Time domain modelling using unstructured TLM meshes

Principal Investigator: Dr P D Sewell

Recognised Researchers: Mr J Wykes

Starts: 1 February 2005
Ends: 31 January 2008

Value: £169,116

Electromagnetics is the branch of science that explains how much of the electronic equipment that is so common in modern day life works. Examples are radio wave and light travel from one place to another, data transmission inside a computer and why some equipment may interfere with the operation of other equipment. Therefore, to design computers and communications systems with the best possible performance, it is necessary to predict their electromagnetic behaviour in advance. At relatively low-frequencies design problems are dominated by topological considerations and therefore analysis based on network concepts was acceptable. However, as designs migrate to higher frequencies, their operation is dominated by the geometry (not just the topology) of the circuits and therefore by field concepts. It is in this crucial technological area of field modelling and simulation of complex high-speed circuits that this current project aims to make a contribution.
For this purpose, computer programs are produced that simulate the “real world” by dividing it up into many small pieces in the same manner that biological objects are divided into cells. It is fairly easy to calculate the electromagnetic properties of each cell as long as it is small and as we know how cells are connected together and how they are influenced by their neighbours, it is possible to predict how an electromagnetic effect spreads throughout the whole “real world”. Unfortunately, there are two problems. The first is that the number of small cells is huge for many practical problems so that the computer program may take days to finish. The second is that usually the small cells used must be square in shape and all the same size and this means that any smooth surface, for example the skin of a ball, appears to the computer to be “staircased “ like the pyramids. This causes the simulation to be less accurate unless we use even smaller squares, in which case we need many more and the computer now takes weeks to finish the calculations.
In this project, we aim to solve both these problems for a particular simulation technique called TLM by using small triangular or pyramid shaped cells instead of squares and cubes. As each cell can be a different shaped triangle, it is possible to smoothly match them to the surface of any curved object thus leaving no gaps between them. This means the triangles can be generally larger than the squares, we need less of them and the computer finishes the simulation more quickly. The other advantage is that as the triangles can be radically different in size, we can use very small triangles around any very small objects in the problem to model them accurately but then use large triangles in the empty regions between the objects. This means overall we obtain good accuracy with relatively few triangles and again this provides fast simulations.
Although this basic idea has been demonstrated in principle to work in both two and three dimensions, it is necessary to perform more studies before the approach is as useful as it promises to be. It is necessary to determine the most accurate way of calculating the electromagnetics of each small triangle and whether there are any restrictions on the shapes of the triangle – for example it can’t be too long and skinny. Also, as the computer programs to perform these simulations are very complex, it is necessary to identify the most efficient way of programming the computer to do the simulation. In this we can also take advantage of computers that can do many things at once, so that a slow part of the operation does not block the progress of other faster parts of the program.
We will also be investigating some other exciting possibilities. Is it possible to embed very small objects within a moderately large cell rather than have to use tiny triangles? Is it possible to let the triangles move about – to follow the electromagnetic “action” and always be at the most useful place at the right time which would save on the number of cells needed? Finally, what about unusual materials, for example those to make aircraft invisible to radar, is it possible to have special triangles that will work in this case? These are additional features which are available in regular Cartesian meshes and will also be needed in the unstructured meshes if their benefits are to be realised fully. The proposed work will bring the benefits of unstructured meshes used extensively at LF (e.g. in connection with the finite element method) to high-frequencies and in the time-domain.