Development of advanced ADI-FDTD based techniques for electromagnetics and microwave modeling.
Date
2006
Authors
Ahmed, Iftikhar.
Journal Title
Journal ISSN
Volume Title
Publisher
Dalhousie University
Abstract
Description
With the development of more complicated structures in the field of electrical engineering, the importance of the computational electromagnetics increases. With computational electromagnetics, a designer can know what happens inside circuit structures, namely, which components or elements radiate and how signals travel and reflect. For microwave frequencies and wide band systems applications, time-domain methods are increasingly preferred of their capability in handling wide band signals. Among time domain methods, FDTD (Finite Difference Time Domain) method has attracted more attention due to its simplicity and direct applicability to Maxwell's equations. It has been used in a large number of applications, and FDTD based software has been developed commercially. Nevertheless, due to CFL (Courant-Friedrich-Levy) stability constraint and numerical dispersion error, it takes large memory and simulation time for electrically large and high Q structures. To circumvent the problems, many improved FDTD methods have been developed. For instance, to make FDTD method memory efficient, PSTD (Pseudospectral Time Domain) method was proposed, and to reduce its dispersive error MRTD (Multiresolution Time Domain) was developed. To remove the CFL constraint, unconditionally stable ADI-FDTD method was introduced recently, although it takes more memory and is more dispersive at larger time steps.
To further improve the computational efficiency, in this thesis, hybrid FDTD and ADI-FDTD method is introduced. By using this hybrid approach, advantages of both FDTD and ADI-FDTD methods can be taken. In it, FDTD is applied in coarse mesh and ADI-FDTD in fine mesh areas. The time step is the same as that of the FDTD region even with smaller cell size in ADI-FDTD region. In this way, optimum saving in memory and computation time can be achieved without sacrificing the accuracy.
Accuracy of the ADI-FDTD method deteriorates at larger time steps. To mitigate this problem, two different error-reduced ADI-FDTD methods are presented. These error-reduced methods are based on the more accurate Crank Nicolson (CN) method but the simulation procedure is like the ADI-FDTD method. In these methods, modified splitting error term, which is missing in ADI-FDTD formulation and causes inaccuracy, is introduced to reduce the errors. The first method is found to be more accurate than the second one, but both are better than the conventional ADI-FDTD method.
ADI-FDTD also has relatively large dispersion error in comparisons with the FDTD method. To reduce it, dispersion optimized ADI-FDTD methods with different cases are also developed in this thesis. In them, dispersion controlling parameters are introduced, which result in different degrees of dispersion controls.
In summary, all the methods proposed in this thesis are aimed at improving the efficiency of FDTD method and the ADI-FDTD method. To improve computational efficiency an efficient hybrid method is introduced. To have better results with larger time steps, error-reduced ADI-FDTD methods are introduced, and to control the dispersion of ADI-FDTD method dispersion optimized ADI-FDTD methods are proposed. These proposed methods are then numerically tested for validity and effectiveness.
Thesis (Ph.D.)--Dalhousie University (Canada), 2006.
To further improve the computational efficiency, in this thesis, hybrid FDTD and ADI-FDTD method is introduced. By using this hybrid approach, advantages of both FDTD and ADI-FDTD methods can be taken. In it, FDTD is applied in coarse mesh and ADI-FDTD in fine mesh areas. The time step is the same as that of the FDTD region even with smaller cell size in ADI-FDTD region. In this way, optimum saving in memory and computation time can be achieved without sacrificing the accuracy.
Accuracy of the ADI-FDTD method deteriorates at larger time steps. To mitigate this problem, two different error-reduced ADI-FDTD methods are presented. These error-reduced methods are based on the more accurate Crank Nicolson (CN) method but the simulation procedure is like the ADI-FDTD method. In these methods, modified splitting error term, which is missing in ADI-FDTD formulation and causes inaccuracy, is introduced to reduce the errors. The first method is found to be more accurate than the second one, but both are better than the conventional ADI-FDTD method.
ADI-FDTD also has relatively large dispersion error in comparisons with the FDTD method. To reduce it, dispersion optimized ADI-FDTD methods with different cases are also developed in this thesis. In them, dispersion controlling parameters are introduced, which result in different degrees of dispersion controls.
In summary, all the methods proposed in this thesis are aimed at improving the efficiency of FDTD method and the ADI-FDTD method. To improve computational efficiency an efficient hybrid method is introduced. To have better results with larger time steps, error-reduced ADI-FDTD methods are introduced, and to control the dispersion of ADI-FDTD method dispersion optimized ADI-FDTD methods are proposed. These proposed methods are then numerically tested for validity and effectiveness.
Thesis (Ph.D.)--Dalhousie University (Canada), 2006.
Keywords
Engineering, Electronics and Electrical.