Fast Integral Equation Solution Techniques for Planar-3D Structures in Multilayered Media

Abstract

In this contribution, a hybrid space/spectral domain integral equation approach is presented for the characterization of quasi-3D structures in multilayered media. The verti- cal conductors for the quasi-3D components like vias, through holes, airbridges, flnite dielectric regions etc. can cross an arbitrary number of dielectric layers with arbitrary vertical discretiza- tion. The electrodynamic behavior of the vertical currents is incorporated by extended spectral domain Green's functions derived by analytical integrations over the vertical direction and by a summation over the Cartesian wavenumbers which must be computed only once and stored in a database. For short lateral distances, the couplings are computed with a subtraction tech- nique based on asymptotic representations of the extended Green's functions, whereas for larger distances and for group coupling computations in context with fast matrix vector product evalu- ations, adaptive integration path deformations with extended Laguerre quadrature methods are applied. For the solution of the linear systems of equations, a GMRES solver was implemented together with a diakoptic preconditioner based on the group decomposition of larger structures, combined with a reversed Cuthill McKee reordering applied to the submatrix pattern of the system matrix. With all these techniques, the analysis of complex quasi-3D structures can be carried out with the same performance than pure planar microstrip and/or slotline structures.