scholarly journals ADI-MRTD Algorithm for Periodic Structures Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Xiaohua Dong ◽  
Yiwang Chen ◽  
Pin Zhang ◽  
Yichao Teng ◽  
Xiaobo Zhuansun
Keyword(s):  
Time Domain ◽  
Periodic Structures ◽  
Sampling Rate ◽  
Wave Number ◽  
Wavelet Theory ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Structure Simulation ◽  
The Time Domain ◽  
Difference Time

In this paper, a novel algorithm based on the alternating direction implicit (ADI) multiresolution time-domain (MRTD) method for periodic structure simulation is proposed. By applying the multiresolution analysis in accordance with wavelet theory, the spatial sampling rate of the conventional finite-difference time-domain (FDTD) is significantly reduced by the MRTD method. The ADI method is then used to remove the Courant-Friedrich-Levy (CFL) limit that the MRTD method experiences. The periodic boundary condition (PBC) is directly implemented in the time domain using a constant transverse wave-number (CTW) wave. Numerical results are presented to confirm the efficiency and accuracy of the proposed method.

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 The Alternating Direction Implicit Body of Revolution Multiresolution Time Domain Method with Convolution Perfect Matched Layer

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Chen Yiwang ◽  
Ni Jiazheng ◽  
Liu Yawen ◽  
Dong Xiaohua ◽  
Zhang Pin
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Three Dimension ◽  
Body Of Revolution ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Perfect Matched Layer ◽  
Difference Time

Overmuch memory and time of CPU have been taken by multiresolution time domain (MRTD) method in three-dimension issues. In order to solve this problem, the alternating direction implicit body of revolution multiresolution time domain (ADI-BOR-MRTD) scheme is presented. Firstly, based on body of revolution finite difference time domain (BOR-FDTD) method, equations of body of revolution multiresolution time domain (BOR-MRTD) method are implemented. Then alternating direction implicit (ADI) is introduced into BOR-MRTD method. Lastly, convolution perfect matched layer (CPML) is applied for ADI-BOR-MRTD method. Numerical results demonstrate that ADI-BOR-MRTD method saves more memory and time of CPU than FDTD and MRTD methods.

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