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.

Electromagnetic modelling is an essential tool for electromagnetic compatibility characterisation of electrical equipment. All electrical equipment must satisfy international standards for electromagnetic compatibility (EMC) to ensure that it does not interfere with other equipment or is susceptible to external interference. The use of simulation software greatly reduces the design and development of new equipment that confirms compliance to EMC standards, so it is widely used throughout the electrical industry. The increasing processor clock signal speeds and the decreasing size of electronic devices has made electromagnetic simulation very demanding. It is not possible to fully model the complexity of electronic devices with full 3D electromagnetic simulators. Some form of simplification of the electronic devices is required. A recent EPSRC funded project by the George Green Institute for Electromagnetics Research has developed a way of characterising the electromagnetic emissions from printed circuit boards (PCBs) using near field scan data so that a simplified model of their behaviour can be constructed. The produced models have been demonstrated to be suitable for use in electromagnetic simulators. This work was very successful and achieved all the project objectives, but was only demonstrated on simple PCB structures and in the frequency domain. For this method to be fully incorporated in the industrial sector, however, it needs to encompass all common PCB structures, their interconnects and be extended into a time domain approach. This proposal will research extending the techniques developed so far using near field scans of PCBs so that it can provide simplified models of all common types of PCBs and include their interconnects and a way of combining their characteristics into complete system models. The work will also look at ways of extending the method into the time domain. In this was it is hoped that models suitable for use in full 3D electromagnetic simulators can be developed to enable engineers to provide EMC characterisation at the design stage.

Electronic consumer goods and internet-enabled smart infrastructures require highly integrated miniature electronic systems. One of the main problem with this miniaturisation is that unwanted interactions can arise between different components. Depending on the rate of change of currents within electronic components, these components radiate electromagnetic (EM) waves which can couple into other parts of the structure and can cause interferences. Controlling electromagnetic interferences within electronic devices is becoming an increasingly important challenge. Digital clock speeds are relentlessly increasing already exceeding 10 GHz in high-performance systems and expected to reach 20 GHz by 2020. This is within range of highly sensitive radio frequencies where analogue blocks and chip-sized components become efficient radiators and receivers. In addition, increasing circuit density and decreasing voltage supplies will result in decreased immunity levels. Future design processes of integrated electronic systems will therefore have to include a much more detailed electromagnetic compatibility (EMC) characterisation than is done at present. Carrying out EMC studies for complex multi-signal components within a device in a fast and efficient way will simplify design decisions in industry enormously and will help to bring down costs. The challenges of delivering fast and reliable EMC modelling tools at high frequencies are enormous; determining EM fields in a complex multi-source environment and in the GHz range including multiple-reflections, diffraction and interferences is a hard task already. For realistic electronic devices, the underlying source fields depend in addition on the (a-priori unknown) mode of operation and are thus aperiodic and time dependent; they act in many ways like stochastic, uncorrelated input signals. Indeed, no EMC methodology for modelling transient signals inside and outside of electronic devices originating from decorrelated, noisy sources exists today. This proposal sets out to meet this challenge head-on by developing an efficient numerical method and accompanying measurement techniques for the modelling of radiated transient EM fields inside and outside of multifunction electronic devices. The new numerical method is based on ideas from wave chaos theory using Wigner-Weyl transformation and phase-space propagation techniques. It makes use of the connections between wave correlation functions and phase space densities. Methods for efficiently propagating these densities have been developed recently by members of the project team. In this way, we can work directly in terms of statistical measures such as averages and field correlation functions appropriate for stochastic fields. This innovative approach demands input data from measurements which require a rethink of standard measurement techniques. In particular, correlated two-probe near-field measurements of electronic components become necessary which will be developed and tested as part of the project. The proposed way of approaching EMC issues is completely new and becomes possible only due to the unique mix of expertise available at the University of Nottingham both from the Mathematical Sciences and the Electrical Engineering side Support provided by two industrial partners, inuTech and Computer Simulation Technology (CST), will be vital throughout. This fresh way of thinking will provide the necessary leap within EMC research to satisfy the demands of the electronics industry; it will enhance the applicability of existing EMC protocols and provide the tools to meet the challenges of the future.

The proposal addresses a critical area in the design of complex high-speed electronic systems, namely, how to perform efficient studies of their electromagnetic behaviour in the presence of extreme geometrical, circuit and material complexity. As it is common in such cases the art is to segment the systems to subsystems and then model each one using a technique best suited to its peculiarities. Then, the various sub-models need to be combined to account fully for all interactions. This process of segmentation, sub-system modelling and aggregation is very challenging in all physical domains but it is particularly so in high-frequency applications (electromagnetic waves do not respect boundaries-they propagate and couple along large distances).In this proposal we aim to address these issues using a range of numerical models, field-based, network-based and behavioural. We combine our own expertise in constructing sophisticated macro-models of multi-scale systems with that of our partners to address a challenging problem of crucial importance to the advanced development of information and communications technologies which pervade all engineering applications. Successful completion of this research programme will make available to Industry a sophisticated hybrid modelling capability to analyse and design complex electromagnetic systems such as typified by a modern mobile phone which combines in a single handheld unit a multitude of complex functions.