Wave Propagation Modeling in Random Environment: Study for Utilizing the Finite Element Domain Decomposition Method

In this work, we present an approach to model large-scale wave propagation phenomena using the finite element method combined with a domain decomposition strategy. Specifically, the Finite Element Tearing and Interconnecting (FETI) approach is employed to create comparable system matrices across subdomains with conforming interfaces. This facilitates the development of surrogate models through regression analysis, which, in principle, enables rapid computation of large-scale scenarios, such as forest modeling. However, our investigation reveals that noise introduced by volumetric mesh variations, caused by geometric changes, poses a significant challenge to the approach. We detail these limiting factors, analyze their implications, and propose potential alternatives. This article aims to share insights into the challenges of statistical finite element model construction and provide a foundation for future work in this area.