We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and spectral content of these sources are developed and numerically tested using Finite Element Mesh simulations. The resulting framework for heat source reconstruction problems, which are ill-posed inverse problems, seems promising and warrants for future research. Possible fields of application for our work are material testing, to detect manufacturing defects, and medical imaging to detect abnormal health conditions.

中文翻译：

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使用解析正向模型检测时变热源

我们为静态和时变点状热源提供了一个简单的解析点源模型，并给出了求解第三维热方程的所得温度曲线。开发了用于检测这些源的位置和光谱含量的简单算法，并使用有限元网格仿真对其进行了数值测试。由此产生的热源重构问题框架，是不适当地提出的反问题，似乎很有希望，并有待进一步研究。我们的工作可能的应用领域是材料测试，检测制造缺陷以及医学成像以检测异常健康状况。