A cholesky-based SGM-MLFMM for stochastic full-wave problems described by correlated random variables

In this letter, the multilevel fast multipole method (MLFMM) is combined with the polynomial chaos expansion (PCE)-based stochastic Galerkin method (SGM) to stochastically model scatterers with geometrical variations that need to be described by a set of correlated random variables (RVs). It is demonstrated how Cholesky decomposition is the appropriate choice for the RVs transformation, leading to an efficient SGM-MLFMM algorithm. The novel method is applied to the uncertainty quantification of the currents induced on a rough surface, being a classic example of a scatterer described by means of correlated RVs, and the results clearly demonstrate its superiority compared to the non-intrusive PCE methods and to the standard Monte Carlo method

Scattering from two-dimensional objects of varying shape combining the multilevel fast multipole method (MLFMM) with the stochastic Galerkin method (SGM)

In this letter, the Multilevel Fast Multipole Method (MLFMM) is combined with the polynomial chaos expansion (PCE) approach to model the stochastic variations of a scatterer. In particular, it is demonstrated how the Stochastic Galerkin Method (SGM) can be combined with an MLFMM accelerated method of moments (MoM) and how the beneficial effects of the MLFMM for electromagnetically large scatterers are retained in the stochastic case

Scattering from two-dimensional objects of varying shape combining the method of moments with the stochastic Galerkin method

In this communication, the combined field integral equation for perfect electrically conducting scatterers is combined with the stochastic Galerkin method (SGM) to model the impact of stochastic variations of the shape of the scatterer on the radar cross-section and on the induced current distribution. The SGM is compared to the stochastic collocation method (SCM) and it is shown that for a modest number of random variables the SGM is a good alternative to the SCM

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