The paper presents a meshfree technique based on the method of fundamental solutions (MFS) and the energy equation associated with the model, to optimize the location of source points. Over the years, the simplest way of distributing the source set has been on a fixed contour lying outside of the considered domain. In this study, a method automates the optimal placement of the source points with the help of the energy conservation equation. The implementation of the scheme is carried forward for the inverse Cauchy problem of heat conduction, and numerical results are provided to establish the new scheme as a superior alternative to MFS.

中文翻译：

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解决导热反柯西问题的新型无网格方案

本文提出了一种基于基本解法（MFS）和与模型关联的能量方程的无网格技术，以优化源点的位置。多年来，分发源集的最简单方法是位于所考虑域之外的固定轮廓上。在这项研究中，借助能量守恒方程，一种方法可以自动优化源点的位置。该方案的实现针对导热的柯西逆问题进行了推导，并提供了数值结果以建立新的方案，以替代MFS。