2025/07/22 by Panchi Li, Zhiwen Zhang, Li, Panchi +1
Computer Science · Engineering · #35J05 #35R60 #65D30 #65N30 #Advanced Mathematical Modeling in Engineering #Elasticity and Wave Propagation #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2507.16647
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose and analyze an accurate numerical approach to simulate the Helmholtz problem in a bounded region with a random refractive index, where the random refractive index is denoted using an infinite series parameterized by stochastic variables. To calculate the statistics of the solution numerically, we first truncate the parameterized model and adopt the quasi-Monte Carlo (qMC) method to generate stochastic variables. We develop a boundary-corrected multiscale method to discretize the truncated problem, which allows us to accurately resolve the Robin boundary condition with randomness. The proposed method exhibits superconvergence rates in the physical space (theoretical analysis suggests O(H4) for L2-error and O(H2) for a defined V-error). Owing to the employment of the qMC method, it also exhibits almost the first-order convergence rate in the random space. We provide the wavenumber explicit convergence analysis and conduct numerical experiments to validate key features of the proposed method.