Performance comparison between alternating direction implicit finite difference time domain method (ADI-FDTD) and conventional finite difference time domain method (FDTD) Adamu Abubakar Isah; Supervisor: Mehmet Kuşaf

Yazar: Katkıda bulunan(lar):Dil: İngilizce Yayın ayrıntıları:Nicosia Cyprus International University 2015Tanım: VIII, 49 p. table, figure, color graphic 30.5 cm CDİçerik türü:
  • text
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  • unmediated
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  • volume
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Eksik içerik
1 CHAPTER ONE
1 INTRODUCTION
1-2 BACKGROUND
3 MOTIVATIONS OF THE WORK
3 APPLICATION
4 THESIS STRUCTURES
5 CHAPTER TWO
5 LITERATURE REVIEW
5 CHARACTERISTICS OF THE FDTD METHOD
6-9 MAXWELL'S EQUATIONS
10 UPDATE EQUATIONS IN 1-D
11-13 FDTD SOLUTIONS OF MAXWELL'S EQUATIONS
14-15 FINITE DIFFERENCE APPROXIMATION
16 TERMINATING THE GRID
16 ABSORBING BOUNDARY CONDITION
17-19 Perfectly Matched Layer ABCs
20 Discretization of Boundary Condition and Numerical Boundary Condition
21 CHAPTER FIVE
21 COMPARISON BETWEEN FDTD METHOD AND ADI-FDTD
21-22 CONVENTIONAL FDTD METHOD
23 Advantages of Conventional FDTD Method
23 Disadvantages of Conventional TDTD Method
24 IMPLICIT FDTD
25 ADI FDTD METHOD
26 Advantage of ADI-FDTD Method
26 Disadvantages of ADI-FDTD Method
27-28 TRIDIAGONAL SOLVERS
29 CHAPTER FOUR
29 METHODOLOGY
29 ADI - IMPLICIT TIME STEPPING ALGORITHM
30 ZHENG, CHAN & ZHANG FORMUALTION ALGORITHM
31 Simplied System of Time Stepping Equations
32 Sources
32 BASIC STABILITY ANALYSIS
33-34 NUMERICAL STABILITY
35 CHAPTER FIVE
35 NUMERICAL RESULTS AND DISCUSSION
36-37 ADI-FDTD simulation results
38-39 FDTD simulation results
41 IMPROVEMENT OF THE METHOD
42 CHAPTER FIVE
42-43 CONCLUSION AND RECOMMENDATION
44-48 REFERENCE
Özet: 'ABSTRACT The Impetus for the work presented here arose from the need that implicit FDTD method (ADI-FDTD) and explicit FDTD method (Conventional FDTD) method have distinguished advantage which is speed and precision respectively. It was proved that ADI-FDTD method is less restrained by Courant-Friedrich Levy (CFL) stability condition, conventional FDTD on the other hand is affected by CFL condition which makes the method difficult to be applied in the solution of large electrical problems which makes the use of Perfectly Matched Layer Absorbing Boundary Conditions (PML ABC) more effective and advantageous in terms of accurate results. Conversely, conventional FDTD method has proved to be generally more accurate than the ADI-FDTD method. Numerical simulation of both ADI-FDTD and conventional FDTD method are presented. The results are compared to find the performance of each method in terms of precision and accuracy with respect to the CPU time and memory usage. Keywords: Conventional FDTD, ADI-FDTD, Courant-Friedrich Levy (CFL) stability condition, Absorbing boundary conditions (ABC), Perfectly matched layer (PML).'
Materyal türü: Thesis
Mevcut
Materyal türü Geçerli Kütüphane Koleksiyon Yer Numarası Durum Notlar İade tarihi Barkod Materyal Ayırtmaları
Thesis Thesis CIU LIBRARY Tez Koleksiyonu Tez Koleksiyonu YL 537 I83 2015 (Rafa gözat(Aşağıda açılır)) Kullanılabilir Computer Engineering Department T593
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Includes CD

Includes references (44-48 p.)

'ABSTRACT The Impetus for the work presented here arose from the need that implicit FDTD method (ADI-FDTD) and explicit FDTD method (Conventional FDTD) method have distinguished advantage which is speed and precision respectively. It was proved that ADI-FDTD method is less restrained by Courant-Friedrich Levy (CFL) stability condition, conventional FDTD on the other hand is affected by CFL condition which makes the method difficult to be applied in the solution of large electrical problems which makes the use of Perfectly Matched Layer Absorbing Boundary Conditions (PML ABC) more effective and advantageous in terms of accurate results. Conversely, conventional FDTD method has proved to be generally more accurate than the ADI-FDTD method. Numerical simulation of both ADI-FDTD and conventional FDTD method are presented. The results are compared to find the performance of each method in terms of precision and accuracy with respect to the CPU time and memory usage. Keywords: Conventional FDTD, ADI-FDTD, Courant-Friedrich Levy (CFL) stability condition, Absorbing boundary conditions (ABC), Perfectly matched layer (PML).'

1 CHAPTER ONE

1 INTRODUCTION

1-2 BACKGROUND

3 MOTIVATIONS OF THE WORK

3 APPLICATION

4 THESIS STRUCTURES

5 CHAPTER TWO

5 LITERATURE REVIEW

5 CHARACTERISTICS OF THE FDTD METHOD

6-9 MAXWELL'S EQUATIONS

10 UPDATE EQUATIONS IN 1-D

11-13 FDTD SOLUTIONS OF MAXWELL'S EQUATIONS

14-15 FINITE DIFFERENCE APPROXIMATION

16 TERMINATING THE GRID

16 ABSORBING BOUNDARY CONDITION

17-19 Perfectly Matched Layer ABCs

20 Discretization of Boundary Condition and Numerical Boundary Condition

21 CHAPTER FIVE

21 COMPARISON BETWEEN FDTD METHOD AND ADI-FDTD

21-22 CONVENTIONAL FDTD METHOD

23 Advantages of Conventional FDTD Method

23 Disadvantages of Conventional TDTD Method

24 IMPLICIT FDTD

25 ADI FDTD METHOD

26 Advantage of ADI-FDTD Method

26 Disadvantages of ADI-FDTD Method

27-28 TRIDIAGONAL SOLVERS

29 CHAPTER FOUR

29 METHODOLOGY

29 ADI - IMPLICIT TIME STEPPING ALGORITHM

30 ZHENG, CHAN & ZHANG FORMUALTION ALGORITHM

31 Simplied System of Time Stepping Equations

32 Sources

32 BASIC STABILITY ANALYSIS

33-34 NUMERICAL STABILITY

35 CHAPTER FIVE

35 NUMERICAL RESULTS AND DISCUSSION

36-37 ADI-FDTD simulation results

38-39 FDTD simulation results

41 IMPROVEMENT OF THE METHOD

42 CHAPTER FIVE

42-43 CONCLUSION AND RECOMMENDATION

44-48 REFERENCE

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