发表机构
Indian Institute of Technology Madras（印度马德拉斯理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种增强的脆性点法（FPM），利用广义有限差分构造不连续形状函数，结合数值通量修正，高效求解非均匀介质中的热传导界面问题，并通过基准测试验证其效率与鲁棒性。
AI 中文摘要
本文提出了脆性点法（FPM）的一种增强公式，这是一种真正的无网格方法，用于高效模拟涉及非均匀材料的二维微分方程中的隐式界面。所提出的框架消除了对专门数值积分技术的需求，并为求解界面问题提供了系统的数学基础。跨越界面的主变量和次变量中的不连续性通过FPM固有的不连续形状函数自然处理。与传统伽辽金方法不同，FPM采用通过广义有限差分方法构造的简单、局部、基于点的多项式试函数和检验函数。这些不连续函数绕过了标准伽辽金框架的连续性要求。为解决由不连续性导致的相应不一致性，我们融入了受不连续伽辽金方法启发的数值通量修正。所提出的方法通过多个基准问题进行验证，展示了其效率和鲁棒性。
英文摘要
This paper presents an enhanced formulation of the Fragile Points Method (FPM), a truly meshless approach for efficiently modeling implicit interfaces in two-dimensional differential equations involving non-homogeneous materials. The proposed framework eliminates the need for specialized numerical integration techniques and provides a systematic mathematical foundation for solving interface problems. Discontinuities in both primary and secondary variables across interfaces are naturally handled through the inherently discontinuous shape functions of FPM. Unlike conventional Galerkin methods, FPM employs simple, local, point-based polynomial trial and test functions constructed via a generalized finite difference approach. These discontinuous functions bypass the continuity requirements of standard Galerkin frameworks. To address the resulting inconsistency due to discontinuities, we incorporate numerical flux corrections inspired by the discontinuous Galerkin method. The proposed method is validated through several benchmark problems, demonstrating its efficiency and robustness.
