scholarly journals A One-Step Leapfrog ADI Procedure with Improved Absorption for Fine Geometric Details

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1135
Author(s):  
Peiyu Wu ◽  
Han Yu ◽  
Yongjun Xie ◽  
Haolin Jiang ◽  
Toshiaki Natsuki
Keyword(s):  
Stability Condition ◽  
Computational Domain ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
Numerical Examples ◽  
Alternating Direction ◽  
One Step ◽  
Overall Performance ◽  
The Stability ◽  
Stable Scheme

Based on the alternating direction implicit (ADI) procedure, leapfrog formulation, and a higher order PML scheme, we propose an unconditionally stable perfectly matched layer (PML) algorithm with improved absorption to treat open regions in a finite computational domain with improved overall performance. The proposed algorithm performed well compared to other algorithms during simulations. We further demonstrated the proposed scheme’s effectiveness using numerical examples. We found that the proposed scheme had enhanced effectiveness and improved the absorption during the whole simulation. Furthermore, it was able to break the stability condition, proving that it is an unconditionally stable scheme.

The One-Step ADI-FDTD for Periodic Structures and its Stability

2014 ◽  
Vol 915-916 ◽  
pp. 1158-1162
Author(s):  
Yun Fei Mao ◽  
Hong Bing Wu ◽  
Lin Ou
Keyword(s):  
Periodic Structures ◽  
Fdtd Method ◽  
Fourier Method ◽  
Numerical Verification ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
One Step ◽  
The Stability ◽  
The One ◽  
Difference Time

In this paper, the stability analysis of the unconditionally stable one-step leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method for periodic structures is presented. The amplification matrix of the proposed leap-frog ADI-FDTD method is obtained through the spatial domain with Fourier method and eigenvalues of the Fourier amplification matrix are obtained analytically to prove the unconditional stability of the periodic leapfrog ADI-FDTD method. Numerical verification is proposed to confirm the theoretical result.

scholarly journals From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Eng Leong Tan
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Fdtd Methods ◽  
Difference Time

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (01) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

One-step alternating direction implicit FDTD algorithm

2004 ◽  
Vol 13 (11) ◽  
pp. 1892-1895 ◽  
Author(s):  
Liu Shao-Bin ◽  
Liu San-Qiu
Keyword(s):  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
One Step

scholarly journals Numerical Method for 2D Quasi-linear Hyperbolic Equation on an Irrational Domain: Application to Telegraphic Equation

2021 ◽  
Vol 69 (2) ◽  
pp. 116-123
Author(s):  
Bishnu Pada Ghosh ◽  
Nepal Chandra Roy
Keyword(s):  
Hyperbolic Partial Differential Equations ◽  
Linear Difference Equations ◽  
Alternating Direction Implicit Method ◽  
Linear Hyperbolic Equation ◽  
Alternating Direction Implicit ◽  
Telegraphic Equation ◽  
Physical Problems ◽  
Alternating Direction ◽  
Second Order In Time ◽  
The Stability

We develop a novel three-level compact method (implicit) of second order in time and space directions using unequal grid for the numerical solution of 2D quasi-linear hyperbolic partial differential equations on an irrational domain. The stability analysis of the model problem for unequal mesh is discussed and it is revealed that the developed scheme is unconditionally stable for the Telegraphic equation. For linear difference equations on an irrational domain, the alternating direction implicit method is discussed. The projected technique is scrutinized on several physical problems on an irrational domain to exhibitthe accuracy and effectiveness of the suggested method. Dhaka Univ. J. Sci. 69(2): 116-123, 2021 (July)

scholarly journals On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

2005 ◽  
Vol 42 (1) ◽  
pp. 199-222 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Stability Condition ◽  
Queue Length ◽  
Length Distribution ◽  
Buffer Size ◽  
Finite Buffer ◽  
Jackson Network ◽  
Numerical Examples ◽  
Queue Length Distribution ◽  
Special Cases ◽  
The Stability

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

scholarly journals A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala ◽  
Kanyuta Poochinapan
Keyword(s):  
Numerical Experiments ◽  
Mass Conservation ◽  
Cost Effective ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
Discrete Fourier Analysis ◽  
Convection Diffusion ◽  
Alternating Direction ◽  
Convection Dominated ◽  
And Diffusion

Abstract In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time, respectively. The resulting matrix at each ADI computation can be obtained by repeatedly solving a penta-diagonal system which produces a computationally cost-effective solver. We prove that the proposed scheme is mass-conserved and unconditionally stable by means of discrete Fourier analysis. Numerical experiments are performed to validate the mass conservation and illustrate that the proposed scheme is accurate and reliable for convection-dominated problems.

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