A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems

12/03/2021
by   Paola F. Antonietti, et al.
0

In this work, we present a new 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 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 applications.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 18

page 22

page 24

11/29/2021

A high-order discontinuous Galerkin in time discretization for second-order hyperbolic equations

The aim of this paper is to apply a high-order discontinuous-in-time sch...
06/23/2021

An entropic method for discrete systems with Gibbs entropy

We consider general systems of ordinary differential equations with mono...
03/23/2021

High-order implicit time integration scheme based on Padé expansions

A single-step high-order implicit time integration scheme for the soluti...
09/30/2019

A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems

A novel discontinuous Galerkin (DG) method is developed to solve time-de...
10/15/2019

A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form

We present a stable discontinuous Galerkin (DG) method with a perfectly ...
01/25/2022

A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of the Nonhomogeneous Bingham Flow

This paper is devoted to the study of non-homogeneous Bingham flows. We ...
09/26/2017

V-cycle multigrid algorithms for discontinuous Galerkin methods on non-nested polytopic meshes

In this paper we analyse the convergence properties of V-cycle multigrid...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.