中文摘要：

运用多项式点插值法（PPIM）和径向基点插值法（RPIM）构造形函数，推导了适合于工程电磁场瞬态涡流问题的多项式基点插值边界无单元方法（BPPIM）和径向基点插值边界无单元方法（BRPIM），这两种方法的空间插值形函数满足Kronecker delta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，证实了两种方法的正确性和有效性，并对两种基类的点插值法进行了精度分析和比较．

英文摘要：

Boundary polynomial point interpolation mesh-free method （BPPIM） and boundary radial point interpolation mesh-free method （BRPIM） were presented, based on polynomial basis and radial basis respectively for transient eddy current analysis, and their interpolation shape functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column was set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM was analyzed as well.