Over the past 20 years, the development in ComputationalElectromagnetics has produced a vast choice of methods based onthe large number of existing mathematical formulations of theMaxwell equations. None of them dominate over the others,instead they complement each other and the choice of methoddepends on the frequency range of the electromagnetic waves.This work is focused on the most popular method in the highfrequency scenario, namely the Geometrical Theory ofDiffraction (GTD). The main advantage of GTD is the ability topredict the electromagnetic field asymptotically in the limitof vanishing wavelength, when other methods, such as the Methodof Moments, become computationally too expensive.
The low cost of GTD is due to both the fact that there is noruntime penalty in increasing the frequency and that the raytracing, which GTD is based on, is a geometrical technique. Thecomplexity is then no longer dependent on electrical size ofthe problem but instead on geometrical sub problems which aremanageable. For industrial applications the geometricalstructures, with which the rays interact, are modelled bytrimmed Non-Uniform Rational B-Spline (NURBS) surfaces, themost recent standard used to represent complex free-formgeometries.
Due to the introduction of NURBS, the geometrical subproblems tend to be mathematically and numerically cumbersome,but they can be highly simplified by proper Object Orientedprogramming techniques. This allowed us to create a flexiblesoftware package, MIRA: Modular Implementation of Ray Tracingfor Antenna Applications, with an architecture that separatesmathematical algorithms from their implementation details andmodelling. In addition, its design supports hybridisationtechniques in combination with other methods such as Method ofMoment (MoM) and Physical Optics (PO).
In a first hybrid application, a triangle-based PO solveruses the shadowing information calculated with the ray tracerpart of MIRA. The occlusion is performed between triangles andtheir facing NURBS surfaces rather than between their facingtriangles, thus reducing the complexity. Then the shadowinginformation is used in an iterative MoM-PO process in order tocover higher frequencies, where the contribution of theshadowing effects, in the hybrid formulation, is believed to bemore significant.
Thesis presented at the Royal Institute of Technology ofStockholm in 2003, for the degree of Licentiate in ScientificComputing.
Stockholm: Numerisk analys och datalogi , 2003. , xii, 100 p.