Icosahedral mesh simulator

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13 Δεκ 2013 (πριν από 3 χρόνια και 7 μήνες)

76 εμφανίσεις

Icosahedral mesh simulator

TSU


07.
0
8. 2012.

K
.
Natobaidze


N
.
Qozashvili


T
.
Aslanishvili


N
.
Chumbadze


B
.
Tsutskhvashvili

G
.
Bakradze

5
th

Georgian
-
German School and
W
orkshop in

Basic
S
cience, 2012

1

5th Georgian
-
German School and Workshop in
Basic Science

Task

icosahedron

2

5th Georgian
-
German School and Workshop in
Basic Science




=
𝑓

,



Tools

3

5th Georgian
-
German School and Workshop in
Basic Science

Users

w
here is ‘start’
button ?

4

5th Georgian
-
German School and Workshop in
Basic Science

5

5th Georgian
-
German School and Workshop in
Basic Science

Features

6

5th Georgian
-
German School and Workshop in
Basic Science

Features

7

min area

max area

min value

max value

5th Georgian
-
German School and Workshop in
Basic Science

Features

8

5th Georgian
-
German School and Workshop in
Basic Science

Effects

9

5th Georgian
-
German School and Workshop in
Basic Science

Effects

10

5th Georgian
-
German School and Workshop in
Basic Science

Effects

11

5th Georgian
-
German School and Workshop in
Basic Science

OpenGL

12

glutCreateWindow
()

glutInitWindowSize
(
x,y
)

glutInitWindowPosition
(
x,y
)

5th Georgian
-
German School and Workshop in
Basic Science

OpenGL

13

glutDisplayFunc
(display)




glutReshapeFunc
(reshape)




5th Georgian
-
German School and Workshop in
Basic Science

OpenGL

14

mouse ‘listener’

keyboard ‘listener’

5th Georgian
-
German School and Workshop in
Basic Science

Structure

start point

end point

15

5th Georgian
-
German School and Workshop in
Basic Science

Structure

16

5th Georgian
-
German School and Workshop in
Basic Science

Subdivision

1) divide container

2) add row

3) add column

17

5th Georgian
-
German School and Workshop in
Basic Science

Subdivision

18

5th Georgian
-
German School and Workshop in
Basic Science

Neighbours

19

5th Georgian
-
German School and Workshop in
Basic Science

Problem

20





=
𝑓

,



t
є
(0,T]


u
0
=

u
0

5th Georgian
-
German School and Workshop in
Basic Science



′


=

𝛼
𝑛


𝑛
(

)
6
𝑛
=
1






(
0
)
=

0







stencil


Differential equation

21






(
1
)



(
2
)



(
3
)



(
6
)



(
5
)



(
4
)

5th Georgian
-
German School and Workshop in
Basic Science

Discretized
analog

Explicit
Euler scheme


𝑢



𝑢



1
𝜏
=

𝛼
𝑛



1

(
𝑛
)
6
𝑛
=
1



Where









,




=
𝑘𝜏
,

0
=
0
,



0


is
known
.


𝜏

is time step.

22

5th Georgian
-
German School and Workshop in
Basic Science

Other
N
umerical
M
ethods


23

5th Georgian
-
German School and Workshop in
Basic Science

24

Second

Order

approximation

T
hird

Order

approximation



)
,
(
0
0
1
y
x
f
k












1
0
0
2
3
1
,
3
1
hk
y
h
x
f
k











2
0
0
3
3
2
,
3
2
hk
y
h
x
f
k













3
2
1
0
1
4
3
0
4
1
k
k
k
h
y
y











3
1
0
1
4
3
4
1
k
k
h
y
y

Fourth

Order

approximation





4
3
2
1
0
1
3
0
0
4
2
0
0
3
1
0
0
2
0
0
1
2
2
6
,
2
1
,
2
1
2
1
,
2
1
)
,
(
k
k
k
k
h
y
y
hk
y
h
x
f
k
hk
y
h
x
f
k
hk
y
h
x
f
k
y
x
f
k



























5th Georgian
-
German School and Workshop in
Basic Science

Future plans

25


Local mesh refinement


Introduce different stencils


E
xtend developed software to concrete equations


Solve concrete problems

5th Georgian
-
German School and Workshop in
Basic Science

26

Special thanks to
Ramaz

Botchorishvili

,

Tinatin

Davitashvili

and Nino
Tkheshelashvili

for their support

5th Georgian
-
German School and Workshop in
Basic Science

waiting for
Batumi

27

5th Georgian
-
German School and Workshop in
Basic Science