Embedding of fine features in multi-scale electromagnetic models
Modelling detailed electromagnetic interactions in Electromagnetic Compatibility predictions is an extremely demanding task, made more difficult by the increasing complexity of modem engineering problems. Over the last decade major innovations in numerical models and methods have been introduced to reduce demands on computational resources or render the simulations of large systems containing a diverse range of physical features possible. This thesis presents one of the methods of dealing with large systems which utilises the concept of sub-cells containing fine geometrical objects. A general approach to embedding fine features into a coarse numerical time-domain techniques such as the Transmission Line Modelling (TLM) method is proposed. A non-standard node has been developed that mimics the electro- magnetic behaviour of virtually any object or group of small objects wholly or partially enclosed by a volume of space represented by the numerical cell. The core of this scheme is to identify a suitable set of local field solutions to Maxwell's equations within the vicinity of the enclosed objects and, by correctly sampling the fields on the boundary of the cell, to integrate these with field solutions represented by the neighbouring nodes, ensuring both field continuity and power conservation. The idea whilst simple leads to an algorithm that is both explicitly stable and conservative as well as only incurring a minor computational overhead compared to a conventional TLM algorithm. It is noted that, as the required identification and evaluation of the local field solutions occurs as a pre-processing stage prior to the main TLM run and that the non-standard nodes are a small proportion of the coarse grid, a significant overall reduction in computational requirements is achieved in comparison to direct fine meshing of the features. Another advantage of this approach lies in the fact that the local solutions to Maxwell's equations calculated in the pre-run process can be obtained by any suitable means. Analytical formulations, numerical results of another simulation or simply experimental measurements are some of the possibilities. The approach is employed to investigate a variety of EMC problems. An analysis of the field scattered from multiple cylindrical geometries embedded within a single two-dimensional cell is presented. Multiple conducting and lossy wires, dielectric rods and dielectric coated wires, conducting strips and slots are also studied. Three-dimensional simulations are shown for an arbitrarily orientated wires, small dielectric and conducting spheres and other canonical shapes. The approach is also successfully applied to other disciplines where modelling plays an important role. The flexibility of the algorithm is demonstrated for simulations of photonic structures with the primary focus placed upon photonic band-gap materials.