Abstract In the first part of this two-paper series, a new computational approach is presented for analyzing transient heat conduction problems in anisotropic nonhomogeneous media. The approach consists of a truly meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. In the present article, extensive numerical results are provided as validations, followed by a discussion on the recommended computational parameters. The FPM + LVIM approach shows its capability in solving 2 D and 3 D transient heat transfer problems in complex geometries with mixed boundary conditions, including preexisting cracks. Both functionally graded materials and composite materials are considered. It is shown that, with appropriate computational parameters, the FPM + LVIM approach is not only accurate, but also efficient, and has reliable stability under relatively large time intervals.

中文翻译：

---

一种新的无网格“脆弱点法”和各向异性非均匀介质中一般瞬态热传导的局部变分迭代法。第二部分：验证和讨论

摘要 在本系列两篇论文的第一部分中，提出了一种新的计算方法，用于分析各向异性非均匀介质中的瞬态热传导问题。该方法包括用于空间离散化的真正无网格脆弱点方法 (FPM) 和用于时间离散化的局部变分迭代 (LVI) 方案。在本文中，提供了广泛的数值结果作为验证，然后讨论了推荐的计算参数。FPM + LVIM 方法显示了其在具有混合边界条件（包括预先存在的裂纹）的复杂几何形状中解决 2D 和 3D 瞬态传热问题的能力。考虑了功能梯度材料和复合材料。结果表明，在适当的计算参数下，