多角形域上Robin问题的边界积分方程的求积法与分裂外推  

Splitting Extrapolations for Solving Boundary Integral Equations of Robin Problem on Polygons by Mechanical Quadrature Method

作　　者：黄晋[1] 吕涛[1] 申慧容 

机构地区：[1]四川大学数学学院,成都610064 [2]成都市水利水电职工大学,成都610016

出　　处：《燕山大学学报》2004年第2期137-140,共4页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(No.10171073)。

摘　　要：提出了解任意区域上Robin问题的边界积分方程的求积法。它拥有高精度,低复杂度。通过估计离散矩阵的特征值,证明了近似解的收敛性;同时,给出了误差的多参数奇次幂渐近展开式,利用分裂外推算法不仅得到了较高精度的近似解,而且获得了后验误差估计。算例证明了该方法的有效性。This paper presents mechanical quadrature method for solving BIE of Robin problems on an arbitrary region, which possesses a high accuracy and low computing complexities. Since multivariate asymptotic expansions of the approximate error with add power are shown, by means of splitting extrapolations we can not only make use of parallel algorithms to get higher precision approximations, but also obtain the a posteriori estimates. Numerical examples show the theoretical estimates.

关 键 词：多角形域 求积法 分裂外推 后验误差估计 ROBIN问题 

分 类 号：TB115[理学—数学]