Symplectic Finite-difference Time-domain Scheme Research Articles

高阶辛算法在典型量子器件模拟中的应用

高阶辛算法在典型量子器件模拟中的应用

A High-Order, Symplectic, Finite-Difference Time-Domain Scheme for Bioelectromagnetic Applications within the Mother/Fetus Model.

An explicit high-order, symplectic, finite-difference time-domain (SFDTD) scheme is applied to a bioelectromagnetic simulation using a simple model of a pregnant woman and her fetus. Compared to the traditional FDTD scheme, this scheme maintains the inherent nature of the Hamilton system and ensures energy conservation numerically and a high precision. The SFDTD scheme is used to predict the specific absorption rate (SAR) for a simple model of a pregnant female woman (month 9) using radio frequency (RF) fields from 1.5 T and 3 T MRI systems (operating at approximately 64 and 128 MHz, respectively). The results suggest that by using a plasma protective layer under the 1.5 T MRI system, the SAR values for the pregnant woman and her fetus are significantly reduced. Additionally, for a 90 degree plasma protective layer, the SAR values are approximately equal to the 120 degree layer and the 180 degree layer, and it is reduced relative to the 60 degree layer. This proves that using a 90 degree plasma protective layer is the most effective and economical angle to use.

High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation

Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrödinger equation. First, the high-order symplectic framework for discretizing a Schrödinger equation is described. Then the numerical stability and dispersion analyses are provided for the FDTD(2, 2), higher-order FDTD(2, 4) and SFDTD(3, 4) schemes. Next, to implement the Dirichlet boundary condition encountered in the quantum eigenvalue problem, the image theory and one-sided difference technique are manipulated particularly for high-order collocated differences. Finally, a detailed numerical study on 1D and 2D quantum eigenvalue problems is carried out. The simulation results of quantum wells and harmonic oscillators strongly confirm the advantages of the SFDTD scheme over the traditional FDTD method and other high-order approaches. The explicit SFDTD scheme, which is high-order-accurate and energy-conserving, is well suited for a long-term simulation and can save computer resources with large time step and coarse spatial grids.

High-order unified symplectic FDTD scheme for the metamaterials

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 dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.

High-oder symplectic FDTD scheme for solving time-dependent Schrdinger equation

Using three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD(3, 4)) scheme is proposed to solve the time-dependent Schrdinger equation. First, high-order symplectic framework for discretizing the Schrdinger equation is described. The numerical stability and dispersion analyses are provided for the FDTD(2, 2), FDTD(2, 4) and SFDTD(3, 4) schemes. The results are demonstrated in terms of theoretical analyses and numerical simulations. The spatial high-order collocated difference reduces the stability that can be improved by the high-order symplectic integrators. The SFDTD(3, 4) scheme and FDTD(2, 4) approach show better numerical dispersion than the traditional FDTD(2, 2) method. The simulation results of a two-dimensional quantum well and harmonic oscillator strongly confirm the advantages of the SFDTD(3, 4) scheme over the traditional FDTD(2, 2) method and other high-order approaches. The explicit SFDTD(3, 4) scheme, which is high-order-accurate and energy-conserving, is well suited for long-term simulation.

WAVEGUIDE SIMULATION USING THE HIGH-ORDER SYMPLECTIC FINITE-DIFFERENCE TIME-DOMAIN SCHEME

Abstract—The high-order symplectic finite-difference time-domain scheme is applied to modeling and simulation of waveguide structures. First, the perfect electric conductor boundary is treated by the image theory. Second, to excite all possible modes, an efficient source excitation method is proposed. Third, the modified perfectly matched layer is extended to its high-order form for absorbing the evanescent waves. Finally, a high-order scattering parameter extraction technique is developed. The cases of waveguide resonator, waveguide discontinuities, and periodic waveguide structure demonstrate that the high-order symplectic finite-difference time-domain scheme can obtain better numerical results than the traditional finite-difference timedomain method and save computer resources.

Application of the high‐order symplectic FDTD scheme to the curved three‐dimensional perfectly conducting objects

AbstractA high‐order symplectic finite‐difference time‐domain (SFDTD) scheme using the diagonal split‐cell model is presented to analyze electromagnetic scattering of the curved three‐dimensional perfectly conducting objects. On the one hand, for the undistorted cells, the fourth‐order accurate spatial difference is employed. On the other hand, for the completely distorted cells, the treatment of the curved surfaces is based on the diagonal split‐cell model. Finally, for the partially distorted cells, the interpolation strategy is proposed to keep the field components continuous. The numerical experiments suggest that the diagonal SFDTD scheme can obtain more accurate results than both the staircased SFDTD scheme and the traditional diagonal FDTD method. Furthermore, in view of the high numerical stability, the improved symplectic scheme does not need to decrease time increment to comply with the stability criterion. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 931–934, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22306

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air–dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources.

A Diagonal Split-cell Model for the High-order Symplectic FDTD Scheme

A high-order symplectic FDTD (SFDTD) scheme using the diagonal split-cell model is presented to analyze electromagnetic scattering of the curved three-dimensional perfectly conducting objects. One the one hand, for the undistorted cells, the fourth-order accurate spatial difierence is employed. On the other hand, for the completely distorted cells, the treatment of the curved surfaces is based on the diagonal split-cell model. Finally, for the partially distorted cells, the interpolation strategy is proposed to keep the fleld components continuous. The numerical experiments suggest that the diagonal SFDTD scheme can obtain more accurate results than both the staircased SFDTD scheme and the traditional diagonal FDTD method. Furthermore, in view of the high numerical stability, the improved symplectic scheme does not need to decrease time increment to comply with the stability criterion.