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

作者：Wang, Zhao-Qing; Li, Shuchen^*; Ping, Yang; Jiang, Jian; Ma, Teng-Fei

来源：Mathematical Problems in Engineering, 2014, 2014: 397327.

DOI：10.1155/2014/397327

• FREE GALERKIN METHOD
• FICTITIOUS-DOMAIN
• EQUATIONS
• TREFFTZ

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.

• 出版日期2014
• 单位山东大学; 山东建筑大学; 中国地震局工程力学研究所