High-order finite elements for the solution of Helmholtz problems
High-order finite elements for the solution of Helmholtz problems
复制标题
DOI：
10.1016/j.compstruc.2017.06.010
复制
发表时间：
2017-10
影响因子：
4.7
通讯作者：
K. Christodoulou;O. Laghrouche;M. S. Mohamed;J. Trevelyan
中科院分区：
文献类型：
--
作者：
K. Christodoulou;O. Laghrouche;M. S. Mohamed;J. Trevelyan
本文研究了两种求解Helmholtz方程所支配的二维波动问题的高阶有限元模型。研究了在单位分解有限元方法中发展起来的平面波富集有限元和基于高阶拉格朗日多项式的有限元。在后一种模型中，采用了切比雪夫-高斯-洛巴托节点分布，这种方法通常被称为谱单元法。这两种策略分别是PUFE和SEM，目前的研究提供了它们在解决特征维度是波长的倍数的短波问题方面的比较数据。所考虑的试验算例包括刚性圆柱体的波浪散射、瞬逝波情况以及具有刚性壁面的管道中波的传播。评估了这两种方法在提高扫描电子显微镜有序度和PUFE富集度方面的准确性。还比较了条件化、离散化程度、存储位置总数和非零条目总数。
In this paper, two high-order finite element models are investigated for the solution of two-dimensional wave problems governed by the Helmholtz equation. Plane wave enriched finite elements, developed in the Partition of Unity Finite Element Method (PUFEM), and high-order Lagrangian-polynomial based finite elements are considered. In the latter model, the Chebyshev-Gauss-Lobatto nodal distribution is adopted and the approach is often referred to as the Spectral Element Method (SEM). The two strategies, PUFEM and SEM, were developed separately and the current study provides data on how they compare for solving short wave problems, in which the characteristic dimension is a multiple of the wavelength. The considered test examples include wave scattering by a rigid circular cylinder, evanescent wave cases and propagation of waves in a duct with rigid walls. The two approaches are assessed in terms of accuracy for increasing SEM order and PUFEM enrichment. The conditioning, discretization level, total number of storage locations and total number of non-zero entries are also compared.