The Radial Point Interpolation Mixed Collocation (RPIMC) method is proposed in this paper for transient analysis of diffusion problems. RPIMC is an efficient purely meshless 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 method's accuracy is evaluated in heat conduction benchmark problems. The RPIMC convergence is compared against the Meshless Local Petrov-Galerkin Mixed Collocation (MLPG-MC) method and the Finite Element Method (FEM). Due to the delta Kronecker property of RPIMC, improved accuracy can be achieved as compared to MLPG-MC. RPIMC is proven to be a promising meshless alternative to FEM for transient diffusion problems.

中文翻译：

---

求解瞬态扩散问题的径向点插值混合搭配（RPIMC）方法

本文提出了径向点插值混合搭配（RPIMC）方法用于扩散问题的瞬态分析。RPIMC 是一种高效的纯无网格方法，其中场变量的解是通过搭配获得的。场函数及其梯度都是内插的（混合搭配方法），与强形式搭配方案相比，减少了 $C$-连续性要求。在热传导基准问题中评估了该方法的准确性。将 RPIMC 收敛与无网格局部 Petrov-Galerkin 混合搭配 (MLPG-MC) 方法和有限元方法 (FEM) 进行比较。由于 RPIMC 的 delta Kronecker 特性，与 MLPG-MC 相比，可以实现更高的精度。RPIMC 被证明是一种有前途的无网格替代 FEM 的瞬态扩散问题。