Adaptive hp-Refinement for 2-D Maxwell Eigenvalue Problems: Method and Benchmarks
Adaptive hp-Refinement for 2-D Maxwell Eigenvalue Problems: Method and Benchmarks
复制标题
二维麦克斯韦特征值问题的自适应 hp 细化：方法和基准
DOI：
10.1109/tap.2022.3145473
复制
发表时间：
2022
影响因子：
5.7
通讯作者：
B. Notaroš
中科院分区：
文献类型：
--
作者：
J. Harmon;B. Notaroš
我们提出了一个应用程序的目标导向的自适应各向同性hp-细化的2-D麦克斯韦特征值问题。我们应用一个简化的目标为导向的误差表达式，以提高本征值的准确性，当与来自解决方案的指标相结合时，可以实现高度针对性的离散化调整。此外，我们引入了一个惠普细化/粗化优化器加上平滑估计细化分类和执行。这些增强产生具有成本效益的资源分配，达到极高的精度迅速甚至奇异特征函数的特征值。最后，我们提供了比现有数值参考值更准确的数值基准，并沿着了高阶模式的新基准，这将促进计算电磁学（PEM）中自适应性和hp有限元新方法的比较和开发。我们的实现是基于开源有限元库deal. II.
We present an application of goal-oriented adaptive isotropic hp-refinement for the 2-D Maxwell eigenvalue problem. We apply a simplified goal-oriented error expression for improving the accuracy of the eigenvalues, which, when combined with indicators derived from the solution, enables highly targeted discretization tuning. Furthermore, we introduce an hp-refinement/coarsening optimizer coupled with smoothness estimation for refinement classification and execution. These enhancements yield cost-effective resource allocations that reach extremely high accuracy rapidly even for eigenvalues of singular eigenfunctions. Finally, we provide numerical benchmarks more accurate than existing numerical reference values, along with new benchmarks for higher order modes that will facilitate the comparison and development of new approaches to adaptivity and hp finite elements in computational electromagnetics (CEM). Our implementation is based on the open-source finite element library deal.II.