Finite-Difference Time-Domain Method and Its Applications

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, [email protected]

Department of Electrical Engineering, orthern Illinois !ni"ersit#, De$al%, I& '*


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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.html


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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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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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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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Cesistor :a*acitor +nductor Diode


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" 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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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


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ireless ersonal /ommunications De"ices




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hantom ;ead .alidation at




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!ltra0ide%and Micro0a"e Detection of Earl#-Stage +reast /ancer




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Focusing lasmonic &ens




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Than1 2ou

Eercise 2D PE:

Finite-Difference Time-Domain Method and Its Applications

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