TSU 07 0 8 2012 K Natobaidze N Qozashvili T Aslanishvili N Chumbadze B Tsutskhvashvili G Bakradze 5 th GeorgianGerman School and ID: 311357
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Slide1
Icosahedral mesh simulator
TSU 07. 08. 2012.
K. Natobaidze N. Qozashvili T. Aslanishvili N. Chumbadze B. Tsutskhvashvili G. Bakradze
5th Georgian-German School and Workshop inBasic Science, 2012
1
5th Georgian-German School and Workshop in Basic ScienceSlide2
Task
icosahedron
2
5th Georgian-German School and Workshop in Basic Science
Slide3
Tools
3
5th Georgian-German School and Workshop in Basic ScienceSlide4
Users
w
here is ‘start’ button ?45th Georgian-German School and Workshop in Basic ScienceSlide5
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5th Georgian-German School and Workshop in Basic ScienceSlide6
Features
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5th Georgian-German School and Workshop in Basic ScienceSlide7
Features
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min area
max area
min value
max value
5th Georgian-German School and Workshop in Basic ScienceSlide8
Features
8
5th Georgian-German School and Workshop in Basic ScienceSlide9
Effects
9
5th Georgian-German School and Workshop in Basic ScienceSlide10
Effects
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5th Georgian-German School and Workshop in Basic ScienceSlide11
Effects
11
5th Georgian-German School and Workshop in Basic ScienceSlide12
OpenGL
12
5th Georgian-German School and Workshop in Basic ScienceSlide13
OpenGL
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OpenGL
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mouse ‘listener’keyboard ‘listener’
5th Georgian-German School and Workshop in Basic ScienceSlide15
Structure
start point
end point
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5th Georgian-German School and Workshop in Basic ScienceSlide16
Structure
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5th Georgian-German School and Workshop in Basic ScienceSlide17
Subdivision
1) divide container
2) add row
3) add column
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5th Georgian-German School and Workshop in Basic ScienceSlide18
Subdivision
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5th Georgian-German School and Workshop in Basic ScienceSlide19
Neighbours
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5th Georgian-German School and Workshop in Basic ScienceSlide20
Problem
20
Differential Equation on the Sphere
tє(0,T] u
u0
is known
now
later
?
!
5th Georgian-German School and Workshop in Basic ScienceSlide21
stencil
Differential equation
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5th Georgian-German School and Workshop in Basic ScienceSlide22
Discretized
analog –Explicit Euler scheme
Where
,
,
is known
.
is time step.
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5th Georgian-German School and Workshop in Basic ScienceSlide23
Other N
umerical Methodsexplicit
Runge–Kutta methods23
5th Georgian-German School and Workshop in Basic ScienceSlide24
Other explicit
Runge
–Kutta methods24
Second
Orderapproximation
ThirdOrderapproximation
Fourth
Order
approximation
5th Georgian-German School and Workshop in Basic ScienceSlide25
Future plans
25
Local mesh refinementIntroduce different stencilsExtend developed software to concrete equations Solve concrete problems5th Georgian-German School and Workshop in Basic ScienceSlide26
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Thank you
გმადლობთSpecial thanks to
Ramaz Botchorishvili
,
Tinatin
Davitashvili
and Nino
Tkheshelashvili
for their support
5th Georgian-German School and Workshop in Basic ScienceSlide27
waiting for Batumi
27
5th Georgian-German School and Workshop in Basic Science