Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics
Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics
复制标题
无缝集成全局狄利克雷到诺伊曼边界条件和变换电磁学的谱元素
DOI：
10.1016/j.cma.2015.12.020
复制
发表时间：
2015-05
影响因子：
7.2
通讯作者：
Baile Zhang
中科院分区：
文献类型：
--
作者：
Zhiguo Yang;Li-Lian Wang;Zhijian Rong;Bo Wang;Baile Zhang
本文提出了一种求解各向异性介质中一般二维Helmholtz方程的谱单元方法，特别是在变换电磁场中产生的多边形隐形斗篷、聚光体和圆形旋转体的精确模拟中得到了应用。在实践中，我们采用以Dirichlet-to-Neumann(DTN)映射为特征的透明边界条件(TBC)来将无界区域中的波传播简化为有界区域。然后，我们引入了一种半解析技术来将全局TBC和局部曲线元素无缝地结合在一起，该技术是通过一种新的元素映射和精确计算谱元素网格上全局傅里叶系数的解析公式来实现的；从TE的角度出发，通过对麦克斯韦方程的奇异坐标变换，设计了一种隐身斗篷，使得覆盖区域的各向异性材料覆盖在斗篷区域，使外部观察者看不到里面的任何物体。一个重要的问题是在隐形区域的外边界施加适当的条件，即隐形边界条件，以实现完美的隐身。根据Yang和Wang(2015)的精神，我们从与奇异变换相关的基本极点条件出发，提出了新的多边形隐身斗篷的CBC。这允许隐形区域内部和外部的控制方程的解耦。有了这个高效的谱元素解算器，我们可以研究在理想多边形斗篷的覆盖层中放置一些缺陷和有损或色散介质时的有趣现象。
In this paper, we present an efficient spectral-element method (SEM) for solving general two-dimensional Helmholtz equations in anisotropic media, with particular applications in accurate simulation of polygonal invisibility cloaks, concentrators and circular rotators arisen from the field of transformation electromagnetics (TE). In practice, we adopt a transparent boundary condition (TBC) characterised by the Dirichlet-to-Neumann (DtN) map to reduce wave propagation in an unbounded domain to a bounded domain. We then introduce a semi-analytic technique to integrate the global TBC with local curvilinear elements seamlessly, which is accomplished by using a novel elemental mapping and analytic formulas for evaluating global Fourier coefficients on spectral-element grids exactly.From the perspective of TE, an invisibility cloak is devised by a singular coordinate transformation of Maxwell’s equations that leads to anisotropic materials coating the cloaked region to render any object inside invisible to observers outside. An important issue resides in the imposition of appropriate conditions at the outer boundary of the cloaked region, i.e., cloaking boundary conditions (CBCs), in order to achieve perfect invisibility. Following the spirit of Yang and Wang (2015), we propose new CBCs for polygonal invisibility cloaks from the essential “pole” conditions related to singular transformations. This allows for the decoupling of the governing equations of inside and outside the cloaked regions. With this efficient spectral-element solver at our disposal, we can study the interesting phenomena when some defects and lossy or dispersive media are placed in the cloaking layer of an ideal polygonal cloak.
登录
查看更多内容
影响因子：
1.3
作者：
D. Werner;D. Kwon
通讯作者：
D. Werner;D. Kwon
DOI：
10.1093/acprof:oso/9780198508885.001.0001
发表时间：
2003-06
期刊：
Proceedings of the 2006 IEEE/ASME Joint Rail Conference
影响因子：
--
作者：
P. Monk
通讯作者：
P. Monk
DOI：
10.1016/0045-7825(92)90109-w
发表时间：
1992-05
期刊：
Applied Mechanics and Engineering
影响因子：
--
作者：
I. Harari;T. Hughes
通讯作者：
I. Harari;T. Hughes
影响因子：
4.1
作者：
C. Ronchi;R. Iacono;P. Paolucci
通讯作者：
C. Ronchi;R. Iacono;P. Paolucci
DOI：
10.1090/conm/754/15143
发表时间：
2019-10
期刊：
ArXiv
影响因子：
--
作者：
P. Monk;Yangwen Zhang
通讯作者：
P. Monk;Yangwen Zhang