A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems. (15th March 2023)

• Record Type: Journal Article
• Authors: Antonietti, Paola F.; Mazzieri, Ilario; Migliorini, Francesco
• Is Part Of: Computers & mathematics with applications. Volume 134(2023)
• Page Start: 87
• Page End: 100
• Publication Date: 2023-03-15
• Subjects: Discontinuous Galerkin methods -- Time integration -- Stability and convergence analysis -- Elastodynamics; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2023.01.016
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work, we present a high-order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the original equation as a system of first-order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable, and retains a super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical simulations.