Preconditioner for a scattering solver based on the intrusive stochastic galerkin method accelerated with MLFMM

We present a preconditioner for an intrusive stochastic Galerkin method (SGM) based scattering solver that also leverages the multilevel fast multipole method (MLFMM). The proposed preconditioner is essential in developing a general and intrusive SGM method. Simulation results are obtained for a canonical scattering structure with perfect electrically conducting strips with statistically varying geometry. Results are reported for the number of iterations, with and without using a preconditioner, and for the time required to setup the preconditioner.