![fdtd algorithm fdtd algorithm](https://www.researchgate.net/profile/Mohammed-Zia-Ullah-Khan/publication/332333025/figure/fig11/AS:746230233718785@1554926560417/Flowchart-of-general-ADE-FDTD-algorithm-Optical-model.png)
Finally, to verify the proposed algorithm, two scattering numerical examples are given. Secondly, the field components on the z-axis are amended with special treatment. Firstly, according to the ideology of the weighted Laguerre polynomial (WLP) FDTD scheme, the WLP-FDTD equations of the proposed algorithm in the 3D cylindrical coordinate system are deduced by introducing the new perturbation term and the nonphysical intermediate variables. Therefore, in order to expand the research field of the FDTD method, we propose an efficient Laguerre-based finite-difference time-domain iterative algorithm in the 3D cylindrical coordinate system. There is not even an article on the Laguerre technology. Perhaps this is why, since 2000, the FDTD method has done little applications in the 3D cylindrical coordinate system.
#Fdtd algorithm how to
In addition, how to conduct direction transformation of the fields on the z-axis is also a research difficult in the 3D cylindrical coordinate system. How to reduce this kind of error in the iterative FDTD calculation has become a difficult problem. In fact, due to the existence of the term in the 3D cylindrical coordinate system, the decomposition of the fields along the direction will lead the splitting error. If we adopt the conventional FDTD method to discretize the cylindrical structure with the Cartesian grid, a significant staircasing error appears.
![fdtd algorithm fdtd algorithm](https://www.researchgate.net/profile/Samy-Ghania/publication/283086918/figure/fig6/AS:668519947595788@1536398984505/The-main-steps-of-the-developed-FDTD-algorithm.png)
Moreover, the geometry of interest may consist of fine structures. However, in many applications, we have to deal with 3D cylindrical structures such as in optical fiber communication, integrated optics, and defense industry. Obviously, the good feasibility of the efficient Laguerre scheme had been conformed in the rectangular coordinate system. To further reduce the splitting error, the modified perturbation term was introduced in meanwhile, the Gauss–Seidel iterative procedure was applied, which made the new Laguerre-based FDTD scheme more efficient and accurate. This provided excellent computational accuracy and can be efficiently parallel-processed on a computing cluster. To overcome this problem, a factorization-splitting scheme was used to resolve the huge sparse matrix into six tridiagonal matrixes, and then the chasing method was used to solve them. The main drawback of the conventional Laguerre-based FDTD algorithm is that it requires solving a very large sparse matrix. Thus, Laguerre-based FDTD formulation has the advantage of less numerical error when a larger time step is used. By transforming the time-domain problem to the Laguerre domain using the temporal Galerkin’s testing procedure, the transient solution is independent of time discretization. In recent years, the unconditionally stable Laguerre-based finite-difference time-domain (FDTD) algorithm has been applied to simulate transient electromagnetic problems in the Cartesian coordinate. Meanwhile, the proposed algorithm is extremely useful for the problems with fine structures in the 3D cylindrical coordinate system. The computation results show that the proposed algorithm can be better than the ADI-FDTD algorithm in terms of efficiency and accuracy. To verify the performance of the proposed algorithm, two scattering numerical examples are given. Such a treatment scheme can reduce the splitting error to a low level and obtain a good convergence in other words, it can improve the efficiency and accuracy than other algorithms.
![fdtd algorithm fdtd algorithm](https://d3i71xaburhd42.cloudfront.net/5582e2a3db0bfba4dc15fecde8b544ce11b7b977/6-Figure1-1.png)
Different from the previously developed iterative procedure used in the efficient FDTD algorithm, a new perturbation term combined with the Gauss–Seidel iterative procedure is introduced to form the new Laguerre-based FDTD algorithm in the 3D cylindrical coordinate system. Numerical results show high efficiency and accuracy of the proposed method.Here an efficient Laguerre-based finite-difference time-domain iterative algorithm is proposed. In addition, because US-FDTD is only used in one of the subdomains, compared with global US-FDTD method, the matrix dimension of hybrid FDTD is reduced, which saves the time for eigenvalue solution. Hybrid FDTD makes the explicit time marching with a uniform time step determined by the size of coarse grid in whole domain, which reduces the iteration time. A compensation scheme is used on the subdomain boundary without compromising accuracy.
#Fdtd algorithm free
Traditional FDTD is used in the remaining coarse grids subdomain and it is a matrix free method. US-FDTD is used in fine grids and the adjacent coarse grids subdomain and it breaks the Courant-Friedrich-Levy (CFL) condition. This hybrid FDTD method combines the superiorities of explicit unconditionally stable FDTD (US-FDTD) and traditional FDTD methods to achieve unconditional stability and high calculation efficiency. A new hybrid Finite-Difference Time-Domain (hybrid FDTD) algorithm is proposed in this paper.