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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 Presentation
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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
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Task
icosahedron
5th Georgian-German School and Workshop in Basic Science
𝑢′ (𝑡 )= 𝑓 ( 𝑡 ,𝑢 (𝑡 ) )
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Tools5th Georgian-German School and
Workshop in Basic Science
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Userswhere is ‘start’
button ?
5th Georgian-German School and Workshop in Basic Science
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MethodEulerClass
Fields
data1data2data3data4data5ficomaxValuevEndvStart
Methods
~MethodEulerdrawPointdrawPointsdrawSolutionPointsgetNeighbourSuminitinitMatrixMethodEulerminimizeForDrawsolvesolveMatrix
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Features5th Georgian-German School and
Workshop in Basic Science
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Features
min area max area min value max value
5th Georgian-German School and Workshop in Basic Science
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Features5th Georgian-German School and
Workshop in Basic Science
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Effects5th Georgian-German School and
Workshop in Basic Science
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Effects5th Georgian-German School and
Workshop in Basic Science
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Effects5th Georgian-German School and
Workshop in Basic Science
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OpenGL
glutCreateWindow()
glutInitWindowSize(x,y)
glutInitWindowPosition(x,y)
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OpenGL
glutDisplayFunc(display)• glutReshapeFunc(reshape)•
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OpenGL
mouse ‘listener’ keyboard ‘listener’
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Structure
start point
end point
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Structure5th Georgian-German School and
Workshop in Basic Science
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Subdivision1) divide container
2) add row
3) add column
5th Georgian-German School and Workshop in Basic Science
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Subdivision5th Georgian-German School and
Workshop in Basic Science
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Neighbours5th Georgian-German School and
Workshop in Basic Science
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ProblemDifferential Equation on the Sphere• tє(0,T] •u u0 is known
now later
?!
5th Georgian-German School and Workshop in Basic Science
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•
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
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Discretized analog –Explicit Euler scheme
• Where , , is known.• is time step.
5th Georgian-German School and Workshop in Basic Science
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Other Numerical Methods•explicit Runge–Kutta methods
5th Georgian-German School and Workshop in Basic Science
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•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
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Future plans • Local mesh refinement• Introduce different stencils• Extend developed software to concrete equations • Solve concrete problems
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Thank you გმადლობთ
Special thanks to Ramaz Botchorishvili , Tinatin Davitashvili and Nino
Tkheshelashvili for their support
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waiting for Batumi5th Georgian-German School and
Workshop in Basic Science