Computational Electromagnetics Research Laboratory
Diakoptics Solution Techniques for Electromagnetic Fields in Time and Frequency Domain
Mario Righi, University of Victoria, December 1995.
The solution of complex electromagnetic fields problems cannot usually be found by applying a single technique to the entire solution domain. It is necessary to divide the problem space into manageable subdomains, solve the sub-problems with the most appropriate techniques and then recombine these solutions to obtain the answer to the overall problem. The sub-solutions could be obtained either in the time or in the frequency domain. The main challenge resides in the proper combination or reconnection of the various sub-solutions.
The objective of this thesis is to develop, implement and test a number of diakoptics procedures suitable for the analysis of complex microwave and millimeter wave structures.
The theory of the Transmission Line Matrix (TLM) method is reviewed and two novel hybridization methods based on diakoptics are proposed. In the first approach TLM and the time domain mode matching are combined. This link allows the model to take advantage of an analytical description for uniform sub-volumes while using the tra ditional TLM method in highly complex regions. Applications include: efficient analysis of packaged components, TLM computation of the generalized S-matrix, generation of high quality wideband dispersive multi-modal Absorbing Boundary Conditions (ABCs) for homogenous waveguides. Secondly, the systematic extraction of the lumped element equivalent circuit of distributed components is described. This provides a link with net work based solvers, thus allowing the use of TLM results in connection with SPICE-type simulators and the creation of a library of elementary components.
By taking advantage of these techniques it is possible to incorporate more information of the structure under study into the TLM solution, thus creating an accurate, efficient and flexible CAD tool.
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