采用分段线性电流密度递归卷积(P iecew ise L inear C u rren t D en sity R ecu rsive C onvo lu tion)方法将交替方向隐式时域有限差分方法(AD I-FDTD)推广应用于色散介质—等离子体中,得到了二维情况下等离子体中的迭代差分公式,为...采用分段线性电流密度递归卷积(P iecew ise L inear C u rren t D en sity R ecu rsive C onvo lu tion)方法将交替方向隐式时域有限差分方法(AD I-FDTD)推广应用于色散介质—等离子体中,得到了二维情况下等离子体中的迭代差分公式,为了验证该方法的有效性和可靠性,计算了等离子体涂敷导体圆柱的RC S和非均匀等离子体平板的反射系数,数据仿真结果表明,此算法与传统的FDTD相比,在计算结果吻合的情况下,存储量相当,计算效率更高,时间步长仅仅由计算精度来决定.展开更多
Several new energy identities of the two dimenslonal（2D） Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new ...Several new energy identities of the two dimenslonal（2D） Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction im- plicit finite difference time domain method for the 2D Maxwell equations （2D-ADI-FDTD）. It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta- ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical analysis on stability, convergence and energy conservation are presented.展开更多
This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving...This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.展开更多
The finite-difference time-domain （FDTD） method is extensively applied in dealing with time-domain microwave imaging（MWI） problems since it is robust, fast, simple to implement. However, the FDTD method is an expl...The finite-difference time-domain （FDTD） method is extensively applied in dealing with time-domain microwave imaging（MWI） problems since it is robust, fast, simple to implement. However, the FDTD method is an explicit time-stepping technique, due to the constraint of the Courant-Friedrich-Levy （CFL） stability condition, the time step needs to be as small as the size of the fine cells, which brings a major increase in computational costs. A fast nonlinear electromagnetic reconstruction algorithm for layered loss-y media by using the alternating-direction implicit finite-difference time-domain （ADI-FDTD） method is proposed. This algorithm is based on an adjoint method, and the nonlinear iterations apply the ADI-FDTD method to calculate the forward and adjoint field, and adopt the Polak, Ribiere, Polyar conjugate-gradient （PRP-CG） optimization scheme. By comparing the simulation results based on ADI-FDTD method and the FDTD method, the validity and efficiency of the proposed algorithm have been proved. Furthermore, the relative residual errors （RRE） are introduced as the iterative computation termination conditions, which further prove the accuracy of this algorithm.展开更多
The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, cap...The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, capacitor, and inductor, and three different formulations for each model are analyzed： the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.展开更多
文摘采用分段线性电流密度递归卷积(P iecew ise L inear C u rren t D en sity R ecu rsive C onvo lu tion)方法将交替方向隐式时域有限差分方法(AD I-FDTD)推广应用于色散介质—等离子体中,得到了二维情况下等离子体中的迭代差分公式,为了验证该方法的有效性和可靠性,计算了等离子体涂敷导体圆柱的RC S和非均匀等离子体平板的反射系数,数据仿真结果表明,此算法与传统的FDTD相比,在计算结果吻合的情况下,存储量相当,计算效率更高,时间步长仅仅由计算精度来决定.
基金supported by Shandong Provincial Natural Science Foundation(Y2008A19)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Several new energy identities of the two dimenslonal（2D） Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction im- plicit finite difference time domain method for the 2D Maxwell equations （2D-ADI-FDTD）. It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta- ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical analysis on stability, convergence and energy conservation are presented.
基金supported by Natural Science Foundation of Shandong Province (GrantNo. Y2008A19)Research Reward for Excellent Young Scientists from Shandong Province (Grant No. 2007BS01020)National Natural Science Foundation of China (Grant No. 11071244)
文摘This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.
文摘The finite-difference time-domain （FDTD） method is extensively applied in dealing with time-domain microwave imaging（MWI） problems since it is robust, fast, simple to implement. However, the FDTD method is an explicit time-stepping technique, due to the constraint of the Courant-Friedrich-Levy （CFL） stability condition, the time step needs to be as small as the size of the fine cells, which brings a major increase in computational costs. A fast nonlinear electromagnetic reconstruction algorithm for layered loss-y media by using the alternating-direction implicit finite-difference time-domain （ADI-FDTD） method is proposed. This algorithm is based on an adjoint method, and the nonlinear iterations apply the ADI-FDTD method to calculate the forward and adjoint field, and adopt the Polak, Ribiere, Polyar conjugate-gradient （PRP-CG） optimization scheme. By comparing the simulation results based on ADI-FDTD method and the FDTD method, the validity and efficiency of the proposed algorithm have been proved. Furthermore, the relative residual errors （RRE） are introduced as the iterative computation termination conditions, which further prove the accuracy of this algorithm.
基金the National Natural Science Foundation of China (Grant Nos.60171011 and 60571056)
文摘The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, capacitor, and inductor, and three different formulations for each model are analyzed： the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.
