Boundary Element Methods for Next-Gen Devices in TeraHertz Technology

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.

Academic Impact

This project will have impact on the computational electromagnetics scientific community. Achieving the objectives will remove long standing problems that limit further development.

This project is of great relevance to the research of Prof Amalia Patane, who succeeded in the fabrication of semi-conductor supperlattice devices for TeraHertz communication. This simulation tool developed in this project will enable them to design a cavity and wave guide that will increase the efficiency of their TeraHertz source.

Given the transferable nature of techniques in computational electromagnetics the results of this project are relevant to researchers in other fields as elastodynamics, acoustics, fluid dynamics, geology, climate modelling, and medical imaging.

The academic impact of this project will extend to the international collaborators of the PI in the US, France, Belgium, Saudi-Arabia, Turkey, and Finland. The outcomes can be implemented in research into brain imaging, wearable devices, inverse problems, and stochastic modelling.

Dr Cools will organise short courses at conferences and symposia where the results of this project and the techniques used in this project will be taught to graduate students in boundary integral equation based modelling.

Industrial Impact

The outcomes of this project are of direct interest to the industrial partner CST. In particular the techniques developed can significantly augment the applicability of their range of simulation tools and increase the potential market for their product.

The outcomes are of importance also to a broader range of simulation software developers and industrial users of that software. Not only CST but also companies such as ABAQUS, ANSYS, Keysight Technologies, EMSS-FEKO, and COMSOL would benefit from the advances in boundary element methods. Users of simulation software in the automotive industry, automated control, communications, aerospace, and defence such as Selex, Thales, Dassault, ARM Holdings, Bombardier, and Rolls Royce will benefit from the increased capabilities of available tools and the increased expertise at the George Green Institute for Electromagnetics Research.

Measures for protection and exploitation of intellectual property will be undertaken in consultation with the Business Development Team of the Faculty of Engineering. The IP resulting from this project might be licensed or sold to the industrial partner or other industrial beneficiaries or it can be used to increase the visibility of the research group by incorporating it in an easy to use open source software package.

Impact Activities

The impact activities will be coordinated by the PI Dr Kristof Cools, the head of the electromagnetics group Prof Trevor Benson, the industrial partner CST as represented by lead developer Dr Richard Scaramuzza, and the academic advisor Prof Amalia Patane.

Conferences that are frequented by simulation software developers and their customers will be used as opportunities to engage with external stakeholders and inform them about the research findings. Demonstrations of project results will provide researchers and delegates from industry with a tangible proof of capability and benefits.

Meetings with CST to present outcomes and discuss project strategy and steering will be held. The input of CST into this project is extremely valuable. The Nottingham branch of CST is conveniently located with respect to the University of Nottingham central campus.

This project will benefit from the input of international collaborators such as Prof Francesco Andriulli at TELECOM Bretagne in France. Visits to his research group are planned in the project to present research output, discuss further research avenues, and plan future collaborations in subsequent projects jointly funded by the national research councils of the UK, and other countries.