What is it about?

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 work. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.

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Why is it important?

Design of modern electromagnetic (EM), optical, and photonic devices has to account for unavoidable uncertainties in configuration parameters such as the position, orientation, roughness, and shape of scatterers, as well as internal and/or external excitation characteristics such as the frequency, amplitude, and angle of arrival. These uncertainties often stem from manufacturing tolerances and/or process variations and significantly affect the quantity of interest (QoI), such as scattering and absorption cross-sections, induced voltage and current, and transmitted and received power. To ensure that the QoI stays within design specifications, computational tools, which are capable of generating statistics of the QoI given the uncertainty in the parameters of the configuration and excitation, are required.


It could be very hard to parametrise uncertainties in the geometry/shape and then estimate how they propagate into the solution (electromagnetic scattered fields, radar cross section). In this work we explain how to do it. Additionally, we demonstrate how to combine and apply such state of the art techniques as: fast Fourier transform, fast multiple method, multi-level Monte Carlo. Each of these techniques reduces the computational complexity and storage drastically.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

Read the Original

This page is a summary of: Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method, IEEE Journal on Multiscale and Multiphysics Computational Techniques, January 2019, Institute of Electrical & Electronics Engineers (IEEE),
DOI: 10.1109/jmmct.2019.2897490.
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