The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. RPIMC is an efficient purely meshfree method where the solution of the field variable is obtained through collocation. The field function and its gradient are both interpolated (mixed collocation approach) leading to reduced C-continuity requirement compared to strong-form collocation schemes. The accuracy of RPIMC was evaluated in heat conduction benchmark problems and compared against the Meshless Local Petrov–Galerkin Mixed Collocation (MLPG-MC) method and the Finite Element Method (FEM). These three methods were subsequently applied to solve electrical propagation in a cardiac tissue slab and a biventricular geometry. In benchmark problems, RPIMC achieved high accuracy, of the same order as FEM, and always higher than MLPG-MC due to the delta Kronecker property of RPIMC. In solving cardiac electrical propagation, RPIMC rendered activation time maps similar to those of FEM, with an improved performance compared to MLPG-MC. As a conclusion, RPIMC is shown to be a promising meshfree alternative to FEM for transient diffusion problems.

本文针对扩散问题的瞬态分析，提出了一种径向点插值混合搭配（RPIMC）方法。RPIMC是一种有效的纯无网格方法，其中通过并置获得字段变量的解。场函数及其梯度均被插值（混合搭配方法），从而降低了C-连续性要求与强形式的搭配方案相比。在导热基准问题中评估了RPIMC的准确性，并与无网格局部Petrov-Galerkin混合搭配（MLPG-MC）方法和有限元方法（FEM）进行了比较。随后将这三种方法用于解决心脏组织平板和双心室几何形状中的电传播。在基准测试问题中，由于RPIMC的Kronecker特性，RPIMC达到了与FEM相同数量级的高精度，并且始终高于MLPG-MC。在解决心脏电传播方面，RPIMC提供了类似于FEM的激活时间图，与MLPG-MC相比，性能得到了改善。总之，对于瞬态扩散问题，RPIMC被证明是一种有前途的无网格替代FEM的方法。