arXiv subjects

Safiere Kuijpers

Publications and source records attributed to Safiere Kuijpers.

2 recordsLinked to original sources

arXiv2026

Wavenumber-Explicit Well-Posedness of Bayesian Shape Inversion in Acoustic Scattering

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then extend our results to an exterior Dirichlet (sound-soft) problem. It is well known that higher frequencies yield higher resolution but greater sensitivity to noise; here we give the first rigorous results quantifying how this sensitivity to noise depends on the wavenumber. We model the scatterer as star-shaped, with a prior on its boundary given by a series expansion of the angle-dependent radius with uniformly distributed coefficients. Our main result establishes well-posedness of the Bayesian shape inverse problem with constants explicit in the wavenumber, under problem-specific conditions on the material parameters that exclude quasi-resonant regimes. Stability estimates in the Hellinger and 1-Wasserstein metrics show that the stability constant of the posterior with respect to the data grows exponentially with the square of the wavenumber, whose magnitude must be understood not in absolute terms but relative to the spatial scale of the problem. Numerical experiments illustrate this effect.

math.AP↗

arXiv2026

On Hyperbolic Stochastic Galerkin Projections of Shallow Water Linearised Moment Equations

In this work, we present an intrusive stochastic Galerkin formulation of the one-dimensional shallow water linearised moment equations expressed in conservative variables, using the pseudospectral product for generalised polynomial chaos expansions. The shallow water linearised moment equations constitute a hyperbolic system of partial differential equations with an arbitrary number of equations that enhance the accuracy of the standard shallow water equations. Without loss of generality, we assume for both the theoretical analysis and the simulations that the uncertain parameter is the friction coefficient. For the new stochastic Galerkin shallow water linearised moment equations, we derive an energy equation, analyse the hyperbolicity - since this property is not preserved by the stochastic Galerkin projection - and introduce a regularisation to ensure hyperbolicity for the linear case of the shallow water linearised moment equations. Through numerical tests, we demonstrate the accuracy of the new stochastic Galerkin formulation in comparison with a non-intrusive Monte Carlo method, showing that the stochastic Galerkin approach achieves comparable accuracy with significantly faster run times.

math.NA↗