A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM
A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM
复制标题
完全各向异性 hp 细化的叠加细化方法可提高 CEM 效率
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
B. Notaroš
中科院分区：
文献类型：
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作者：
Jeremiah Corrado;J. Harmon;B. Notaroš
本文提出了一种在四边形网格上的完全各向异性hp-自适应性在计算电磁学（CEM）中的应用。传统上，各向异性的h-自适应一直难以实现的连续Galerkin公式的约束下，然而，细化叠加（RBS）方便各向异性网格自适应非常容易。我们提出了一个一般性的讨论与实施完全各向异性的Hp细化，以及深入讨论的实际考虑2-D有限元的理论考虑。此外，为了证明各向异性的h-和p-细化的好处，我们研究了2-D麦克斯韦本征值问题作为测试用例。数值结果表明，完全各向异性的细化可以提供显着的效率增益，即使在奇异行为的存在下，大大减少了相同的精度与各向同性HP-细化所需的自由度的数量。这有助于加强RBS的相关性和充分的hp适应性，以广泛的学术和工业应用在CEM
We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM
三维问题的多级 hp 方法：任意悬挂节点动态变化的高阶网格细化
影响因子：
7.2
作者：
N. Zander;T. Bog;M. Elhaddad;F. Frischmann;S. Kollmannsberger;E. Rank
通讯作者：
E. Rank
多级HP自适应：高阶网格自适应，没有约束悬挂节点的困难
影响因子：
4.1
作者：
Zander ;Kollmannsberger ;Schillinger
通讯作者：
Schillinger