MLMC method to estimate propagation of uncertainties in electromagnetic fields scattered from objects of uncertain shapes

We estimate the propagation of uncertainties in electromagnetic wave scattering problems. The computational domain is a dielectric object with uncertain shape. Since classical Monte Carlo (MC) method is too expensive, we suggest to use a modified multilevel Monte Carlo (MLMC) method. This method uses a hierarchy of spatial meshes and optimally balances the statistical and discretisation errors. MLMC performs most of the simulations using low-fidelity models and only a few simulations using high-fidelity models. As a result, the final computational cost is becoming significantly smaller.