Higher-Order Time-Domain Simulations of Maxwell's Equations Using Krylov-Subspace Methods

We present a highly efficient numerical method to solve Maxwell's equations in the time domain that employs a Krylov-subspace based operator-exponential technique. As compared to standard finite-difference time-domain (FDTD) methods, this approach allows much larger time steps while at the same time the computations become more accurate. In contrast to other operator-exponential based approaches, the Krylov-subspace technique is directly capable of handling lossy and anisotropic materials as well as advanced boundary conditions such as perfectly matched layers. Owing to its generality, our approach can be extended to more complex problems where the electromagnetic field is coupled to other physical systems.