解弹性力学第二类边界积分方程的求积法与分裂外推

计算物理 ›› 2006, Vol. 23 ›› Issue (6): 706-712.

解弹性力学第二类边界积分方程的求积法与分裂外推

黄晋¹, 朱瑞², 吕涛²

1. 电子科技大学应用数学学院, 四川成都 610054;
2. 四川大学数学学院, 四川成都 610064

收稿日期:2005-07-04 修回日期:2005-12-05 出版日期:2006-11-25 发布日期:2006-11-25
作者简介:黄晋(1962-),男,四川广元,教授,博士,从事计算数学方面的研究.
基金资助:
国家自然科学基金(10711073)资助项目

A Quadrature Method and Splitting Extrapolation for Second-kind Boundary Integral Equations in Elasticity Problems

HUANG Jin¹, ZHU Rui², Lü Tao²

1. College of Applied Mathematics, University of Electronic & Science Technology of China, Chengdu 610054, China;
2. Mathematical College, Sichuan University, Chengdu 610064, China

Received:2005-07-04 Revised:2005-12-05 Online:2006-11-25 Published:2006-11-25

摘要/Abstract

摘要： 利用Sidi奇异求积公式,提出了解曲边多角形域上线性弹性力学第二类边界积分方程的求积法,即离散矩阵的每个元素的生成只需赋值不需计算任何奇异积分.通过估计离散矩阵的特征值和利用Anselone聚紧收敛理论,证明了近似解的收敛性;同时得到了误差的多参数渐近展开式;通过并行地解粗网格上的离散方程,利用分裂外推获得了高精度近似解和后验误差.

关键词: 线性弹性力学, 奇异积分方程, 求积法, 分裂外推, 后验误差, 多角形域

Abstract: With singular quadrature rules,a quadrature method for the second-kind boundary integral equations in linear elasticity problems on polygonal domains is proposed.The discrete matrix can be obtained with no Cauchy singular integral.With the collectively compact convergent theory,we establish a convergence theorem of approximation and get multivariate asymptotic expansions of error.Solving the discrete equations with coarse meshed partitions in paralle,high accurary approximations are obtained by the splitting extrapolation.A posterior error is derived.

Key words: linear elasticity problem, singular integral equation, splitting extrapolation, quadrature method, a posteriori error, polygonal region

中图分类号:

O413.1

黄晋, 朱瑞, 吕涛. 解弹性力学第二类边界积分方程的求积法与分裂外推[J]. 计算物理, 2006, 23(6): 706-712.

HUANG Jin, ZHU Rui, Lü Tao. A Quadrature Method and Splitting Extrapolation for Second-kind Boundary Integral Equations in Elasticity Problems[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 23(6): 706-712.

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