A numerical study of the pollution error and DPG adaptivity for long waveguide simulations
A numerical study of the pollution error and DPG adaptivity for long waveguide simulations
复制标题
长波导模拟污染误差和 DPG 适应性的数值研究
DOI：
10.1016/j.camwa.2020.03.024
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
L. Demkowicz
中科院分区：
文献类型：
--
作者：
Stefan Henneking;L. Demkowicz
高频波传播在声学、弹性动力学和电磁学中有许多重要的应用。不幸的是，这些问题的有限元离散化遭受显着的数值污染误差，随着波数的增加。控制这些误差是获得稳定、准确的方法的关键。我们研究了污染的影响，非常长的波导问题的背景下，强大的不连续彼得罗夫-伽辽金（DPG）有限元离散。我们的数值实验表明，污染主要有扩散效应，造成能量损失的DPG方法，而相位误差似乎不太显着。我们报告的三维矢量时间谐波麦克斯韦问题的波导超过8000个波长的结果。我们的结果证实了Melenk和Sauter（2011）对Helmholtz算子的Galerkin离散化的先前分析。此外，我们还讨论了多模光纤波导的自适应细化策略，其中传播的横模必须得到充分解决。我们的研究表明，适用性的DPG错误指标，这类问题。最后，我们说明了负载平衡的重要性，在这些模拟分布式内存并行计算。
High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these problems suffers from significant numerical pollution errors that increase with the wavenumber. It is critical to control these errors to obtain a stable and accurate method. We study the effect of pollution for very long waveguide problems in the context of robust discontinuous Petrov–Galerkin (DPG) finite element discretizations. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. We report results for 3D vectorial time-harmonic Maxwell problems in waveguides with more than 8000 wavelengths. Our results corroborate previous analysis for the Galerkin discretization of the Helmholtz operator by Melenk and Sauter (2011). Additionally, we discuss adaptive refinement strategies for multi-mode fiber waveguides where the propagating transverse modes must be resolved sufficiently. Our study shows the applicability of the DPG error indicator to this class of problems. Finally, we illustrate the importance of load balancing in these simulations for distributed-memory parallel computing.
影响因子：
1.3
作者：
Jaime Mora;L. Demkowicz
通讯作者：
Jaime Mora;L. Demkowicz
影响因子：
3.1
作者：
Jacob Badger;Stefan Henneking;L. Demkowicz
通讯作者：
Jacob Badger;Stefan Henneking;L. Demkowicz