Abstract This article presents a novel numerical method for steady-state thermal simulation. This method firstly solves the heat flux efficiently by applying the loop-tree basis functions. Then, the temperature is obtained by finding solutions of the gradient equation. The half boundary Rao-Wilton-Glisson (HBRWG) basis functions are employed for handling arbitrary boundary conditions. In addition, the triangulation-based interpolation technique is utilized to interpolate temperature profile with obtained results in post-processing. Three examples with mixed boundary conditions are studied to validate the accuracy of proposed method for simulating steady-state thermal problems. Numerical results show that our method has a good accuracy and is well capable of handling arbitrary boundary conditions.

中文翻译：

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一种基于循环树和HBRWG基函数的稳态热模拟新数值方法

摘要 本文提出了一种新的稳态热模拟数值方法。该方法首先通过应用循环树基函数有效地求解热通量。然后，通过找到梯度方程的解来获得温度。半边界 Rao-Wilton-Glisson (HBRWG) 基函数用于处理任意边界条件。此外，利用基于三角测量的插值技术在后处理中利用获得的结果对温度曲线进行插值。研究了三个具有混合边界条件的例子，以验证所提出的用于模拟稳态热问题的方法的准确性。数值结果表明，我们的方法具有良好的精度，并且能够很好地处理任意边界条件。