算子自定义小波弹性板单元构造及自适应分析

THE CONSTRUCTION OF OPERATOR CUSTOM-DESIGN WAVELET FINITE ELEMENTS AND ADAPTIVE ANALYSIS OF ELASTIC PLATES

提出一类用于分析弹性板问题的算子自定义小波弹性板单元构造方法.该方法的优点在于根据工程问题的求解需要灵活构造具有解耦特性的算子自定义小波基,使得系统多尺度刚阵具有沿对角线的强稀疏性,从而实现了该算法在每个尺度上独立、快速求解,系统方程的求解效率得到较大提高.建立多分辨Lagrange有限元空间和多尺度计算理论,提出基于稳定完备法的算子自定义小波弹性板单元构造方法及解耦条件.依据两尺度相对误差估计,提出自适应算子自定义小波有限元算法.数值算例证明,算子自定义小波弹性板单元具有求解精度与计算效率高等特点.

A new construction method of operator custom-design wavelet finite elements is proposed for analyzing elastic plate problems. The superiority of this method is that the decoupling operator custom-design wavelet bases can be constructed conveniently according to the requirements of engineering prob-lems,which leads to highly sparse multi-scale system stiffness matrix along diagonal line. Using the pro-posed algorithm,the independent and fast computation on each level can be easily realized,thus the compu-tational efficiency of system of equations is greatly improved. A multi-resolution Lagrange finite element space and multi-scale computation theory are constructed, and then the building method and decoupling condition of operator custom-design wavelet finite element are presented for the elastic plate problems. Fi-nally,an adaptive operator custom-design wavelet finite element algorithm is proposed according to two-level relative error estimation. Numerical examples show that the present method is accurate and efficient for solving elastic plate problems.