This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
The problem for calculating near fields of EM radiation systems by using the finitedifference time domain(FD-TD)method are discussed and the annular phased array of dipoleantennas has been simulated numerically by use...The problem for calculating near fields of EM radiation systems by using the finitedifference time domain(FD-TD)method are discussed and the annular phased array of dipoleantennas has been simulated numerically by use of the FD-TD method.For a test run thenear field and current distribution of the single dipole antenna are calculated.The near fieldsof the annular phased array of dipole antennas in central region filled with deionized water arecomputed and the interaction of near fields with an anatomically-based inhomogeneous model ofhuman torso is considered as well.展开更多
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
文摘The problem for calculating near fields of EM radiation systems by using the finitedifference time domain(FD-TD)method are discussed and the annular phased array of dipoleantennas has been simulated numerically by use of the FD-TD method.For a test run thenear field and current distribution of the single dipole antenna are calculated.The near fieldsof the annular phased array of dipole antennas in central region filled with deionized water arecomputed and the interaction of near fields with an anatomically-based inhomogeneous model ofhuman torso is considered as well.
