Research On High Stability Symplectic Algorithm Based On Spatial Filtering Technique

Computational electromagnetic(CEM)is a new multi-disciplinary science.Integrating electromagnetic field theory,numerical method,and computer technology CEM has shown its academic and engineering significance.Though modeling simulation,optimization,and design,electromagnetic filed engineering has penetrated many aspects of industrial and military field.In particular,CEM plays a revolutionary role in advancing electromagnetic field engineering.Over past half century,algorithms of CEM were rapidly developed.Their outstanding representatives involve finite-element method,and finite-difference time-domain(FDTD)method,which are respectively used to discretize vector wave functions,integral equations,and Maxwell equation.It is in 1966 that Yee grid was proposed.Until now,the traditional FDTD method has been widely applied to broad-band,transient,and full-wave analyses owing to simplicity,generality,and facility for parallel computing.However,the FDTD method has two drawbacks.One is the undesirable numerical results caused by the significant accumulated errors from numerical instability,dispersion and anisotropy,especially for long-term simulation and electrically-large objects.Another is the inabilities to accurately model curved conducting surface and material discontinuities by using the staircasing approach with structured grids.Meantime,the efficiency of FDTD is limited by its restrictive stability condition and its pronounced numerical dispersion.The key observation is that while the CFL condition requires that all spatial harmonics of the discrete space-time fields remain stable,only a small portion of them actually contributes to the final solution.As a result,the CFL limit can be extended by letting some of these useless spatial harmonics become unstable,yet filtering them out sequentially at every time step.As in other methods to extend the CFL limit,the use of larger time step comes with additional operations.To solve the problems,the dissertation systematically studies the high-order symplectic FDTD(SFDTD)scheme within spatially filtering.For the temporal direction,the high-order symplectic and spatially filtering are used to keep the global symplectic structure of Maxwell equation for simulation.For the spatial direction,the staggered fourth-order difference scheme is used to reduce numerical dispersion and improve numerical precision.With the help of these matched schemes and techniques,we can build a more fast,low-consumed,and accurate time-domain solver.