基于Maxwell模型的线性粘弹性波传播问题的质量集中杂交应力有限元法  

A hybrid stress finite element method with mass lumping for Maxwell elastodynamic problems of wave propagation

作　　者：周亚婧 陈豫眉 ZHOU Ya-Jing;CHEN Yu-Mei(School of Mathematics,Sichuan University,Chengdu 610064,China;College of Mathematics Education,China West Normal University,Nanchong 637009,China)

机构地区：[1]四川大学数学学院,成都610064 [2]西华师范大学公共数学学院,南充637009

出　　处：《四川大学学报（自然科学版）》2021年第6期1-8,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11971094)。

摘　　要：在用有限元方法解偏微分方程时我们往往需要对质量矩阵求逆.我们对质量矩阵进行质量集中可以将得到的矩阵对角化,大大提高计算效率.本文针对一类求解二维线性粘弹性固体介质波传播问题的全离散杂交应力四边形有限元方法研究其质量集中格式,并利用位移插值节点为求积节点的Gauss-Lobatto数值积分方法来实现质量矩阵的对角化.数值算例验证了该方法的有效性.The inversion of mass matrix is often involved in solving partial differential equations by finite element method.Mass lumping can be used to improve computational efficiency by diagonalizing mass matrix with special numerical integration. In this paper, a fully discrete hybrid stress quadrilateral finite element method for wave propagation in viscoelastic solid media is presented. To realize the diagonalization of mass matrix, the Gauss-Lobatto numerical integration with displacement interpolation nodes as quadrature nodes is used. A numerical example is given to verify the performance of the method.

关 键 词：Maxwell模型 粘弹性波传播 杂交应力有限元 质量集中 

分 类 号：O241.82[理学—计算数学]