Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Litvinenko, Alexander, Abdulkadir C. Yucel, Hakan Bagci, Jesper Oppelstrup, Eric Michielssen, and Raúl Tempone. "Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method", in IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 4, (2019), pp. 37-50
Alexander Litvinenko, Abdulkadir C. Yucel, Hakan Bagci, Jesper Oppelstrup, Eric Michielssen, Raúl Tempone
uncertainty quantiﬁcation in geometry, random geometry, multilevel Monte Carlo method (MLMC), continuation MLMC, integral equation, fast multipole method (FMM), fast Fourier transform (FFT), scattering problem
2019
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization, the number of MC samples has to be large. In this paper, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.
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