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7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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Simulation of Electromagnetic Fields:The Finite-Difference Time-Domain (FDTD)
Method and Its Applications
Veysel Demir, Ph.D.demir@ceet.niu.edu
Department of Electrical Engineering, orthern Illinois !ni"ersit#, De$al%, I& '*
7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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+achelor of Science, Electrical and Electronics Engineering, Middle East Technical
ni!ersity, "n#ara, Tur#ey, 1$$%.
S#stem Anal#st and rogrammer, Pamu#&an#, 'o(t)are De!elo*ment De*artment,
+stan&ul, Tur#ey, uly 1$$% - "ugust 2.
Master of Science, Electrical Engineering, 'yracuse ni!ersity, 'yracuse, 0, 22.
Doctor of hilosoph#, Electrical Engineering, 'yracuse ni!ersity, 'yracuse, 0, 24.
esearch Assistant, 'onnet 'o(t)are, +nc. i!er*ool, 0, "ugust 2 - uly 24.
.isiting research scholar, ni!ersity o( Mississi**i, Electrical Engineering De*artment,
ni!ersity, M', uly 24 - Present.
Assistant rofessor, Department of Electrical Engineering, orthern Illinois
!ni"ersit#, De$al%,I&,"ugust 2% - *resent
.e#sel Demir
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+ntegral euation
methodsDi((erential euation methods
/omputational Electromagnetics
Ma)ells euations can &e gi!en in di((erential or integral (orm
5inite6di((erence
time6domain
75DTD8
5inite6di((erence
(reuency6domain
75D5D8
Method o( Moments
7MoM8
5ast multi*ole
method 75MM8
5inite element
method 75EM8
Transmission line
matri 7TM8
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5reuency domain methods
Time6domain methods
/omputational Electromagnetics
Ma)ells euations can &e gi!en in time domain or (reuency domain
5inite6di((erence
time6domain
75DTD8
5inite6di((erence
(reuency6domain
75D5D8
Method o( Moments
7MoM8
5ast multi*ole
method 75MM8
5inite element
method 75EM8
Transmission line
matri 7TM8
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/ommercial soft0are pac1ages
:ommercial so(t)are *ac#ages
5inite6di((erence time6domain 75DTD8
Method o( Moments 7MoM85inite element method 75EM8
Transmission line matri 7TM8
:'T Microstri*es
;5''
"D' Momentum
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FDTD +oo1s
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2earl# FDTD u%lications
The most *o*ular method in com*utational electromagnetics
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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Ma30ell4s E5uations
The &asic set o( euations descri&ing the electromagnetic )orld 'ho)s that light is an electromagnetic )a!e.
:onstituti!e relations
0
vD
B
BE
t
DH J
t
=
=
=
= +
Bausss la)
Bausss la) (or magnetism
"m*eres la)
5aradays la)
,andD E B H = =
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FDTD 6"er"ie0 7 Finite Differences
Ce*resent the deri!ati!es in Ma)ells curl euations &y (inite di((erences e use the second6order accurate central di((erence (ormula
( ) ( ) ( )( )
2
df x f x x f x xf x
dx x
+
=
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FDTD 6"er"ie0 7 /ells
" three6dimensional *ro&lem s*ace is com*osed o( cells
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FDTD 6"er"ie0 7 The 2ee /ell
The 5DTD 75inite Di((erence Time Domain8 algorithm )as (irst esta&lished
&y 0ee as a three dimensional solution o( Ma)ells curl euations.
K. Yee, IEEE Transactions on Antennas and Propagation, May 1966.
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FDTD 6"er"ie0 7 Material grid
" three6dimensional *ro&lem s*ace is com*osed o( cells
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FDTD 6"er"ie0 7 !pdating E5uations
Three scalar euations can &e o&tained (rom one !ector curl euation.
EH
t
=
yx zx
y x zy
y xzz
HE H
t y z
E H H
t z x
H HE
t x y
=
=
=
HE
t
=
yx zx
y xzy
yxzz
EH E
t z y
H EE
t x z
EEH
t y x
=
=
=
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FDTD 6"er"ie0 7 !pdating E5uations
Ce*resent deri!ati!es &y (inite6di((erences
yx zx
HE H
t y z
=
1
0.5 0.50.5 0.5
( , , ) ( , , )( , , )
( , , ) ( , , 1)( , , ) ( , 1, )
n n
x xx
n nn ny yz z
E i j k E i j ki j k
t
H i j k H i j kH i j k H i j k
y z
+
+ ++ +
=
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FDTD 6"er"ie0 7 !pdating E5uations
E*ress the (uture com*onents in terms o( the *ast com*onents
0.5 0.5
1
0.5 0.5
( , , ) ( , 1, )
( , , ) ( , , )( , , ) ( , , ) ( , , 1)
n n
z z
n n
x x n nx y y
H i j k H i j k
ytE i j k E i j k
i j k H i j k H i j k
z
+ +
+
+ +
=
0.5
0.5 0.5
( , , 1) ( , , )
( , , ) ( , , )( , , ) ( , 1, ) ( , , )
n n
y y
n n
x x n nx z z
E i j k E i j kt z
H i j k H i j ki j k E i j k E i j k
y
+
+ + = + +
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FDTD 6"er"ie0 7 &eap-frog Algorithm
Eercise 1D
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A%sor%ing +oundar# /onditions
The three6dimensional *ro&lem s*ace is truncated &y a&sor&ing
&oundaries
Most *o*ular a&sor&ing &oundary is Per(ectly Matched layers 7PM8
Eercise 2D PM
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Acti"e and assi"e &umped Elements
"cti!e and *assi!e lum*ed elements can &e modeled in 5DTD
EH E J
t
= + +
Voltage source :urrent source
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Acti"e and assi"e &umped Elements
Cesistor :a*acitor +nductor Diode
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Acti"e and assi"e &umped Elements
" diode circuit
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Transformation from Time-Domain to Fre5uenc#-Domain
Cesults can &e o&tained (or (reuency domain using 5ourier Trans(orm
" lo)6*ass (ilter
'11
'22
Eercise 2D o&Fect
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24
ear-Field to Far-field Transformations
"n in!erted65 antenna
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Modeling fine geometries
+t is *ossi&le to model (ine structures using a**ro*riate (ormulations
" )ire loo* antenna
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Scattering ro%lems
( ) ( )inc scat inc scat H H E Et
+ = + 0inc inc
H Et
=
" dielectric s*hereEercise 3D PM
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Scattering from a Dielectric Sphere
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Earth 8 Ionosphere Models in 9eoph#sics
'na*shots o( 5DTD6:om*uted Blo&al Pro*agation o( E5
Electromagnetic Pulse Benerated &y Vertical ightning 'tri#e o(( 'outh
"merica :oast
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,
Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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ireless ersonal /ommunications De"ices
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,
Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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hantom ;ead .alidation at
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,
Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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!ltra0ide%and Micro0a"e Detection of Earl#-Stage +reast /ancer
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,
Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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Focusing lasmonic &ens
'ource> "llen Ta(lo!e, ?" Pers*ecti!e on the 460ear ;istory o( 5DTD :om*utational Electrodynamics,
Applied /omputational Electromagnetics Societ# (A/ES) /onference, Miami, Florida, March 19, 2//))).ece.north)estern.edu/ece(aculty/"llen1.html
http://www.ece.northwestern.edu/ecefaculty/Allen1.htmlhttp://www.ece.northwestern.edu/ecefaculty/Allen1.html7/21/2019 Finite-Difference Time-Domain Method and Its Applications
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Than1 2ou
Eercise 2D PE:
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