求解流固振动Laplace模型的基于Rayleigh商移位反迭代的多网格方案  

Multiscale Discretization Scheme Based on the Rayleigh Quotient Inverse Iteration Method for the Laplace Model for Fluid-Solid Vibrations

作　　者：杜小虎 闭海 

机构地区：[1]贵州师范大学数学科学学院,贵州 贵阳

出　　处：《应用数学进展》2021年第6期2226-2239,共14页Advances in Applied Mathematics

摘　　要：本文讨论流固振动Laplace模型,首先建立该问题的基于Rayleigh商移位反迭代的多网格离散方案,利用该方案将在细网格上求解特征值问题归结为在粗网格上解特征值问题和在细网格上解一系列线性代数系统。其次分析多网格离散方案的误差。最后给出数值算例验证离散方案的有效性。In this paper, for the Laplace model for fluid-solid vibrations we establish the multiscale discretization scheme based on the Rayleigh quotient inverse iteration method. With this scheme, the solution of an eigenvalue problem on fine meshes is reduced to the solution of the eigenvalue problem on coarse meshes and the solutions of linear algebraic systems. Then we analyze and give the error estimates of the proposed scheme. Finally we present numerical experiments to validate the efficiency of the scheme.

关 键 词：流固振动模型 有限元 多网格方案 Rayleigh商迭代 误差估计 

分 类 号：O15[理学—数学]