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Parallelisation of Implicit Time Domain Methods: Progress with ADI-FDTD

Timothy David Drysdale, Tomasz P. Stefanski
2009 PIERS Online  
First we describe a domain decomposition scheme for parallel ADI-FDTD in three dimensions that is suitable for implementation on widely available high performance computer architectures such as symmetric  ...  We provide an overview of our work to date on the parallelization of implicit time domain methods, in particular the alternating direction implicit finite-difference time-domain method (ADI-FDTD).  ...  Our investigations of the ADI-FDTD method resulted in improvements to the standard implementations of the Mur 1st order ABC [7] and CPML boundary condition [8] .  ... 
doi:10.2529/piers080905063810 fatcat:qudbhtyewfew7e3tyhkmgufbsy

The Simplest V-Cycle Fast Adaptive Composite Grid ADI-FDTD Method for Two-Dimensional Electromagnetic Simulations

Ki-Bok Kong, Yong-Sun Shin, Seong-Ook Park, Jong-Sung Kim
2008 IEEE Antennas and Wireless Propagation Letters  
A comparison of the computational efficiency between the FAC-ADI and ADI-FDTD is presented.  ...  ADI-FDTD is derived from the Crank-Nicolson (CN) ADI scheme, and its efficiency is investigated.  ...  The splitting error between the ADI-FDTD and CN FDTD methods does not occur on the boundary of global and local domain and the effectiveness of the iterative scheme is realized only in the interior domain  ... 
doi:10.1109/lawp.2008.2002316 fatcat:dpen7jsxxbazhf3tze4dhwaeqi

Split-field PML implementations for the unconditionally stable LOD-FDTD method

V.Ed. Nascimento, B.-H.V. Borges, F.L. Teixeira
2006 IEEE Microwave and Wireless Components Letters  
The LOD-FDTD formalism is expanded in terms of a symmetric source implementation.  ...  We introduce and compare two split-field implementations of the perfectly matched layer (PML) for the unconditionally stable locally one-dimensional (LOD) finite-difference timedomain (FDTD) method.  ...  Second Scheme In this case, the forward approximation is applied to the conduction terms on the left hand side of (1)-(4), akin to the ADI-FDTD implementation in [13] .  ... 
doi:10.1109/lmwc.2006.877132 fatcat:5n2yypt5qjaarlpcdwwlaj64uy

An efficient PML implementation for the ADI-FDTD method

Shumin Wang, F.L. Teixeira
2003 IEEE Microwave and Wireless Components Letters  
Index Terms-Alternating-direction implicit (ADI) method, finite-difference time-domain (FDTD) method, perfectly matched layer (PML).  ...  A novel implementation of the perfectly matched layer (PML) absorber for the alternating-direction implicit finite-difference time-domain method is proposed and implemented.  ...  CONCLUSION In this letter, we have introduced an improved implementation of the PML absorbing boundary condition for the ADI-FDTD method.  ... 
doi:10.1109/lmwc.2003.808705 fatcat:yd2zy3lr4rdutdidjgcntcwvzu

Reduced splitting error in the ADI-FDTD method using iterative method

Ki-Bok Kong, Jong-Sung Kim, Seong-Ook Park
2008 Microwave and optical technology letters (Print)  
In this study, a new method is introduced to reduce the splitting error in the ADI-FDTD method using iterative method. The proposed method includes two procedures.  ...  First we solve the procedure of ADI-FDTD method and secondly a new iterative scheme is adopted. The improvement of reduced splitting error is investigated by numerical examples.  ...  It is not necessary to improve the accuracy on the boundary domain whatever we use PML or Mur boundary conditions. The boundary condition is applied to solve only the ADI-FDTD method of Eq. (2) .  ... 
doi:10.1002/mop.23618 fatcat:sbv6pbwnzrcaldmnlh52dncv5u

BANDPASS UNCONDITIONALLY STABLE CE-BOR-PML SCHEME WITH CNDG ALGORITHM FOR ROTATIONAL SYMMETRIC SIMULATION

Shihong Wu, Lining Liu, Yunyun Dong, Feng Su, Xiangguang Chen
2021 Progress In Electromagnetics Research M  
To be more specific, this implementation is based upon the CN Douglas-Gunn (DG) procedure and the complex envelope (CE) method in body of revolution (BOR) finite-difference time-domain (FDTD) lattice.  ...  Meanwhile, it can also verify that the proposed scheme is stable without the limitation of Courant-Friedrich-Levy (CFL) condition.  ...  As can be concluded, the original ADI, LOD, SS schemes are implemented by the split step procedure. Such condition results in the degeneration of accuracy and efficiency.  ... 
doi:10.2528/pierm21051401 fatcat:6ug4jonyprhphetysufkxrt56m

Efficient Enhanced Hybrid Implicit-Explicit Procedure to Gyrotropic plasma in Open Regions with Fine Geometry Details along Single Direction

Peiyu Wu, Han Yu, Yongjun Xie, Haolin Jiang, Toshiaki Natsuki
2021 IEEE Access  
In open region problems, it has been demonstrated that the absorbing boundary condition must be employed for the termination of unbounded domains [4] [5] .  ...  Thus, the two components should be updated at the same time to maintain the stability of the algorithm.  ...  He is currently Editorial Board member of three international Journals.  ... 
doi:10.1109/access.2021.3081986 fatcat:7ebkgfmz5vbd3ezaeoottixfua

