The application of Trefftz-FLAME to electromagnetic wave problems /

Numerical analysis of the electromagnetic fields in large, complex structures is very challenging due to the high computational overhead. Recently, it has been shown that a new method called Trefftz-FLAME ( Flexible Local Approximation MEthod) is suitable for problems where there exist a large number of similar structures.This thesis develops Trefftz-FLAME in two areas. First, a novel 2D Trefftz-FLAME method incorporates the modal analysis and port boundary condition that are essential to an accurate calculation of reflection and transmission coefficients for photonic crystal devices. The new technique outperforms existing methods in both accuracy and computational cost.The second area pertains to the 3D, vector problem of electromagnetic wave scattering by aggregates of identical dielectric particles. A methodology for the development of local basis functions is introduced, applicable to particles of any shape and composition. Boundary conditions on the surface of the finite FLAME domain are described, capable of representing the incident wave and absorbing the outgoing radiation. A series of problems involving dielectric spheres is solved to validate the new method. Comparison with exact solutions is possible in some cases and shows that the method is able to produce accurate near-field results even when the computational grid spacing is equal to the radius of the spheres