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

Alexander Litvinenko, Abdulkadir C. Yucel, Hakan Bagci, Jesper Oppelstrup, Eric Michielssen, Raul Tempone

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 work, 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.
Original languageEnglish (US)
Pages (from-to)37-50
Number of pages14
JournalIEEE Journal on Multiscale and Multiphysics Computational Techniques
StatePublished - Feb 6 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported in part by the King Abdullah University of Science and Technology, and in part by the Alexander von Humboldt Foundation.


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