Component splitting for semi-discrete Maxwell equations

A time-integration scheme for semi-discrete linear Maxwell equations is proposed. Special for this scheme is that it employs component splitting. The idea of component splitting is to advance the greater part of the components of the semi-discrete system explicitly in time and the remaining part implicitly. The aim is to avoid severe step size restrictions caused by grid-induced stiffness emanating from locally refined space grids. The proposed scheme is a blend of an existing second-order composition scheme which treats wave terms explicitly and the second-order implicit trapezoidal rule. The new blended scheme retains the composition property enabling higher-order composition.