$ 1.3 droiT areSi sasruli sxvaobebis ( FDTD ) meTodi maqsvelis da

biosiTbis gantolebebisaTvis

droiT areSi sasruli sxvaobebis meTodi ( FDTD ) warmoadgens maqsvelis

gantolebebis diskretizacias centraluri sxvaobebis meTodiT. amocana aris

(1.1) gantolebebis diskretizacia kompiuteruli modelirebisaTvis.

; 0

(1.14)

; 0

BE M D

t

DH J B

t

sadac D E

da B H

; eleqtruli SeRwevadoba da magnituri

mimReblobaa, romlebic moicema Semdegi saxiT 0r da 0 sadac r da

r fardobiTi xolo 0 da 0 Tavisufali sivrcisTvis ( 128,854*10 f/m da74 *10 h/m Sesabamisad). xolo s EJ J

da *

sM M H

sadac sJ da sM

gare wyaroebia xolo da * eleqtruli gamtaroba(sim/m) da magnituri

danakargebi(omi/m). Tu am formulebs SevitanT (1.14) da gadavwerT maT

integraluri saxiT miviRebT

*( ) (1.15)s

C S S

Edl Bds M H dst

( ) (1.16)s

C S S

Hdl Dds J E dst

anu gvaqvs faradeis da amperis kanonebi Sesabamisad. am integraluri

gantolebebis diskretizireba mocemul sivrce drois badeze saSualebas

gvaZlevs amovxsnaT maqsvelis gantolebebi mocemuli

wyaroebis da fizikuri parametrebis SemTxvevaSi.

iees [] algoriTmi mdgomareobs SemdegSi: vakeTebT

(1.15-16) gantolebebis diskretizirebas. yoveli

“ujredisTvis” zE velis komponentis ganaxleba

xdeba misi mezobeli B

velebis komponentebis

aRebuli drois ½ bijis ukan da E Sesabamisi

komponentis saSualebiT wina bijze. Semdeg vzrdiT

dros droiTi bijis naxevariT da Sesabamisad xdeba

B

komponentebis ganaxleba.

SemovitanoT aRniSvnebi: , ,i j k -warmoadgenen sivrcul ( , ,x y z ) indeqsebs, n

droiT indeqss, , ,x y zN N N kvanZebis raidenobaa sivrcul badeze.

sur.1.1 E da Hvelebi

; , ;; , ; ( . )

; , ;

i i i x

j j j y

k k k z

x x x i N

y y y j N

z z z k N

1

1

1

1 1

1 1 117

1 1

elementaruli ujredis centeris koordinatebi iqneba:

/ / // ; / ; / ; ( . )i i i j j j k k kx x x y y y z z z 1 2 1 2 1 22 2 2 1 18

xolo centrebs Soris manZili :

( ) / ; ( ) / ; ( ) / ; ( . )i i i j j j k k kh x x h y y h z z 1 1 12 2 2 1 19

E velebi mocemulia ujredis wiboebis centrebSi, xolo B velebi ujredis

waxnagebis centrebSi. maSin mocemuli ujrisaTvis (1.15-1.16) diskretizacia

gvaZlevs Semdeg sqemas E da B komponentebisTvis: qvemoT moyvanilia sqema Ez

komponentisTvis.

zE

1 12 2

1 1 1 1 1 1 1 12 2 2 2 2 2 2 2

1 11 1 1 12 2 2 2

, , , ,

, , , , , ,

, , , , , , , ,(1.20)

