工程瞬态涡流问题的边界无单元方法求解

A boundary nodes-type mesh-free method for transient eddy current in engineering problems

以点插值方法构造形函数,推导了一种适合于求解工程电磁场瞬态涡流问题的边界点型无单元方法(BMFM),进行了详细的理论分析.与一般无单元方法以及边界元法构造形函数不同,BMFM对边界积分方程采用点插值法构造空间插值形函数,使空间插值形函数满足Kroneckerdelta条件,从而强加边界条件可以直接施加在边界点上.以金属长方柱的瞬态涡流分析作为数值算例证实了方法的正确性和有效性.

A boundary nodes-type mesh-free method (BMFM) for transient eddy based on point interpolation method (PIM) was presented, and the theoretical analysis of the BMFM given. Differing from the general mesh-less methods and the traditional boundary element methods (BEMs), the BMFM combines a point interpolation method (PIM) for construction of spatial interpolation functions with boundary integral formulation for the governing equations, thus the spatial interpolation functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed to the boundary nodes. An example of transient eddy current of a square metal column was set to prove the validity of the proposed method.