Numerical Methods in System Simulations

The numerical methods used in the discussed system simulations are not basically new, but the generally available ones are adequately selected and adapted to the specific wide range of system applications. The simulation problem discussed here is a tridimensional one from the beginning. The antennas, the ground and the objects have to be treated and modeled adequately. The objects range from large cubical metallic buildings or aircraft with curved surfaces to wire and skeleton type masts or tower-cranes which may interact with each other or with the exciting systems antenna. The most important condition to be met is that all the methods has to be strictly applied only within their range of definitions and their applicability. Otherwise the results are questionable and speculations – in principle worthless.

The preferred methods are the asymptotic ones, e.g. the Geometrical Theory of Diffraction GTD and its derivatives the UTD etc. The first system simulation method developed was the tridimensional GTD/UTD-method applied for the ILS-system /1/, later for VOR/DVOR and other systems. The GTD/UTD-method was the preferred one compared with the PO-method and derivatives due to the wider range of general applicability. For single objects the Physical Optics Method PO with its improvements IPO (rim currents and shadow Fock-currents). However, limitations in the GTD/UTD-method and an increasing demand to treat objects not reasonably possible with PO nor with GTD/UTD has led to the introduction of the moment method technique MoM in the applied system simulations. This is for wire type cranes on airports, for electrically medium size objects or for the bistatic scattering of a complete aircraft.

A further recently expanded numerical method has been introduced now and integrated into the entire system simulation, namely the parabolic equation method which can handle in the forward propagation mode complicated ground and material structures. Extentions for the 3D case and the backward propagation are under way. A multilayer ground (e.g. dry and wet snow) is treated in this approach by an approximate reflection-refraction transmission line method.

All these methods are combined in an applied novel modular hybrid system simulation approach:

• 3D GTD/UTD as the basic method for the 3D scattering of multi-scatterers and ground (Fig. 2)
• PO and IPO method for curved surface objects (aircraft) (Fig. 4)
• Moment method for the antennas and adequate objects (cranes, masts, wind generators etc.) (Fig. 3)
• parabolic equation PE for the wave propagation on irregular and complicated 3D ground (Fig. 2)
• reflection-refraction transmission line method for multilayer problems