一种适用于高频亥姆霍兹问题的迭代域分解、谱有限元方法，适用于非匹配网格
An iterative domain decomposition, spectral finite element method on non-conforming meshes suitable for high frequency Helmholtz problems
AI总结：
本文提出了一种高效的迭代方法，用于求解高频时谐散射问题的高精度解，通过局部多项式次数细化和非匹配网格细化，结合层次约束方程，提高了高频问题的求解效率。
摘要：
本文旨在描述一种高效的迭代方法，用于获得高频时谐散射问题的高精度解。该方法允许局部多项式次数细化和非匹配网格细化，包括每边多个悬挂节点。与全局组装有限元系统不同，我们描述了一种迭代域分解方法，可以使用大次数元素的元素级快速求解器。由于通过动量方程强制元素间连续性，所得到的约束方程是层次化的。我们证明，对于高频问题，应直接强制一部分这些约束，提供双亲域分解方法中的粗空间。该约束子集基于涉及网格尺寸和波数的色散准则选择。通过根据此准则增加粗空间的大小，域分解方法中的迭代次数仅弱依赖于波数。我们在此标准域分解测试问题上展示了这种收敛行为，并在论文结尾将该方法应用于二维电磁问题。这些例子包括通过透镜的波束定向、光子晶体波导，以及用于介电、完美电导体和电磁伪装散射体的雷达截面计算。
英文摘要：
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree and non-conforming mesh refinement, including multiple hanging nodes per edge. Rather than globally assemble the finite element system, we describe an iterative domain decomposition method which can use element-wise fast solvers for elements of large degree. Since continuity between elements is enforced through moment equations, the resulting constraint equations are hierarchical. We show that, for high frequency problems, a subset of these constraints should be directly enforced, providing the coarse space in the dual-primal domain decomposition method. The subset of constraints is chosen based on a dispersion criterion involving mesh size and wavenumber. By increasing the size of the coarse space according to this criterion, the number of iterations in the domain decomposition method depends only weakly on the wavenumber. We demonstrate this convergence behaviour on standard domain decomposition test problems and conclude the paper with application of the method to electromagnetic problems in two dimensions. These examples include beam steering by lenses and photonic crystal waveguides, as well as radar cross section computation for dielectric, perfect electric conductor, and electromagnetic cloak scatterers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