2

y y j x x i

n n n nz z z z

i j i ji j k i j k

H i j k H i j k hy H i j k H i j k hx

E i j k E i j k E i j k E i j khx hy hx hy

t

aqedan 1nzE Tvis miviRebT

1 12 2

1 1 1 12 2 2 2

, , , ,1 1 12 2

, , , , , , , ,

1 1 1 1 1 1 1 12 2 2 2 2 2 2 2

2 2, , , ,2 2

1 1, , , , , , (1.21)

i j k i j kn nz z

i j k i j k i j k i j k

y y x xi j

t tE i j k E i j k

t t

H i j k H i j k H i j k H i j khx hy

analogiurad gveqneba danarCeni komponentebisTvisac. sxvadasxva sivrculi

bijis gaTvaliswineba programaSi orive tipis,erTgavrovani da adaptiuri

badis, agebis saSualebas iZleva. aseve nivTierebaTa parametrebi mocemulia

badis kvanZebze da damokidebulia indeqsebze i,j,k rac araerTgavrovani

obieqtebis saSualebas iZleva. droiTi biji gamoiTvleba kurantis pirobidan

21,, kjiEz

21,,21 kjiH y

21,,21 kjiH y

21,21, kjiH x 21,21, kjiH x 21 ii

i

xxhx

21 jj

j

yyhy

3t FDTD

c

3t

c

sadac minimaluri sivrciTi bijia badeze.

dawvrilebiT FDTD meTodi aRwrilia [taflovis ssilka]

biosiTbos gantolebis (1.22) modelireba (1.23) sasazRvro pirobiT

maqsvelis gantolebebis modelirebis analogiuria.

0 ( ) (1.22)b

TC K T SAR A B T T

t

( ) (1.23)a

TK h T T

n

siTburi gantolebis modelirebisas viyenebT igive sivrcul bades rac

gvaqvs maqsvelis gantolebebis SemTxvevaSi, viyenebT nivTierebebs rac gavqvs

ujredis centrSi.

vwerT siTburi balansis gantolebas1 1 1 1

1

0* *

( ) * (1.24)

n n n n

n n n n

n

n

t t t t

t V t S t V t V

t

b

t V

Tdt C dV dt Gds dt SAR dV dt A dV

t

dt B T T dV

sadac V elementaruli ujredis moculobaa S zedapiri, xolo

G K T

aris siTbos nakadi mocemuli ujredis zedapirze. nakadebis enaze

(1.22-24) gantolebebis modelireba metad moxerxebulia sxvadasxva sasazRvro

pirobebis modelirebisaTvis. aseve aseTi formulireba moxerxebulia amocanis

mrudwirul koordinatebSi formulirebisas. (1.23) pirobis gaTvaliswineba

niSnavs G nakadze pirobis dadebas elementaruli ujredis sazRvarze. Cvens

SemTxvevaSi, vinaidan bade orTogonaluria es niSnavs rom ujredis waxnagebze

gvaqvs mxolod erTi komponenta , ,x y zG G G Sesabamisad , ,x y z waxnagebze. (1.24)

diskretizeba sabolood gvaZlevs

11/2, 1/2, 1/2 1/2, 1/2, 1/2 , , , , 1, ,

1/2, 1/2, 1/2 1/2, 1/2, 1/2

1/2, 1/2, 1/2 1/2, 1/2, 1/21/2, 1/2, 1/2 1/2, 1/2, 1/2

( )

( & )

( ) (

n n n ni j k i j k x i j k x i j k

i j k i j k

ni j k i j k b

i j k i j k

tT T G G

C

x y x z terms

tB T T

C

1/2, 1/2, 1/2

1/2, 1/2, 1/2 1/2, 1/2, 1/21/2, 1/2, 1/2 1/2, 1/2, 1/2

0

1.24)

(

)i j k

i j k i j ki j k i j k

tSAR

C

A

sadac 1, , , , 1/ 2, 1/ 2, 1/ 2 1/ 2, 1/ 2, 1/ 2, , ,

, , 1, , , 1( )

n ni j k i j k i j k i j kn

x i j ki j k i j k x i

k k T TG

k k h

(1.25) konveqciuri

sasazRvro pirobebis SemTxvevaSi Sesabamisi nakadis formula icvleba (1.23)

diskretizaciiT. (1.24-25) formulaSi koeficintebis cvlilebiT advilad

SeiZleba sxvadasxva sasazRvro pirobebis (konveqcia, mudmivi temperatura,

adiabaturi sasazRvro piroba) modelireba.