Iterative Operator-Splitting Methods For Wave Equations With Stability Results And Numerical Examples.

Juergen Geiser , Lena Noack

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 15 pp.

MSC 2000

80A20 Heat and mass transfer, heat flow

80M25 Other numerical methods

Abstract
We are motivated by simulating a three-dimensional wave equation for an anisotropic material with stress-free boundary conditions. The applications are suited in the earthquake simulation that is based on seismic model problems. In this paper we discuss the efficiency of a higher-order time-discretization method, that is based on an iterative operator-splitting method. The main contribution is deriving the initial starting conditions for the iterative method; we propose different ideas and results for a pre-stepping method. The operator-splitting methods are well-know to solve such complex multi-dimensional and multi-physical problems. By decoupling the complex systems of differential equations into simpler equations, we save memory and computational resources. The iterative splitting method is discussed with its stability and consistency analysis. We verify our numerical methods with computational results based on our software tool $OPERA-SPLITT$. We present 2D and 3D wave equations with different higher-order splitting ideas. Finally we discuss the next works.