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| Institution: | (Institute of Applied Mathematics and Mechanics,Ningxia University,Yinchuan 750021,China) |
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| Abstract: | The fourth-order compact difference scheme and preconditioned iterative methods are employed to conduct numerical study on three dimensional convection-diffusion equation.The incomplete LU decomposition preconditioner with fill-ins(ILUT(τ,s)) and the FGMRES(20) iterative accelerators are applied to solve the discrete linear equations.The accuracy of the fourth-order compact difference scheme is verified,and the advantages of preconditioned iterative methods are sufficiently demonstrated by comparing the iteration numbers and CPU time with the conventional Gauss-Seidel and successive over relaxation methods. |
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| Keywords: | three dimensional convection-diffusion equation fourth-order compact scheme iterative methods preconditioned technique incomplete LU decomposition |
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