Purpose - This paper aims to present a modified preciseintegrationtimedomain (PITD) method for the numerical solution of 2D scalar wave equation. Design/methodology/approach - The split step (SS) scheme is applied ...
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Purpose - This paper aims to present a modified preciseintegrationtimedomain (PITD) method for the numerical solution of 2D scalar wave equation. Design/methodology/approach - The split step (SS) scheme is applied to factorize the conventional PITD calculation into two sub-steps procedures and then field components can be updated along one spatial direction only in each sub-step. The perfectly matched layer (PML) absorber is extended to this method for modeling open region problems by using the stretched coordinate approach. Findings - It is shown that this method requires less computation time and storage space in comparison with the conventional PITD method, yet maintains the numerical stability despite using large time steps. Research limitations/implications - The WE-PITD method requires the divergence free region, which may be a limit on its usage. Hence, there is a challenge of using this technique in the 3D problems. Originality/value - Based on the SS scheme, the PITD method is used to solve the scale wave equation rather than Maxwell's equations, leading to a significant reduction in the computation time and memory usage.
Propagation properties of photonic crystals with defect are analyzed by the preciseintegrationtimedomain (PITD) method in the paper. The preciseintegration is applied to the finite difference timedomain in this m...
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Propagation properties of photonic crystals with defect are analyzed by the preciseintegrationtimedomain (PITD) method in the paper. The preciseintegration is applied to the finite difference timedomain in this method. The Yee cell differential discretization technique is used in space, and the preciseintegrationmethod is adopted in time. The correctness of the method is demonstrated by calculating the one-dimensional photonic crystals with defect. The transmission coefficients of the transverse electric (TE) and transverse magnetic (TM) modes in the two-dimensional photonic crystals with defect are also obtained by the method. Furthermore, the stability, precision and efficiency of the method are discussed. Numerical results reveal that the PITD method is not limited by the Courant stability condition and has higher calculation precision and efficiency, which provides a new and effective analytical method for studying the propagation properties of photonic crystals with defect.
Based on the three-stage split-step scheme, a second-order split-step precise-integrationtime-domain (SS2-PITD) method is proposed for solving Maxwell's equations, which has a better performance in computational ...
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ISBN:
(纸本)9798350348958;9798350348965
Based on the three-stage split-step scheme, a second-order split-step precise-integrationtime-domain (SS2-PITD) method is proposed for solving Maxwell's equations, which has a better performance in computational accuracy and efficiency than the previously proposed split-step precise-integrationtime-domain (SS1-PITD) method. Then, the numerical stability of the SS2-PITD method is analyzed, showing that the time step size in SS2-PITD can be a value much larger than the Courant-Friedrichs-Lewy limit. Finally, numerical examples are simulated to show the effectiveness of the proposed method.
Purpose - The purposes of this paper are to numerically analyse the distribution of the electromagnetic field in the electromagnetic device wherein a high-speed unit exists and to develop a strong tool to analyse the ...
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Purpose - The purposes of this paper are to numerically analyse the distribution of the electromagnetic field in the electromagnetic device wherein a high-speed unit exists and to develop a strong tool to analyse the evolution of an electromagnetic field tangled with moving parts. Design/methodology/approach - The preciseintegrationtimedomain (PITD) method and parameter weighted averaging approximation scheme. Findings - It is shown that that the electromagnetic field in the device is significantly affected by the velocity of the moving unit and the parameters of the base material. The computation resources of the proposed method are saved and the efficiency is enhanced. Originality/value - The parameter approximation (PA)-PITD method can be an effective and efficient timedomainmethod to analyse the evolution of the electromagnetic field in electromagnetic devices with moving parts and similar problems.
Based on the fourth-order finite difference (FD) scheme, a modified compact two dimensional preciseintegrationtimedomain (CPITD) method, called CPITD(4), is proposed to mitigate the numerical dispersion errors of t...
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Based on the fourth-order finite difference (FD) scheme, a modified compact two dimensional preciseintegrationtimedomain (CPITD) method, called CPITD(4), is proposed to mitigate the numerical dispersion errors of the CPITD algorithm when modeling electrically large and longitudinally invariant wave-guiding structures. Both the stability condition and the dispersion equation of the CPITD(4) method are derived analytically. It is found that the dispersion error of the CPITD(4) method is much smaller than that of the CPITD method. In particular, it should be pointed out that the CPITD(4) method can improve the performance of the CPITD method when beta(z)/beta leaves away from 1. Numerical experiments of typical waveguide structures validate and verify that the CPITD(4) method can decrease the calculated error without increasing the memory requirement and the execution time for all the cases.
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