Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 397327, 9 pages
http://dx.doi.org/10.1155/2014/397327
Research Article

A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains

1Institute of Engineering Mechanics, Shandong Jianzhu University, Jinan 250101, China
2Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China

Received 15 December 2013; Accepted 8 March 2014; Published 23 April 2014

Academic Editor: Miaojuan Peng

Copyright © 2014 Zhao-Qing Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method.