2020/09/29 by Debopriya Mukherjee, Thanh Tran, Mukherjee, Debopriya +1
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2009.13783
arxiv created 2020/09/29 · openalex publication_date 2020/09/29 · arxiv updated 2020/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments of the random solutions are approximated by those of the shape derivative and shape Hessian, and the approximations are of third order accuracy in terms of the size of the boundary perturbation. Our theoretical results are supported by an analytical example on a square domain.