PML Method for the Stochastic Acoustic Scattering Problem Driven by an Additive Gaussian Noise

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 perfectly matched layers (PML) method and establish the convergence analysis with explicit dependence on the PML thickness and medium properties, as well as the piecewise constant approximation of the white noise.