Simultaneous multi-frequency simulation by recycling Krylov subspaces in FDFD formulation

Novel time-harmonic formulation of a full-wave electromagnetic problem based on FDFD scheme is introduced and solved efficiently by recycling Krylov subspaces for multiple frequencies. In order to apply the COCR and COCG methods our formulation preserves the symmetric character of the matrix for PML by introducing asymmetric intellectual materials at outer boundaries. Our formulation can be fit into a family of shifted linear systems, that has identical right-hand sides and their coefficient matrices differ from each other only by complex scalar multiples of the identity matrix. Shifted-COCR and shifted-COCG methods are applied to exploit the special structure and the numerical costs are shown to be as the same as that for a single linear system.