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.

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 Short Review of FDTD-Based Methods for Uncertainty Quantification in Computational Electromagnetics

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Theodoros T. Zygiridis
Keyword(s):  
Finite Difference ◽  
Uncertainty Quantification ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Computational Electromagnetics ◽  
Short Review ◽  
Electromagnetic Problems ◽  
Difference Time

We provide a review of selected computational methodologies that are based on the deterministic finite-difference time-domain algorithm and are suitable for the investigation of electromagnetic problems involving uncertainties. As it will become apparent, several alternatives capable of performing uncertainty quantification in a variety of cases exist, each one exhibiting different qualities and ranges of applicability, which we intend to point out here. Given the numerous available approaches, the purpose of this paper is to clarify the main strengths and weaknesses of the described methodologies and help the potential readers to safely select the most suitable approach for their problem under consideration.

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.

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