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Q: Quantenoptik und Photonik
Q 20: Photonische Kristalle I
Q 20.5: Vortrag
Dienstag, 14. März 2006, 11:40–11:55, HI
Unconditionally stable time-domain simulations using Krylov-subspace methods — •Jens Niegemann1,2, Martin Pototschnig1, Lasha Tkeshlashvili3,2, and Kurt Busch1,3,2 — 1Institut für theoretische Festkörperphysik, Universität Karlsruhe — 2DFG Forschungszentrum Center for Functional Nanostructures (CFN), Universität Karlsruhe — 3Institut für Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft
Over the past decades, many numerical methods have been developed to solve the time-dependent Maxwell equations. The most popular one is the so-called Finite-Difference Time-Domain (FDTD) method. While FDTD is very easy to implement and relatively fast, it exhibits some inherent problems. In particular, it is only of second order in time and only conditionally stable. Therefore, to obtain accurate results one has to take very small timesteps. We propose to solve Maxwell’s equations with an unconditionally stable and more accurate method based on operator exponentials using Krylov-subspace techniques. We compare the performance of our method with standard FDTD and other methods. In addition, we demonstrate how to include absorbing boundary conditions and sources into this method while still maintaining the unconditional stability. Furthermore, we show how this method can be extended to nonlinear and coupled systems, by using nonlinear exponential integrators.