An -sided polygonal cell-node-based smoothed finite element method is proposed to analyze two-dimensional heat conduction problems. Through the gradient smoothing technique, the internal integral of the polygonal element is transformed into the boundary integral based on the smoothing domain, thus reducing the continuity requirement of the trial function, and only requiring the shape function value of the smoothing domain boundary calculated using the Wachspress coordinates. Therefore, when constructing the smoothed finite element form of the heat conduction problems, coordinate mapping is avoided, which greatly improves the computational efficiency. Furthermore, a new division of the cell-based smoothing domain is put forward to improve the accuracy of the solution, where the divisions of the node-based and cell-based smoothing domains are combined in background elements to form cell-node-based smoothing domains. Extensive numerical experiments are carried out to show that the current model performs better in the estimation of the accuracy of the solution, the computational cost, the equivalent energy, and the temperature gradient while maintaining the same precision as the polygonal finite element method (PFEM).

中文翻译：

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求解二维热传导问题的基于n边多边形单元节点的平滑有限元方法


提出了一种基于多边形单元节点的平滑有限元方法来分析二维热传导问题。通过梯度平滑技术，将多边形单元的内积分转化为基于平滑域的边界积分，从而降低了试探函数的连续性要求，只需要使用以下计算得到的平滑域边界的形函数值Wachspress 坐标。因此，在构造热传导问题的平滑有限元形式时，避免了坐标映射，大大提高了计算效率。此外，为了提高求解的精度，提出了一种新的基于单元的平滑域的划分，其中基于节点的平滑域和基于单元的平滑域的划分在背景元素中结合起来形成基于单元节点的平滑域。大量的数值实验表明，当前模型在求解精度、计算成本、等效能量和温度梯度的估计方面表现更好，同时保持与多边形有限元法（PFEM）相同的精度。