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This paper introduces a novel boundary integral approach of shape uncertaintyquantification for the Helmholtz scattering problem in the framework of theso-called parametric method. The key idea is to construct an integration gridwhose associated weight function encompasses the irregularities andnonsmoothness imposed by the random boundary. Thus, the solution can beevaluated accurately with relatively low number of grid points. The integrationgrid is obtained by employing a low-dimensional spatial embedding using thecoarea formula. The proposed method can handle large variation as well asnon-smoothness of the random boundary. For the ease of presentation the theoryis restricted to star-shaped obstacles in low-dimensional setting. Higherspatial and parametric dimensional cases are discussed, though, not extensivelyexplored in the current study.

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