Computational and Applied Mathematics seminar

Abstract: Network models are used to describe complex structures in fiber-based materials, like paper, and biological tissues, such as blood vessels. In these models, fibers are represented as beams connected at nodes, capturing mechanical properties while reducing computational costs compared to full 3D simulations. This talk addresses two problems: (1) the elastic deformation of beam networks in a stationary setting, and (2) the elastic wave propagation in time-dependent simulations. Both problems, derived from linear elasticity, describe how materials respond to applied forces and moments. I will present the key steps in the convergence analysis and error estimates, supported by numerical results. Finally, I will introduce a two-level overlapping domain decomposition method for efficient parallelization.