The finite cell method for polygonal meshes: poly-FCM
The finite cell method for polygonal meshes: poly-FCM
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DOI：
10.1007/s00466-016-1307-x
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发表时间：
2016-06
影响因子：
4.1
通讯作者：
S. Duczek;U. Gabbert
中科院分区：
文献类型：
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作者：
S. Duczek;U. Gabbert
在本文中，我们将有限单元法（FCM）的二维版本（迄今为止仅用于结构化四边形网格）扩展到非结构化多边形离散化。为此，对基于自适应四叉树的数值积分技术进行了重新表述，并引入了广义重心坐标的概念。我们表明，当且仅当结构的几何结构得到充分解决时，所得到的多边形（多）FCM方法保持最佳收敛率。该方法的主要优点是继承了多边形有限元的局部网格细化和过渡单元（如无挂节点的四叉树网格）构造的能力。通过静态和动态情况下的几个基准问题，说明了这些特性以及poly-FCM的性能。
In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.