Shape Uncertainty Quantification for Electromagnetic Wave Scattering via First-Order Sparse Boundary Element Approximation

TL;DR

This paper introduces an accessible open-source framework for applying a first-order sparse boundary element method to quantify shape uncertainties in electromagnetic wave scattering, enabling efficient statistical analysis of complex objects.

Contribution

The paper presents a practical implementation of FOSB for complex geometries, simplifying its application and demonstrating its effectiveness through extensive computational experiments.

Findings

FOSB computes statistical moments with poly-logarithmic complexity.

The framework is easy-to-use and suitable for complex objects.

Experimental results confirm the method's accuracy and applicability.

Abstract

Quantifying the effects on electromagnetic waves scattered by objects of uncertain shape is key for robust design, particularly in high precision applications. Assuming small random perturbations departing from a nominal domain, the first-order sparse boundary element method (FOSB) has been proven to directly compute statistical moments with poly-logarithmic complexity for a prescribed accuracy, without resorting to computationally intense Monte Carlo simulations. However, implementing the FOSB is not straightforward. To this end, we introduce an easy-to-use with open-source framework to directly apply the technique when dealing with complex objects. Exhaustive computational experiments confirm our claims and demonstrate the technique's applicability as well as provide pathways for further improvement.