On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
Journal of Computational Physics
Multisymplectic box schemes and the Korteweg-de Vries equation
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Geometric space-time integration of ferromagnetic materials
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
Linear PDEs and Numerical Methods That Preserve a Multisymplectic Conservation Law
SIAM Journal on Scientific Computing
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
Journal of Computational Physics
Energy-conserved splitting FDTD methods for Maxwell’s equations
Numerische Mathematik
Dispersive properties of multisymplectic integrators
Journal of Computational Physics
Numerical Methods for Evolutionary Differential Equations
Numerical Methods for Evolutionary Differential Equations
On the multisymplecticity of partitioned Runge-Kutta and splitting methods
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Splitting multisymplectic integrators for Maxwell's equations
Journal of Computational Physics
Computational Electromagnetics
Computational Electromagnetics
Journal of Computational Physics
Local structure-preserving algorithms for the "good" Boussinesq equation
Journal of Computational Physics
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In this paper, we compare the behaviour of one symplectic and three multisymplectic methods for Maxwell's equations in a simple medium. This is a system of PDEs with symplectic and multisymplectic structures. We give a theoretical discussion of how some numerical methods preserve the discrete versions of the local and global conservation laws and verify this behaviour in numerical experiments. We also show that these numerical methods preserve the divergence. Furthermore, we extend the discussion on dispersion for (multi)symplectic methods applied to PDEs with one spatial dimension, to include anisotropy when applying (multi)symplectic methods to Maxwell's equations in two spatial dimensions. Lastly, we demonstrate how varying the Courant-Friedrichs-Lewy (CFL) number can cause the (multi)symplectic methods in our comparison to behave differently, which can be explained by the study of backward error analysis for PDEs.