Transmission Line Modelling using unstructured triangular meshes

Research Staff: Jim Wykes, Phillip Sewell , Christos Christopoulos, Trevor Benson, Ana Vukovic, David Thomas

This work is supported by The Engineering and Physical Sciences Research Council (EPSRC), UK

A novel formulation of the Transmission Line Modelling (TLM) method has been developed to work with 2D unstructured triangular meshes.

TLM is an established technique for modelling EM problems, but current implementations are restricted to structured Cartesian meshes. Unstructured meshes offer tremendous versatility for mapping complex geometries and the result is their widespread use in a variety of modelling applications across the scientific and engineering disciplines. This provides the motivation to develop TLM algorithms capable of working with these types of unstructured triangular mesh.

Unstructured meshes are particularly beneficial where a range of feature sizes need to be accurately modelled. For example, in many EMC problems, large homogenous spaces exist between fine-featured objects which need to be correctly described for useful simulations. Unstructured meshes easily lend themselves to non-uniform meshing, employing the necessary computational resources around small features whilst minimising computational effort in the empty spaces. Alternatively, they can be used to facilitate the connection of several different Cartesian mesh gradings; i.e. as a multigrid ‘glue’.

Another key advantage of unstructured triangular meshes is their superiority in mapping boundaries or material interfaces that are curved. Current TLM methods based on Cartesian coordinates are forced to employ staircase approximations to such boundaries, which leads to inaccuracies in the positioning of discontinuities, as well as in the matching of the fields across them.

Publications

[1] P. Sewell, J. Wykes, A. Vukovic, D.W.P. Thomas, T.M. Benson and C. Christopoulos, Multi-grid interface in computational electromagnetics, IEE Electronics Letters, Vol. 40, No. 3, Feb 2004, ISSN 0013-5194
[2] P. Sewell, J.G. Wykes, T.M. Benson, C. Christopoulos, D.W.P. Thomas and A. Vukovic, Transmission Line Modelling using unstructured triangular meshes, accepted for publication in the IEEE Transaction on Microwave Theory and Techniques
[3] J.G. Wykes, P. Sewell, T.M. Benson, D.W.P. Thomas, A. Vukovic, C. Christopoulos, TLM using unstructured triangular meshes, accepted for the IEE Fifth International Conference on Computation in Electromagnetics (CEM), 19-22 April 2004, Stratford-upon-Avon, UK