Wave-Scattering processes: path-integrals designed for the numerical handling of complex geometries

TL;DR

This paper introduces a novel path-integral approach based on Feynman-Kac methodology for analyzing wave single-scattering by complex 3D objects, enhancing computational methods for electromagnetic scattering problems.

Contribution

It develops a new statistical framework for wave scattering analysis using path-integrals, applicable to complex geometries and implemented on multiple scattering models.

Findings

Path-integral approach improves analysis of complex scatterers.

Monte Carlo methods become more effective for complex geometries.

Framework addresses interpretative difficulties in scattering moments.

Abstract

Relying on Feynman-Kac path-integral methodology, we present a new statistical perspective on wave single-scattering by complex three-dimensional objects. The approach is implemented on three models -- Schiff approximation, Born approximation and rigorous Born series -- and usual interpretative difficulties such as the analysis of moments over scatterer distributions (size, orientation, shape...) are addressed. In terms of computational contribution, we show that commonly recognized features of Monte Carlo method with respect to geometric complexity can now be available when solving electromagnetic scattering.