A symplectic integration algorithm for separable Hamiltonian functions
Journal of Computational Physics
The development of variable-step symplectic integrators with application to the two-body problem
SIAM Journal on Scientific Computing
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Fourier analysis of numerical algorithms for the Maxwell equations
Journal of Computational Physics
Applied Numerical Mathematics - Special issue on time integration
Journal of Computational Physics
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Journal of Computational Physics
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In this work, we derive a discrete action principle for electrodynamics that can be used to construct explicit symplectic integrators for Maxwell's equations. Different integrators are constructed depending on the choice of discrete Lagrangian used to approximate the action. By combining discrete Lagrangians in an explicit symplectic partitioned Runge-Kutta method, an integrator capable of achieving any order of accuracy is obtained. Using the von Neumann stability analysis, we show that the integrators greatly increase the numerical stability and reduce the numerical dispersion compared to other methods. For practical purposes, we demonstrate how to implement the integrators using many features of the finite-difference time-domain method. However, our approach is also applicable to other spatial discretizations, such as those used in finite element methods. Using this implementation, numerical examples are presented that demonstrate the ability of the integrators to efficiently reduce and maintain a minimal amount of numerical dispersion, particularly when the time-step is less than the stability limit. The integrators are therefore advantageous for modeling large, inhomogeneous computational domains.