Boundary Element Methods for Next-Gen Devices in TeraHertz Technology

太赫兹技术下一代器件的边界元方法

• 批准号: EP/M025217/1
• 负责人: Kristof Cools
• 金额: $ 12.66万
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2015
• 资助国家: 英国
• 起止时间: 2015 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FM025217%2F1
• 关键词: Boundary; Element; Methods; Next; Gen

Today's telecommunication technology is based on either electronics or photonics. Electronic devices operate in the MegaHertz to GigaHertz frequency region, whereas photonic devices operate in the TeraHertz region. Recently, there has been growing interest into devices that can operate in the TeraHertz region. They offer exciting new possibilities in communication, biomedical sensing, security, and system identification. The design of TeraHertz devices is challenging because thes devices are inherently multi-scale and contain many materials, often are arranged in complex configurations. By enabling the modelling of these devices this project contributes to the TeraHertz priority defined within the growing RF and Microwave Devices research area of the EPSRC.The boundary element method (BEM) is very popular in electronic and photonic design because it provides excellent accuracy and efficiency. The BEM, despite its many advantages is limited by the efficiency of the iterative methods that are being used to solve the underlying linear system. The solution time required by iterative methods is proportional to the number of unknowns and the number of iterations required. The number of iterations in turn is proportional to the condition number of the linear system, which unfortunately grows very fast with the number of unknowns. If small details are present or if a highly accurate solution is required, the number of unknowns can run in the millions, with solution times that can be in the order of weeks. This problem is exacerbated in the presence of complex geometries and materials with wildly varying properties, exactly the features found in novel opto-electronic devices for operation in the TeraHertz region.Solutions to this so-called dense grid breakdown come under the form of preconditioners: rather than solving Ax=b, both sides are multiplied with a preconditioner, resulting in the system PAx=Pb. The preconditioner is chosen such that the matrix PA has a much smaller condition number and as a result can be solved very efficiently. For the BEM the so-called Calderon preconditioner is an extremely efficient method and speeds up the solution time by a factor of ten or more. It is based on the self-regularising property of the single layer potential operator T: the operator TT turns out to be very well-conditioned. Calderon Preconditioning is highly efficient because it explicitly leverages the underlying physics of the system. The key to applying Calderon preconditioners in BEM is the identification of a dual finite element space. These spaces exist for simple open and closed surfaces but for more general geometries they remained elusive. Recent research conducted with my research team has resulted in the description of a dual finite element space that can be used as the basis of a Calderon preconditioner for the scattering by a conducting T-junction. Numerical experiments show that this method is highly efficient. These preliminary results provide the direct basis of the work proposed here.In this project a BEM solver will be created that is flexible enough to model scattering by very complex TeraHertz devices. This solver will be optimised by extended the Calderon preconditioning approach to this general context by constructing the correct dual finite element spaces. In order to further extend the solver's applicability, it will be parallelised to scale perfectly with the design complexity. This solver will be verified by comparison with results from the industrial partner CST and it will be applied to the design of TeraHertz cavities for semi-conductor supperlattice sources that are developed in the School of Physics and Astronomy at the University of Nottingham.

当今的电信技术基于电子或光子学。电子设备在Megahertz到Gigahertz频率区域运行，而光子设备在Terahertz区域运行。最近，人们对可以在Terahertz地区运行的设备越来越兴趣。他们在沟通，生物医学感应，安全性和系统识别方面提供了令人兴奋的新可能性。 Terahertz设备的设计具有挑战性，因为这些设备本质上是多尺度的，并且包含许多材料，通常以复杂的配置布置。通过启用这些设备的建模，该项目有助于在EPSRC的不断增长的RF和微波设备研究领域定义的Terahertz优先级。边界元素方法（BEM）在电子和光子设计中非常流行，因为它提供了出色的准确性和效率。尽管BEM具有许多优势，但受到迭代方法的效率的限制，该方法用于解决基础线性系统。迭代方法所需的解决方案时间与未知数和所需的迭代次数成正比。迭代的数量依次与线性系统的条件数量成正比，不幸的是，随着未知数的数量，该数量的生长非常快。如果存在较小的细节或需要高度准确的解决方案，则可以在数百万美元中运行的未知数数量，而解决方案时间可以在数周的时间内进行。 This problem is exacerbated in the presence of complex geometries and materials with wildly varying properties, exactly the features found in novel opto-electronic devices for operation in the TeraHertz region.Solutions to this so-called dense grid breakdown come under the form of preconditioners: rather than solving Ax=b, both sides are multiplied with a preconditioner, resulting in the system PAx=Pb.选择预处理程序，以使矩阵PA的条件数要小得多，因此可以非常有效地求解。对于BEM而言，所谓的Calderon预处理是一种极其有效的方法，并将解决方案时间加快了十倍或更多。它基于单层电位运算符的自我调节属性t：运算符TT的条件非常好。 Calderon预处理非常有效，因为它明确利用了系统的基本物理。在BEM中应用Calderon预调节器的关键是识别双有限元空间。这些空间存在于简单开放和封闭的表面，但对于更一般的几何形状，它们仍然难以捉摸。与我的研究团队进行的最新研究导致了对双有限元空间的描述，该空间可以用作Calderon预处理的基础，用于通过导电T型结的散射。数值实验表明该方法高效。这些初步结果提供了此处提出的工作的直接基础。在该项目中，将创建一个BEM求解器，该求解器足够灵活，可以通过非常复杂的Terahertz设备来建模散射。该求解器将通过构造正确的双重有限元元素空间来通过扩展到这种一般环境的Calderon预处理方法来优化该求解器。为了进一步扩展求解器的适用性，它将平行于设计复杂性完美缩放。该求解器将通过与工业合作伙伴CST的结果进行比较来验证，并将其应用于在诺丁汉大学物理与天文学学院开发的半导体晚餐来源的Terahertz腔设计。

项目成果

An enriched RWG basis for enforcing global current conservation in EM modelling of capacitance extraction

丰富的 RWG 基础，用于在电容提取的 EM 建模中实施全局电流守恒

• DOI: 10.1109/iceaa.2017.8065531
• 发表时间: 2017
• 作者: Lasisi S

Mixed Discretization of the Time-Domain MFIE at Low Frequencies

低频时域 MFIE 的混合离散化

• DOI: 10.1109/lawp.2017.2651045
• 发表时间: 2017
• 期刊: IEEE Antennas and Wireless Propagation Letters
• 影响因子: 4.2
• 作者: Ulku H

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

• DOI: 10.1016/j.jcp.2016.08.002
• 发表时间: 2016-11
• 期刊: J. Comput. Phys.
• 作者: D. Simmons;K. Cools;P. Sewell

On a Low-Frequency and Refinement Stable PMCHWT Integral Equation Leveraging the Quasi-Helmholtz Projectors

• DOI: 10.1109/tap.2017.2738061
• 发表时间: 2017-08
• 期刊: IEEE Transactions on Antennas and Propagation
• 影响因子: 5.7
• 作者: Y. Beghein;R. Mitharwal;K. Cools;F. Andriulli

Spectral and algorithmic strategies for penetrable scatterers on simply and non-simply connected geometries

• DOI: 10.1109/iceaa.2017.8065629
• 发表时间: 2017-09
• 期刊: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA)
• 作者: Y. Beghein;R. Mitharwal;K. Cools;F. Andriulli