A non-iterative domain decomposition time integrator combined with discontinuous Galerkin space discretizations for acoustic wave equations

TL;DR

This paper introduces a new non-iterative domain decomposition time integrator for acoustic wave equations that leverages discontinuous Galerkin spatial discretization, allowing higher-order accuracy and heterogeneous materials.

Contribution

It presents a novel non-iterative method combining local Crank-Nicolson and prediction steps, improving upon previous linear finite element approaches.

Findings

Enables higher-order spatial approximations.

Supports heterogeneous material parameters naturally.

Avoids iterative procedures in domain decomposition.

Abstract

We propose a novel non-iterative domain decomposition time integrator for acoustic wave equations using a discontinuous Galerkin discretization in space. It is based on a local Crank-Nicolson approximation combined with a suitable local prediction step in time. In contrast to earlier work using linear continuous finite elements with mass lumping, the proposed approach enables higher-order approximations and also heterogeneous material parameters in a natural way.