scholarly journals 2D Efficient Unconditionally Stable Meshless FDTD Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Kang Luo ◽  
Yun Yi ◽  
Yantao Duan ◽  
Boao Xu ◽  
Bin Chen
Keyword(s):  
Time Domain ◽  
Finite Difference Time Domain ◽  
Sparse Matrix ◽  
Laguerre Polynomials ◽  
Splitting Scheme ◽  
System Matrix ◽  
Absorbing Boundary ◽  
Unconditionally Stable ◽  
Cpu Time ◽  
Difference Time

This paper presents an efficient weighted Laguerre polynomials based meshless finite-difference time domain (WLP-MFDTD). By decomposing the coefficients of the system matrix and adding a perturbation term, a factorization-splitting scheme is introduced. The huge sparse matrix is transformed into two N×N matrices with 9 unknown elements in each row regardless of the duplicated ones. Consequently, compared with the conventional implementation, the CPU time and memory requirement can be saved greatly. The perfectly matched layer absorbing boundary condition is also extended to this approach. A numerical example demonstrates the capability and efficiency 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 A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhuo Su ◽  
Yongqin Yang ◽  
Yunliang Long
Keyword(s):  
Time Domain ◽  
Finite Difference Time Domain ◽  
Symmetric Operator ◽  
Numerical Dispersion ◽  
Stable Method ◽  
Unconditionally Stable ◽  
Electromagnetic Problems ◽  
Performance Analyses ◽  
Computational Expenditure ◽  
Difference Time

Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

Research on the transmission coefficient of plasma photonic crystals based on the ICCG–SFDTD method

2015 ◽  
Vol 29 (12) ◽  
pp. 1550052 ◽  
Author(s):  
Ying-Jie Gao ◽  
Hong-Wei Yang ◽  
Rui Weng ◽  
Qing-Xia Niu ◽  
Yu-Jie Liu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Photonic Crystals ◽  
Transmission Coefficient ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Sparse Matrix ◽  
Fdtd Method ◽  
Computational Time ◽  
Plasma Photonic Crystals ◽  
Difference Time

Compared with the traditional finite-difference time-domain (FDTD) method, the symplectic finite-difference time-domain (SFDTD) method has the characteristics of high precision and low dispersion. However, because the higher-order difference is necessary for the calculation, a large sparse matrix is generated. It causes that the computational time is relatively long and the memory is more. To solve this problem, the incomplete Cholesky conjugate gradient (ICCG) method for solving the large sparse matrix needs to be taken into the SFDTD differential equations. The ICCG method can accelerate the iterations of the numerical calculation and reduce the memory with fast and stable convergence speed. The new ICCG–SFDTD method, which has both the advantages of the ICCG method and SFDTD method, is proposed. In this paper, the ICCG–SFDTD method is used for research on the characteristic parameters of the plasma photonic crystals (PPCs) under different conditions, such as the reflection electric field and the transmission coefficient, to verify the feasibility and accuracy of this method. The results prove that the ICCG–SFDTD method is accurate and has some advantages.

Sign in / Sign up

Export Citation Format

Share Document