Title :
The stability and numerical dispersion analyses of high-order symplectic FDTD scheme for solving time-dependent Schrödinger equation
Author :
Jing Shen ; Sha, Wei E. I. ; ZhiXiang Huang ; Mingsheng Chen ; Xianliang Wu
Author_Institution :
Key Lab. of Intell. Comput. & Signal Process., Anhui Univ., Hefei, China
Abstract :
A high-order symplectic FDTD (SFDTD) framework for solving the time-dependent Schrödinger equation is established. The third-order symplectic integrators and fourth-order collocated differences are employed in the time and space domains, respectively. The stabilities and numerical dispersions of FDTD(2,2), higher-order FDTD(2,4), and SFDTD(3,4) schemes are analyzed. We found that the stability limit of the SFDTD(3,4) scheme can be larger than that of the traditional FDTD(2,2) method through careful optimization of symplectic integrators. Moreover, the SFDTD(3,4) scheme and the FDTD(2,4) approach show better numerical dispersions than the traditional FDTD(2,2) method.
Keywords :
Schrodinger equation; dispersion relations; finite difference time-domain analysis; nonlinear differential equations; numerical stability; fourth-order collocated differences; high-order symplectic FDTD framework; high-order symplectic FDTD scheme; numerical dispersion analyses; numerical stability; space domains; symplectic integrator optimization; third-order symplectic integrators; time domains; time-dependent Schrodinger equation; Dispersion; Equations; Finite difference methods; Mathematical model; Numerical stability; Stability analysis; Time domain analysis;
Conference_Titel :
Microwave and Millimeter Wave Technology (ICMMT), 2012 International Conference on
Conference_Location :
Shenzhen
Print_ISBN :
978-1-4673-2184-6
DOI :
10.1109/ICMMT.2012.6230409
