Operator-splitting methods for wave-equations

Abstract

The motivation to our studies came from simulation of earth-quakes, that are modeled with elastic wave equations. In our paper we focus on the study of the stiff problems for the wave-equations. Due to this contribution we discuss iterative operator splitting methods for wave-equations motivated from a realistic problem in seismic sources and waves. The operator-splitting methods are wel-know to solve such complicated multidimensional and multi physics problems. We present the consistency analysis for the iterative methods as theoretical background for the wave-equation with respect to the underlying boundary conditions. From the algorithmic point of view we discuss the application of the decoupling and non-decoupling the equations, with respect to the eigenvalues. We verify our methods for test problems with known analytical solutions. Multi-dimensional examples are presented for realistic applications in wave equations. Finally we discuss the results.