An improved boundary element-free method (IBEFM) for two-dimensional potential problems

• 来源期刊: 中国物理B（英文版）
• 关键词: moving least-squares approximation interpolating moving least-squares method mesh-less method improved boundary element-free method potential problem
• 年，卷（期）: 2009,（10）
• 页码范围: 4065-4073
• 页数: 9页
• 语种: 英文

摘要

The interpolating moving least-squares (IMLS) method is discussed first in this paper. And the formulae of theIMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method (BEFM),combining the boundary integral equation (BIE) method with the IMLS method, the improved boundary element-freemethod (IBEFM) for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFMare obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does notsatisfy the property of the Kronecker & function. This is a problem of the BEFM, and must be solved theoretically.In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundaryconditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on theIMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the realsolution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greatercomputational precision. Some numerical examples are presented to demonstrate the method.