PML method for the stochastic acoustic scattering problem driven by an additive Gaussian noise

TL;DR

This paper develops a PML method for stochastic acoustic scattering in time domain with Gaussian noise, proving solution existence, uniqueness, and providing error estimates for the approximation.

Contribution

It introduces a novel PML approach for stochastic acoustic scattering driven by white noise, with rigorous convergence analysis and error estimates.

Findings

Proved existence and uniqueness of solutions.

Constructed an approximate wave solution with error bounds.

Established convergence of the PML method.

Abstract

This paper is concerned with the time-domain stochastic acoustic scattering problem driven by a spatially white additive Gaussian noise. The main contributions of the work are twofold. First, we prove the existence and uniqueness of the pathwise solution to the scattering problem by applying an abstract Laplace transform inversion theorem. The analysis employs the black box scattering theory to investigate the meromorphic continuation of the Helmholtz resolvent defined on rough fields. Second, based on the piecewise constant approximation of the white noise, we construct an approximate wave solution and establish the error estimate. As a consequence, we develop a PML method and establish the convergence analysis with explicit dependence on the PML layer's thickness and medium properties, as well as the piecewise constant approximation of the white noise.