论文标题
HDGLAB：MATLAB中杂交不连续的Galerkin方法的开源实现
HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB
论文作者
论文摘要
本文介绍了HDGLAB，这是杂交不连续Galerkin（HDG）方法的开源MATLAB实现。主要目标是提供有关HDG方法的详细描述，以解决椭圆问题及其实现HDGLAB。最终，预计这将使计算工程社区更容易获得这种相对较新的高级离散方法。 HDGLAB介绍了在自由域中可以找到的HDG方法的其他实现中没有可用的一些功能。首先，它实现高阶多项式函数，直至9度，具有相同的间隔和fekete节点分布。其次，它支持两个维度和三个维度的弯曲的等级简单元素。第三，它支持非均匀度的多项式近似值，并提供了一种灵活的结构来设计程度适应性策略。最后，提供了与开源高阶网格发电机GMSH的接口，以促进其在实际工程问题上的应用。
This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems.
