Additive, Multiplicative and Iterative Splitting Methods for Maxwell Equations: Algorithms and Applications

We are motivated to optimise splitting methods for Maxwell's equations. The methods are based on additive, multiplicative and iterative splitting approaches and embed an optimised computation of the Maxwell operators. We decompose Maxwell's equations into sub-operators and apply the different splitting methods. We obtain numerical benefits, while we apply iterative splitting approaches and optimise the computations of the sub-operators. Standard methods, such as additive and multiplicative methods, are more effective in fast results, which iterative approaches could reduce iteratively the errors. We present some initial numerical examples for the optimised splitting approaches.