Solution of the time dependent Maxwell equations is an important problem arising in many applications ranging from nanophotonics to geoscience and astronomy. The problem is far from trivial, and solutions typically exhibit complicated wave properties as well as damping behavior. Usually, special staggered time stepping schemes are used [Botchev,Verwer,2009]. Although their time step may be severely restricted by the CFL condition, performance of these schemes is hard to beat by modern implicit or exponential time integration schemes [Verwer,Botchev,2009]. We show that in some cases so-called time-stepping-free schemes provide a very efficient alternative to the standard schemes. These schemes employ the matrix exponential function and can be implemented by special block Krylov subspace techniques [Botchev,Grimm,Hochbruck,2013],[Botchev,2013].
Numerical examples demonstrating the efficiency of the proposed approach are presented, coming from the fields of nanophotonics and geoscience.
|Publisher||Russian Academy of Sciences, Keldysh Institute of Applied Mathematics|
|Conference||International Conference "Difference schemes and applications" in Honor of the 90-th Birthday of Prof. V.S. Ryaben'kii|
|Period||27/05/13 → 31/05/13|
|Other||May 27-31, 2013|
- Time domain modeling
- Maxwell equations
- Exponential time integration