A high efficiency finite difference time-domain method based on high order compact scheme is shown.It not only improves accuracy,but also has the advantages of fewer grid nodes,lower memory consumes and CPU time.Numerical simulations of electromagnetic wave propagation in a lossless waveguide and photonic crystals fibers are realized.They prove efficiency and accuracy of the algorithm.

Based on a fact that impedance matrix in the method of moments(MoM) is independent of incident angles,a compressive sensing(CS) technique is introduced in constructing an incident source,in which much information about incident angle is included.Under the incident source,measurement of induced currents can be obtained with MoM.With orthogonal matching pursuit(OMP) technique,induced currents are reconstructed with few measurements.Compared with conventional MoM,high accuracy numerical results are obtained while computational time is reduced to one third.Computational complexity of wide angle electromagnetic scattering is reduced greatly.

Euler-Hamilton equations are provided using Hamiltonian function of Maxwell's equations.High order symplectic schemes of three-dimensional time-domain Maxwell's equations are constructed with symplectic integrator technique combined with high order staggered difference.The method is used to analyzing stability and numerical dispersion of high order time-domain methods and symplectic schemes with matrix analysis and tensor product.It confirms accuracy of the scheme and super ability compared with other time-domain methods.

Multi-step high-order finite difference schemes for infinite dimensional Hamiltonian systems with split operators are proposed to solve time domain Maxwell's equations. Maxwell's equations are discretized in time direction and in spatial direction with different order of sympleetie schemes and fourth-order finite difference approximations, respectively. Stability analysis and numerical results are presented. A five-stage fourth-order multi-step high-order finite difference scheme proves accurate and efficient, and applicable to long time simulations.