Isogeometric analysis and hierarchical refinement for higher-order phase-field models
Isogeometric analysis and hierarchical refinement for higher-order phase-field models
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DOI：
10.1016/j.cma.2016.01.022
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发表时间：
2016-05-01
影响因子：
7.2
通讯作者：
Weinberg, K.
中科院分区：
文献类型：
--
作者：
Hesch, C.;Schuss, S.;Weinberg, K.
虽然在物理学和力学的高阶模型的兴趣增长，他们的数值模拟仍然构成了挑战，特别是对于任意形状的三维域。这一贡献提出了数学框架，以及在材料科学，断裂力学和扩散问题领域的不同问题的应用。所有的模型都需要至少C-1连续性，这就阻碍了标准有限元分析和局部网格细化的应用，在有限元框架中引入等几何分析（伊加）进行离散化使我们能够处理这些要求。此外，本文还提出了一种适用于一维、二维和三维模拟的基于细分投影的一般分层加密方案。这种技术允许在每一层上使用更精细的样条来增强近似空间，但保留了单位分割以及原始离散化的连续性。一个网，适应的热扩散模拟和计算的先验未知的裂纹扩展在不同的断裂模式强调了多功能性的分层精化方案(C)2016爱思唯尔B. V.保留所有权利。
While the interest in higher-order models in physics and mechanics grows, their numerical simulation still poses a challenge, especially for arbitrary shaped three-dimensional domains. This contribution presents the mathematical framework as well as the application to different problems in the field of material science, fracture mechanics and diffusion problems. All models under consideration require at least C-1 continuity, which prevents the application of standard finite element analysis and local mesh refinements.Introducing isogeometric analysis (IGA) for the discretization in a finite element framework enables us to deal with these requirements. Moreover, a general hierarchical refinement scheme based on a subdivision projection is presented here for one, two and three dimensional simulations. This technique allows to enhance the approximation space using finer splines on each level but preserves the partition of unity as well as the continuity properties of the original discretization.Using this mathematical framework, the improved convergence of a Kuramoto-Sivashinsky model, a mesh-adapted thermal diffusion simulation and computations of a priori unknown crack propagation in different fracture modes underline the versatility of the presented hierarchical refinement scheme. (C) 2016 Elsevier B.V. All rights reserved.