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 non-smoothness 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.








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Harness, Y. Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering by 2D Star Shaped Obstacles. J Sci Comput 78, 1601–1631 (2019). https://doi.org/10.1007/s10915-018-0818-3
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DOI: https://doi.org/10.1007/s10915-018-0818-3
Keywords
- Uncertainty quantification
- Shape uncertainty
- Helmholtz
- Parametric method
- Low-dimensional embedding
- Coarea formula