Domain Decomposition Methods for Elastic Wave Propagation

Explore domain decomposition methods for solving elastic wave propagation problems in this 39-minute conference talk that examines the numerical solution of the first-order formulation of the elastic wave equation on networks of Timoshenko beams coupled by rigid joint conditions. Learn how these networks model complex, heterogeneous geometries found in fiber-based materials such as paper, and discover the application of hybrid discontinuous Galerkin methods for space discretization that result in symmetric positive systems of linear equations. Understand the challenges posed by heterogeneous material coefficients and multi-scale resolution requirements that create large, poorly conditioned global system matrices necessitating implicit time integration using the theta scheme. Examine the implementation of preconditioned conjugate gradient methods for solving the global system of linear equations iteratively in each timestep, utilizing a two-level delta-overlap additive Schwarz method as a preconditioner with partition of unity basis construction through algebraic network partitioning. Gain insights into the theoretical proof demonstrating convergence of the iterative method with respect to the number of subdomains under appropriate homogeneity and multiplicity conditions, and review numerical experiments that validate these theoretical findings.