Computational and Applied Mathematics seminar

Abstract: Network models are used to describe complex structures found in fiber-based materials such as paper, or biological tissues. In these models, fibers are represented as edges connected at nodes, and are modeled as Timoshenko beams to capture the mechanical behavior of the material. Understanding wave propagation in such networks is important for predicting material response and improving performance in applications such as papermaking.

We present a hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of the wave equation on fiber networks, combined with a θ-scheme for time integration. Through hybridization, the problem is reformulated as a symmetric positive definite system on the network nodes. The HDG spatial discretization achieves arbitrary-order convergence under mesh refinement without increasing the size of the global system. We establish convergence and error estimates, supported by numerical experiments.