ONE-STEP ABSOLUTELY STABLE FDTD METHODS FOR ELECTROMAGNETIC SIMULATION

Faxiang Chen, Kang Li
2021 Progress In Electromagnetics Research Letters  
In the present paper, two novel one-step absolutely stable FDTD methods including one-step alternating-direction-implicit (ADI) and one-step locally-one-dimensional (LOD) methods are proposed.  ...  , various implicit methods have been proposed to tackle the problem, while many of them adopt time-splitting schemes that generally need at least two sub-steps to finish update at a full time step, and  ...  As the complexity of the splitting-step methods increases, the implementations of the two algorithms in the main computation domain, the treatment of boundary conditions, and the implementation of source  ... 
doi:10.2528/pierl21080503 fatcat:k5d3j5rcwbcozkdjjxvzqg6vcy

Alternating Direction Implicit Methods for FDTD Using the Dey-Mittra Embedded Boundary Method

T. M. Austin, J. R. Cary, D. N. Smithe, C. Nieter
2014 The Open Plasma Physics Journal  
To date, the ADI method applied to the FDTD method for curved domains has been used within the context of subgridding (i.e., local refinement) or for stairstepped boundaries that are only first-order accurate  ...  The alternating direction implicit (ADI) method is an attractive option to use in avoiding the Courant-Friedrichs-Lewy (CFL) condition that limits the size of the time step required by explicit finite-difference  ...  One approach to modeling curved domains is to use a subgridding scheme on the boundary [5] . For such a subgridding scheme, a hybrid ADI-FDTD method was proposed in Ref.  ... 
doi:10.2174/1876534301003010029 fatcat:ccj45zlsnrbcrgts7mag7gximq

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

V.E. do Nascimento, Kyung-Young Jung, B.-H.V. Borges, F.L. Teixeira
2009 Journal of Lightwave Technology  
We assess the performance of three unconditionally stable finite-difference time-domain (FDTD) methods for the modeling of doubly dispersive metamaterials: 1) locally one-dimensional FDTD; 2) locally one-dimensional  ...  FDTD with Strang splitting; and (3) alternating direction implicit FDTD.  ...  updated once (on increment) for two substpes in LOD-FDTD, but twice (on increment) for two substeps in ADI-FDTD.  ... 
doi:10.1109/jlt.2009.2023089 fatcat:gzxhlgc33vgbrib3xjan5j4fly

Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

Konrad Kowalczyk, Maarten van Walstijn
2008 Acta Acustica united with Acustica  
In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces.  ...  The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on the rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital  ...  An outer corner has two boundary conditions (in xand y-direction), the discretised versions of which are used for the elimination of the two ghost points in the discretised 2D wave equation.  ... 
doi:10.3813/aaa.918107 fatcat:rafkmtlhdjeipditjeocbjebe4

A HYBRID IMPLICIT-EXPLICIT SPECTRAL FDTD SCHEME FOR OBLIQUE INCIDENCE PROBLEMS ON PERIODIC STRUCTURES

Yunfei Mao, Bin Chen, Hao-Quan Liu, Jing-Long Xia, Ji-Zhen Tang
2012 Electromagnetic Waves  
Compared with the ADI-SFDTD method it only needs to solve two untridiagonal matrices when the PBC is applied to, other four equations can be updated directly, while four untridiagonal matrices, two tridiagonal  ...  condition (PBC) can be implemented easily for both normal and oblique incident waves.  ...  it needs to solve six matrices and six explicit updates in ADI-SFDTD scheme.  ... 
doi:10.2528/pier12032306 fatcat:ezj5qciu5ncazn2fvl5lzpsiwu

Time-domain hybrid methods to solve complex electromagnetic problems

A.R. Bretones, S. Gonzalez Garcia, R. Godoy Rubio, R. Gomez Martin, A. Monorchio
2003 2003 IEEE International Symposium on Electromagnetic Compatibility, 2003. EMC '03.  
, or that of the ADI-FDTD formulation of not imposing conditions on the duration of the temporal interval.  ...  This communication describes the FDTD-FETD-MoMTD and the ADI-FDTD/MoMTD time-domain hybrid techniques.  ...  The ADI-FDTD scheme [7, 8] eliminates the restrictions imposed by the Courant stability condition.  ... 
doi:10.1109/icsmc2.2003.1429045 fatcat:et6a74aevzhspe5soxwfvfdchi

STABILITY AND DISPERSION ANALYSIS FOR THREE-DIMENSIONAL (3-D) LEAPFROG ADI-FDTD METHOD

Theng Huat Gan, Eng Leong Tan
2012 Progress In Electromagnetics Research M  
The leapfrog ADI-FDTD method is reformulated in the form similar to conventional explicit FDTD method by introducing two auxiliary variables.  ...  of the leapfrog ADI-FDTD method.  ...  These examples demonstrated the stability of the leapfrog ADI-FDTD method only in numerical way with some boundary conditions.  ... 
doi:10.2528/pierm11111803 fatcat:7b54d4z3indrpcrqlprpkftwk4

Alternating-Direction Implicit Formulation of the Finite-Element Time-Domain Method

Masoud Movahhedi, Abdolali Abdipour, Alexandre Nentchev, Mehdi Dehghan, Siegfried Selberherr
2007 IEEE transactions on microwave theory and techniques  
In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented.  ...  A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived.  ...  ACKNOWLEDGMENT The authors would like to thank the three reviewers of this paper for their constructive comments and helpful suggestions.  ... 
doi:10.1109/tmtt.2007.897777 fatcat:omobrrcynbatdlv2tb2thlgwlq
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