Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering

TL;DR

This paper presents a boundary integral method utilizing low-dimensional spatial embedding to efficiently quantify shape uncertainty in acoustic scattering problems, especially for irregular and non-smooth boundaries.

Contribution

It introduces a novel integration grid construction using the coarea formula for improved accuracy with fewer grid points in shape uncertainty quantification.

Findings

Effective handling of large boundary variations

Accurate solution evaluation with fewer grid points

Applicable to non-smooth, irregular boundaries

Abstract

This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose associated weight function encompasses the irregularities and nonsmoothness imposed by the random boundary. Thus, the solution can be evaluated accurately with relatively low number of grid points. The integration grid is obtained by employing a low-dimensional spatial embedding using the coarea formula. The proposed method can handle large variation as well as non-smoothness of the random boundary. For the ease of presentation the theory is restricted to star-shaped obstacles in low-dimensional setting. Higher spatial and parametric dimensional cases are discussed, though, not extensively explored in the current study.