Fast Transform based Preconditioner for 3D Finite-Difference Frequency-Domain - Application to Waveguides

The fields scattered by dielectric objects placed inside metallic waveguides can efficiently be computed via a finite-difference frequency-domain (FDFD) method. This involves large, sparse linear systems of equations that may be solved using preconditioned Krylov-subspace methods. We propose a preconditioner that uses fast discrete trigonometric transforms and is based on a physical approximation. Simulations show significant gain in terms of iteration count and computation time. Moreover, with the new preconditioner, the required number of iterations is independent of the grid size.