This paper presents computational algorithms that make it possible to overcome some difficulties in the numerical solving boundary value problems of thermal conduction when the solution domain has a complex form or the boundary conditions differ from the standard ones. The boundary contours are assumed to be broken lines (the 2D case) or triangles (the 3D case). The boundary conditions and calculation results are presented as discrete functions whose values or averaged values are given at the geometric centers of the boundary elements. The boundary conditions can be imposed on the heat flows through the boundary elements as well as on the temperature, a linear combination of the temperature and the heat flow intensity both at the boundary of the solution domain and inside it. The solution to the boundary value problem is presented in the form of a linear combination of fundamental solutions of the Laplace equation and their partial derivatives, as well as any solutions of these equations that are regular in the solution domain, and the values of functions which can be calculated at the points of the boundary of the solution domain and at its internal points. If a solution included in the linear combination has a singularity at a boundary element, its average value over this boundary element is considered.

中文翻译：

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线性组合算法：导热

本文提出了一种计算算法，当求解域的形式复杂或边界条件与标准条件的边界条件不同时，它可以克服数值求解导热边界值问题的一些困难。边界轮廓假定为虚线（2D情况）或三角形（3D情况）。边界条件和计算结果以离散函数的形式给出，其值或平均值在边界元素的几何中心给出。边界条件可以施加在流过边界元素的热流上，也可以施加在温度上，温度和热流强度在溶液域边界和内部的线性组合。边界值问题的解决方案以拉普拉斯方程及其偏导数的基本解以及这些方程在解域中有规律的解以及函数值的线性组合的形式给出可以在解域边界的边界点及其内部点进行计算。如果线性组合中包含的解在边界元素处具有奇异性，则考虑该边界元素上的平均值。