A novel hybrid polygonal finite element is proposed for simulating the heat conduction in two-dimensional cellular materials based on the hybrid fundamental-solution-based finite element method (HFS-FEM). The proposed method assumes two independent temperature fields in the domain and boundary of the element, respectively. The intra-element temperature field is approximated by a combination of fundamental solutions satisfying the governing equation of the problem. The charge simulation method is introduced so that the required fundamental solution can be established for the domain with an arbitrarily-shaped hole. To satisfy the continuity condition between adjacent elements, a conforming frame temperature field is approximated by the conventional finite element interpolation functions. Combing two independent fields into the modified variational functional leads to the resultant finite element formulation avoiding the need for domain integration. Such boundary-type feature endows a great capability of constructing any polygonal element with different number of sides and makes a great flexibility in mesh generation. The accuracy and efficiency of HFS-FEM are demonstrated through three numerical examples which includes triangular, astroid and irregular hole elements.

基于混合基本解法（HFS-FEM），提出了一种新的混合多边形有限元，用于模拟二维蜂窝材料中的热传导。所提出的方法分别假设单元的域和边界中有两个独立的温度场。单元内温度场由满足问题控制方程的基本解的组合来近似。引入电荷模拟方法，可以为具有任意形状孔的域建立所需的基本解。为了满足相邻元素之间的连续性条件，通过传统的有限元插值函数来近似一致的框架温度场。将两个独立的域组合到修改后的变分泛函中，可以得到最终的有限元公式，从而避免了域积分的需要。这种边界型特征赋予了构造任何具有不同边数的多边形元素的能力，并且在网格生成方面具有很大的灵活性。HFS-FEM 的准确性和效率通过三个数值例子来证明，包括三角形、星状和不规则孔元素。