A Three-Dimensional Unconditionally Stable Five-Step LOD-FDTD Method

Int J Numerical Modelling

2017

In this paper, the convolution perfectly matched layer (CPML) absorbing boundary conditions (ABC) in five‐step locally one‐dimensional finite‐difference time‐domain (LOD5‐FDTD) method are deduced. The formulation of the LOD5‐FDTD is derived and numerical results are demonstrated for different Courant Friedrich Levy numbers (CFL) in the simulation domain in the test. Then, using a sinusoidal source, the field phase distribution surrounded by the CPML‐ABC is calculated. The results of these simulation experiments illustrate that the CPML‐ABC can be used efficiently in the LOD5‐FDTD method.

- \frac{normalΔ t}{6 ε_{0} Δ^{3}} \frac{dP}{dt}

. Similarly, the source also could be added in the right side of the original E z final form equations at the location place for sub‐step 2, 4 and 5, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The ψ quantities are introduced into the above five steps for the implementation of the CPML-ABC. 1,12 Form (4)-(32), it can be seen that each equation contains one extra auxiliary variable ψ compare with the traditional LOD5-FDTD method. These auxiliary variables are only used in the CPML region, and zero in rest of the regions.…”

Section: Formulationmentioning

confidence: 99%

Study of the CPML for the Three‐Dimensional Five‐Step LOD‐FDTD method

Xuejian

Int J Numerical Modelling

2017

“…Although having one additional procedure with extra cost of solving tridiagonal systems, the CPU time incurred by the second-order FLOD-FDTD scheme is still around 0.93 that of first-order LOD-FDTD scheme in [12] due to RHS flops count reduction. Compared with the method in [13], the proposed fundamental scheme is almost two times faster while maintaining second-order temporal accuracy due to one substep fewer and matrix-operator-free RHS. The memory requirements of all the three schemes are also the same.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Here, A and B in [12] are different from (more sparse than) those in [11]. While the temporal accuracy of LOD-FDTD method with three split matrices is also of first order, it tends to be much more costly to realize second-order temporal accuracy in the traditional (Strang) way due to many more noncommutative terms AC, CA, BC and CB [13]. The associated noncommutative error may also be more significant compared to those of LOD-FDTD with two split matrices A and B [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Second-Order Temporal-Accurate Scheme for 3-D LOD-FDTD Method With Three Split Matrices

Antennas Wirel. Propag. Lett.

Tan

Heh

2015

This letter presents second-order temporal-accurate scheme for three-dimensional (3-D) LOD-FDTD method with three split matrices. The main iterations of the proposed scheme comprise only one more procedure in addition to the existing three procedures. Using proper (initial only) input and (often infrequent, field-point only) output processings, the secondorder temporal accuracy is achieved and verified analytically. To further enhance the efficiency, the proposed scheme is implemented based on the principle of fundamental schemes for unconditionally-stable FDTD methods, which feature a matrixoperator-free right-hand side (RHS). Stability analysis is provided to ascertain the unconditional stability of the proposed scheme and numerical results are demonstrated to justify its higher accuracy.Index Terms-LOD-FDTD, second-order temporal accuracy, unconditional stability.

“…The three-dimensional five-step LOD-FDTD (LOD5-FDTD) method [1] is an unconditionally stable method whose time step is not restricted by the Courant-Friedrich-Lewy (CFL) stability condition [2]. It is worth mentioning that the LOD5-FDTD method has second-order accuracy in time domain and yields less numerical dispersion than the ADI-FDTD [3,4], two-step LOD-FDTD [5], and three-step LOD-FDTD [6] methods.…”

Section: Introductionmentioning

confidence: 99%

Study of Upml Absorbing Boundary Condition for the Five-Step Lod-FDTD Method

Xuejian

Chen

2016

PIER M

Abstract-In this paper, the uniaxial anisotropic perfectly matched layer (UPML) absorbing boundary condition in unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD5-FDTD) method is deduced. The UPML absorbing boundary condition (ABC) is validated based on comparison with a simulation in larger domain (and thus without reflection) in the first test. Then using a sinusoidal source, target field phase distribution surrounded by the UPML-ABC is analyzed. The results further illustrate the stability and efficiency of the UPML absorbing boundary condition.