Optimized Operator-Splitting Methods in Numerical Integration of Maxwell's Equations

Optimized Operator-SplittingMethods in Numerical Integration of Maxwell’s Equations

Optimized operator splitting methods for numerical integration of the time domain Maxwell’s equations in computational electromagnetics (CEM) are proposed for the first time. The methods are based on splitting the time domain evolution operator of Maxwell’s equations into suboperators, and corresponding time coefficients are obtained by reducing the norm of truncation terms to a minimum. The ge...

Operator Splitting Methods for Wave Equations

Abstract The motivation for our studies is coming from simulation of earthquakes, that are modelled by elastic wave equations. In our paper we focus on stiff phanomenons for the wave equations. In the course of this article we discuss iterative operator splitting methods for wave equations motivated by realistic problems dealing with seismic sources and waves. The operator splitting methods are...

Splitting and composition methods in the numerical integration of differential equations

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE can be decomposed into several pieces and each of them is integrable. This class of integrators are explicit, simple to implement and preserve structural pr...

Higher-order operator splitting methods for deterministic parabolic equations

Operator splitting for delay equations

for the E-valued unknown function u, where E is a Banach space, B is the generator of a (linear) C0-semigroup on E, ut is the history function defined by ut(s) = u(t + s) and Φ is the delay operator. We will employ the semigroup approach on L-phase space (in the spirit of [4] and [5]) to be able to apply numerical splitting schemes to this problem. We prove convergence of theses schemes, invest...