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The tetrahedral finite cell method: higher-order immersogeometric analysis on adaptive non-boundary-fitted meshes

机译:四面体有限元法:自适应非边界拟合网格的高阶沉浸几何分析

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摘要

The finite cell method (FCM) is an immersed domain finite element method that combines higher-order non-boundary-fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Due to its ability to improve the geometric resolution of intersected elements, it can be characterized as an immersogeometric method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher-order non-boundary-fitted tetrahedral meshes, based on a reformulation of the octree-based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for h- and p-refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase-field fracture analysis of a human femur bone.
机译:有限元方法(FCM)是一种沉浸域有限元方法,它结合了高阶非边界拟合网格,Dirichlet边界条件的弱执行力以及基于递归细分的自适应正交。由于其具有提高相交元素的几何分辨率的能力,因此可以将其表征为沉浸几何方法。在本文中,我们基于对四面体元素基于八叉树的细分算法的重新表述,将迄今为止仅用于笛卡尔六面体元素的FCM扩展到了高阶非边界拟合四面体网格。我们表明,在浸没几何学意义上,所得的TetFCM方案是完全准确的,也就是说,如果以足够的精度解析沉浸的几何体,则解决方案领域将达到h和p细化的最优和指数收敛速度。 TetFCM可以利用四面体元素的自然能力在三个维度上进行局部网格细化。对人股骨的浸入几何相场断裂分析表明了其适用于尖锐梯度和高度局部化特征的问题。

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