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

TL;DR

This paper introduces a multilevel Monte Carlo approach combined with a surface integral equation solver to efficiently compute electromagnetic scattering from objects with uncertain shapes, significantly reducing computational costs.

Contribution

The work applies the continuation multilevel Monte Carlo method to electromagnetic scattering problems with shape uncertainties, optimizing the balance between sampling and discretization errors.

Findings

Significant reduction in computational time compared to standard Monte Carlo methods.

Effective handling of geometric uncertainties in electromagnetic scattering simulations.

Demonstrated efficiency with hierarchical discretizations from coarse to fine.

Abstract

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.