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Global-element-based free element method for solving non-linear and inhomogeneous heat conduction problems

机译：基于全局元素的自由元方法，用于解决非线性和非均匀导热问题

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In this paper, a family of global elements (GEs) are constructed for modeling geometries and representing physical variables, based on a set of complete basis functions formulated in terms of normalized global coordinates. The main benefits of using GEs are that the elemental nodes can be distributed and numbered in an arbitrary manner and the global spatial partial derivatives of geometries and physical variables appearing in the governing equations of engineering problems can be directly derived. Based on the constructed GEs and their spatial derivatives of global shape functions, a simple and robust new numerical method, called as the Global-Element-based FRee Element Method (GEFREM), is proposed for solving general two-dimensional heat conduction problems. GEFREM inherits the advantages of the finite element method, mesh free method and free element method. A detailed description of GEFREM for solving general non-linear and inhomogeneous heat conduction problems will be presented in the paper and a number examples are given to verify the correctness and demonstrate the potential of the proposed method.
机译：在本文中，基于以归一化的全局坐标表示的一组完整基函数，构造了一组全局元素（GE）用于建模几何并表示物理变量。使用GE的主要好处是，可以以任意方式对元素节点进行分布和编号，并且可以直接导出出现在工程问题的控制方程中的几何形状和物理变量的全局空间偏导数。基于构造的GE及其全局形状函数的空间导数，提出了一种简单而强大的新数值方法，称为基于全局元素的FRee元素方法（GEFREM），用于解决一般的二维热传导问题。 GEFREM继承了有限元法，无网格法和自由元法的优点。本文将介绍GEFREM解决一般非线性和非均匀热传导问题的详细说明，并给出一些例子，以验证该方法的正确性并证明该方法的潜力。

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