A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator

Hirono, T.; Lui, W.W.; Seki, S.; Yoshikuni, Y.

doi:10.1109/22.942578

Cited by 99 publications

(104 citation statements)

References 21 publications

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“…Many physical evolution equations, from classical mechanics 1,2,3,4 , electrodynamics 5 , statistical mechanics 6,7 to quantum mechanics 8,9,10 , all have the form ∂w ∂t = (T + V )w, (1.1) where T and V are non-commuting operators. Such an equation can be solved iteratively via w(t + ǫ) = e ǫ(T +V ) w(t), (1.2) provided that one has a suitable approximation for the short time evolution operator e ǫ(T +V ) .…”

Section: Introductionmentioning

confidence: 99%

Structure of positive decompositions of exponential operators

Chin

2005

Phys. Rev. E

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The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For time-reversible equations, such as the Hamilton or the Schrödinger equation, it is immaterial whether or not the decomposition coefficients are positive. In fact, most symplectic algorithms for solving classical dynamics contain some negative coefficients. For time-irreversible systems, such as the Fokker-Planck equation or the quantum statistical propagator, only positive-coefficient decompositions, which respect the time-irreversibility of the diffusion kernel, can yield practical algorithms. These positive time steps only, forward decompositions, are a highly effective class of factorization algorithms. This work introduce a framework for understanding the structure of these algorithms. By a suitable representation of the factorization coefficients, we show that specific error terms and order conditions can be solved analytically. Using this framework, we can go beyond the Sheng-Suzuki theorem and derive a lower bound for the error coefficient eV T V . By generalizing the framework perturbatively, we can further prove that it is not possible to have a sixth order forward algorithm by including only theThe pattern of these higher order forward algorithms is that in going from the (2n) th to the (2n+2) th order, one must include a new commutator [V T 2n−1 V ] in the decomposition process.

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Section: Introductionmentioning

confidence: 99%

Structure of positive decompositions of exponential operators

Chin

2005

Phys. Rev. E

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“…As to (5), the evolution of the electromagnetic field during the timestep ∆t can be exactly expressed by the exponential operator [2]:…”

Section: Symplectic Scheme In Temporal Discretizationmentioning

confidence: 99%

“…Using the symplectic integrator propagator technique [2], the evolution matrix exp(∆t(A + B)) can be presented as:…”

Section: Symplectic Scheme In Temporal Discretizationmentioning

confidence: 99%

“…Therefore, a nonphysical dispersion is introduced and affects the accuracy limits of simulations. The radian frequency ω of the numerical mode is expressed as [2,14]:…”

Section: Dispersionmentioning

confidence: 99%

“…As the Maxwell's equations can be treated as a Hamiltonian system, some researchers adopted symplectic integrators for use in computational electromagnetics (CEM) in recent years. Hirono et al [2], Sha et al [3][4][5] and Kusaf et al [6] have done lots of work on combining this method with the FDTD scheme, and have got excellent results.…”

Section: Introductionmentioning

confidence: 99%

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Multiresolution Time Domain Scheme Using Symplectic Integrators

Sun¹,

Shi²,

Zhang³

et al. 2013

PIER M

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Abstract-We incorporate high-order symplectic time integrators into multiresolution time domain (MRTD) schemes. The stability and numerical dispersion analysis are presented. The proposed scheme preserves the symplectic structure of Maxwell's equations and can be easily implemented in program codes. Compared to Runge-Kutta (RK)-MRTD, the suggested scheme is more accurate in long-term simulations and requires less computational resource.

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Factorization‐splitting algorithm based on system incorporated method for periodic nonuniform domains in open regions

Wang

Qiao

2023

Int J Numerical Modelling

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The original Factorization‐Splitting (FS) algorithm solves large number of coefficients and components in each iteration cycle which significantly affects the computational resources and calculation efficiency. Meanwhile, it can merely solve problems in uniform domains due to the limitation of discretized mesh sizes. In order alleviate these drawbacks, system incorporated factorization‐splitting algorithm is proposed to efficiently solve problems in nonuniform domains. The finite‐difference time‐domain (FDTD) domain is terminated by the higher order perfectly matched layer (PML) formulation which shows advantages in improving the absorbing performance. As the employment of the original domain decomposition method results in the algorithm unstable, an alternative domain decomposition method is proposed which can split the entire nonuniform domain into several sub‐regions. Metamaterial structure is introduced to demonstrate the performance of the proposed algorithms. Through results, the proposed algorithm can decrease memory consumption and simulation duration due to the calculation prevention of repeated components and coefficients. The absorption can be further improved especially in the low‐frequency band due to the enhanced absorption of propagation waves. In addition, the alternative domain decomposition method shows considerable advantages in the simulation of nonuniform domains.

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A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator

Cited by 99 publications

References 21 publications

Structure of positive decompositions of exponential operators

Structure of positive decompositions of exponential operators

Multiresolution Time Domain Scheme Using Symplectic Integrators

Factorization‐splitting algorithm based on system incorporated method for periodic nonuniform domains in open regions

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