We give a systematic method for discretizing Hamiltonian partial differential equations
(PDEs) with constant symplectic structure, while preserving their energy exactly. The same …

To discretize Maxwell's equations, a variety of high-order symplectic finite-difference time-
domain schemes, which use th-order symplectic integration time step** and th-order …

When I started this book project, I proposed to write a book about my recent advances in
mathematical modelling problems to multicomponent and multiscale systems. I considered …

We present several high-order accurate finite element methods for the Maxwell's equations
which provide time-invariant, non-drifting approximations to the total electric and magnetic …

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 …

In this paper, a (2M, 4) scheme of the finite-difference time-domain (FDTD) method is
proposed, in which the time differential is of the fourth order and the spatial differential using …

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic
integrator is applied to electromagnetic simulation. A feasible numerical implementation of …

A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is
energy conserved, for modeling the metamaterials is proposed. The lossless Drude …

Continental magmatic arcs are characterized by the accretion of voluminous mantle-derived
magmatic rocks and the growth of juvenile crust. However, significant volumes of meta …

Abstract The Symplectic Finite-Difference Time-Domain (SFDTD) method was applied to
simulate the one-dimensional unmagnetized Plasma Photonic Crystal (PPC) with a …