John Nielsen, Bell Northern Research, Ottawa: The fact that TLM is now being used as an engineering tool, as demonstrated in several workshop papers and software demonstrations, is exciting and indicates that the technique has reached a certain level of maturity. As an industrial user he would like to be able to model a complete circuit board containing active and passive elements such as coils, diodes, transistors, capacitors and multi-layer boards. The model should include the various parasitic interactions between the elements of the structure, and should be amenable to field-based optimization in order to arrive at designs which minimize parasitic effects.
Pierre Saguet, University of Grenoble, France: In spite of the considerable memory size and speed of modern computers, very complex structures cannot be modeled by the TLM approach alone. TLM is suitable for discretizing and solving compact subregions, but propagation space between such subregions should be modeled with other methods. Hybrid methods must thus be developed to combine TLM with other techniques such as the Method of Moments, Mode Matching, or Ray Tracing Methods.
Fred German, Texas Instruments, U.S.A.: For TLM to be useful to practicing engineers, in particular younger engineers, appropriate user interfaces are a must. More development in this area is needed; this requires a good knowledge of both electromagnetic engineering and numerical electromagnetics. The language of the interface must be brought to the level of the practitioner. Suggested new developments for TLM are "smart" cells and efficient methods for local mesh refinement or mesh modification.
Peter Russer, Technical University of Munich, Germany: The theoretical background of TLM should be researched further in order to render algorithms more efficient and remove redundancies in present schemes. On the application side, absorbing boundary conditions need to be improved, and signal processing techniques (Prony, ARMA) must be implemented in order to reduce or cope with the large amount of data generated by TLM simulations. All these features must be combined in a software tool so that they can benefit a large number of users.
Dominique Pompei, University of Nice-Sophia Antipolis, France: One of the great assets of TLM is its inherent simplicity and its closeness to experiments. This feature should be preserved as much as possible. Suggested new developments for TLM are inverse time modeling of radiating arrays and improvements in advanced signal processing techniques.
Neil Simons, Communications Research Centre, Ottawa, Canada: Any new development in TLM should be judged by its suitability for applications. More emphasis should be placed on finding useful applications that exploit the specific features and advantages of TLM.
Michel Ney, E.N.S.T. Bretagne, France: Complex three-dimensional geometries can only be solved with methods such as TLM, however, the required memory and CPU time are prohibitive in many real size problems. It is therefore important to concentrate future research on reducing computational requirements, and to find effective methods for partitioning larger problems into smaller subgrids.
Christos Christopoulos, University of Nottingham, U.K.: The critical issues in TLM are:
Donard De Cogan, University of East Anglia, U.K.: TLM has reached maturity. In the future, TLM will be applied to fast heating involving traveling solutions for heat transport, and to the simulation of coupled systems, combining electromagnetic, thermal and mechanical phenomena in a single model. TLM modeling efforts should not be fractured, and researchers in TLM should keep in touch even though they work on different applications.
Michael Krumpholz, University of Michigan, Ann Arbor, U.S.A.: Redundancy in present TLM schemes must be reduced, and we must seriously look at new developments in FD-TD in which local basis functions (impulse functions) are replaced by more extended basis functions (wavelets), thus considerably reducing the number of unknowns in a given problem.
Ruediger Vahldieck, University of Victoria, Canada: Typical problems arising in microwave and millimeter-wave engineering do not always require the full power of time domain TLM, and frequency domain TLM formulations (the equivalent of Finite Differences in the frequency domain) may be more efficient. In particular, if the structure under test has dimensions which differ by one or several orders of magnitude, the requirement of synchronism in time domain TLM may require excessive computer resources. The respective merits of time domain and frequency domain TLM solutions need to be thoroughly studied and compared in order to clarify these issues.
Zhizhang Chen, Technical University of Nova Scotia, Halifax, Canada: Future efforts must be directed towards modeling larger and more complex structures with TLM. Accuracy of the solution is not always a priority for users, but other qualities are sought in a modeling procedure, such as stability and convergence, absence of artifacts in the solution, and versatility and ease of application to new problems. Hybrid techniques, i.e. the combination of TLM with other numerical techniques, are the key to solving larger and more complex problems. The reduction of the number of degrees of freedom of the TLM model is another effective technique for reducing computational expenses.
Joe LoVetri, University of Western Ontario, London, Canada: The potential of TLM has not yet been fully exploited, and further progress can be made through theoretical investigations of the modeling process. Boundary treatment needs to be improved as well, and comparative studies of related numerical techniques (FD-TD, FEM, Monte Carlo methods) provide additional inspiration and new ideas for improvement.
David Johns, KCC, Nottingham, U.K.:
