icosahedral mesh simulator
DESCRIPTION
Icosahedral mesh simulator. TSU 07. 0 8. 2012. . K . Natobaidze N . Qozashvili T . Aslanishvili N . Chumbadze B . Tsutskhvashvili G . Bakradze. 5th Georgian-German School and Workshop in Basic Science. 5 th Georgian-German School and W orkshop in Basic S cience, 2012. Task. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/1.jpg)
1
Icosahedral mesh simulatorTSU 07. 08. 2012.
K. Natobaidze N. Qozashvili T. Aslanishvili
N. Chumbadze
B. Tsutskhvashvili G. Bakradze
5th Georgian-German School and Workshop inBasic Science, 2012
5th Georgian-German School and Workshop in Basic Science
![Page 2: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/2.jpg)
2
Task
icosahedron
5th Georgian-German School and Workshop in Basic Science
𝑢′ (𝑡 )= 𝑓 ( 𝑡 ,𝑢 (𝑡 ) )
![Page 3: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/3.jpg)
3
Tools5th Georgian-German School and
Workshop in Basic Science
![Page 4: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/4.jpg)
4
Userswhere is ‘start’
button ?
5th Georgian-German School and Workshop in Basic Science
![Page 5: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/5.jpg)
5
MethodEulerClass
Fields
data1data2data3data4data5ficomaxValuevEndvStart
Methods
~MethodEulerdrawPointdrawPointsdrawSolutionPointsgetNeighbourSuminitinitMatrixMethodEulerminimizeForDrawsolvesolveMatrix
5th Georgian-German School and Workshop in Basic Science
![Page 6: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/6.jpg)
6
Features5th Georgian-German School and
Workshop in Basic Science
![Page 7: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/7.jpg)
7
Features
min area max area min value max value
5th Georgian-German School and Workshop in Basic Science
![Page 8: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/8.jpg)
8
Features5th Georgian-German School and
Workshop in Basic Science
![Page 9: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/9.jpg)
9
Effects5th Georgian-German School and
Workshop in Basic Science
![Page 10: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/10.jpg)
10
Effects5th Georgian-German School and
Workshop in Basic Science
![Page 11: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/11.jpg)
11
Effects5th Georgian-German School and
Workshop in Basic Science
![Page 12: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/12.jpg)
12
OpenGL
glutCreateWindow()
glutInitWindowSize(x,y)
glutInitWindowPosition(x,y)
5th Georgian-German School and Workshop in Basic Science
![Page 13: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/13.jpg)
13
OpenGL
glutDisplayFunc(display)• glutReshapeFunc(reshape)•
5th Georgian-German School and Workshop in Basic Science
![Page 14: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/14.jpg)
14
OpenGL
mouse ‘listener’ keyboard ‘listener’
5th Georgian-German School and Workshop in Basic Science
![Page 15: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/15.jpg)
15
Structure
start point
end point
5th Georgian-German School and Workshop in Basic Science
![Page 16: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/16.jpg)
16
Structure5th Georgian-German School and
Workshop in Basic Science
![Page 17: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/17.jpg)
17
Subdivision1) divide container
2) add row
3) add column
5th Georgian-German School and Workshop in Basic Science
![Page 18: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/18.jpg)
18
Subdivision5th Georgian-German School and
Workshop in Basic Science
![Page 19: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/19.jpg)
19
Neighbours5th Georgian-German School and
Workshop in Basic Science
![Page 20: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/20.jpg)
20
ProblemDifferential Equation on the Sphere• tє(0,T] •u u0 is known
now later
?!
5th Georgian-German School and Workshop in Basic Science
![Page 21: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/21.jpg)
21
•
stencil
Differential equation
𝑢𝑖𝑗
𝑢𝑖𝑗(1) 𝑢𝑖𝑗 (2)
𝑢𝑖𝑗(3)𝑢𝑖𝑗 (6 )
𝑢𝑖𝑗 (5) 𝑢𝑖𝑗(4 )
5th Georgian-German School and Workshop in Basic Science
![Page 22: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/22.jpg)
22
Discretized analog –Explicit Euler scheme
• Where , , is known.• is time step.
5th Georgian-German School and Workshop in Basic Science
![Page 23: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/23.jpg)
23
Other Numerical Methods•explicit Runge–Kutta methods
5th Georgian-German School and Workshop in Basic Science
![Page 24: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/24.jpg)
24
•Other explicit Runge–Kutta methods
SecondOrderapproximation
ThirdOrderapproximation
),( 001 yxfk
1002 3
1,31 hkyhxfk
2003 3
2,32 hkyhxfk
32101 4
3041 kkkhyy
3101 4
341 kkhyy
FourthOrderapproximation
432101
3004
2003
1002
001
226
,21,
21
21,
21),(
kkkkhyy
hkyhxfk
hkyhxfk
hkyhxfk
yxfk
5th Georgian-German School and Workshop in Basic Science
![Page 25: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/25.jpg)
25
Future plans • Local mesh refinement• Introduce different stencils• Extend developed software to concrete equations • Solve concrete problems
5th Georgian-German School and Workshop in Basic Science
![Page 26: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/26.jpg)
26
Thank you გმადლობთ
Special thanks to Ramaz Botchorishvili , Tinatin Davitashvili and Nino
Tkheshelashvili for their support
5th Georgian-German School and Workshop in Basic Science
![Page 27: Icosahedral mesh simulator](https://reader035.vdocument.in/reader035/viewer/2022062315/56816381550346895dd4650b/html5/thumbnails/27.jpg)
27
waiting for Batumi5th Georgian-German School and
Workshop in Basic Science