Two-dimensional singular vector elements for finite-element analysis
Two-dimensional singular vector elements for finite-element analysis
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DOI：
10.1109/22.660984
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发表时间：
1998-02
影响因子：
4.3
通讯作者：
Z. Pantic-Tanner;J. S. Savage;D. Tanner;A. Peterson
中科院分区：
文献类型：
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作者：
Z. Pantic-Tanner;J. S. Savage;D. Tanner;A. Peterson
有限元方法在分析含有尖锐边缘且电磁场奇异的几何问题时，收敛速度较慢。通过引入奇异单元来模拟解析预测的奇异行为，可以提高方法的收敛速度。许多作者已经开发出与标量有限元兼容的奇异单元。在本文中，我们提出了一种新的奇异单元，它与基于边的矢量有限元相兼容，在保持有限元方程稀疏性的同时，可以处理任何阶奇性。基于边的奇异单元更准确地模拟了奇异场，因此需要更少的未知数，同时避免在数值解中引入虚假模式。数值结果表明，有限元方法的收敛速度有了明显的提高。
The finite-element method (FEM) exhibits a reduced convergence rate when used for the analysis of geometries containing sharp edges where the electromagnetic field is singular. The convergence of the method can be-improved by introducing singular elements that model analytically predicted singular behavior. A number of authors have developed singular elements that are compatible with the scalar FEM. In this paper, we propose a new singular element that is compatible with edge-based vector finite elements and can cope with any order of singularity while preserving the sparsity of the FEM equations. Edge-based singular elements more correctly model singular fields and thus require fewer unknowns, while avoiding the introduction of spurious modes in the numerical solution. Numerical results verify that the convergence of the FEM is significantly improved.