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FreeFEM Python
FreeFEM Python
1
1
clock@LiberalArtsCommunity
clock@LiberalArtsCommunity
2019/10/19
2019/10/19
1
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2
( )
(Poisson )
( )
( )
= α∇ u
∂t
∂u 2
−∇ u = f(r)
2
= ∇ u
c2
1
∂t2
∂ u
2
2
∇ =
2 +
∂x2
∂2
∂y2
∂2
2 . 2
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(field):
( )
( )
2 . 3
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1.
( )
n n
2 . 4
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2.
( ) Fourier
etc
( ) etc
2 . 5
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FreeFEM
FreeFEM
3 . 2
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Dirichlet Poisson
( ) u
−∇ u = f(r), u = 0 on ∂Ω.
2
3 . 3
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( ) ( )
v v =
∣
∂Ω
0
u
∇u ⋅ ∇v dV = fv dV
∫
Ω
∫
Ω
3 . 4
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2
FreeFEM
3 . 5
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1.
2.
3.
3 . 6
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1.
2. 1
P1 1 , P2 2
3.
:
int n = 100;
border C(t=0,1){x=cos(2*pi*t); y=sin(2*pi*t);};
mesh Th = buildmesh(C(n));
fespace Vh(Th,P1);
∇u ⋅
∫
Ω
∇v dV = fv dV
∫
Ω
Vh u,v;
problem Poisson(u,v) =
int2d(Th)( dx(u)*dx(v)+dy(u)*dy(v) )
- int2d(Th)( f*v );
Poisson;
3 . 7
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FreeFEM
FreeFEM
4 . 1
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Poisson
Poisson
2
(Dirichlet )
Poisson
( )
−T∇ u = −ρg
2
g T
4 . 2
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:
( ):
:
= α∇ u
∂t
∂u 2
∼
∂t
∂u
Δt
u −u
i i−1
v dV + α∇u ⋅ ∇v dV = 0
∫
Ω
(
Δt
u − u
i i−1 ) ∫
Ω
i
4 . 4
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2
(i) 0 ( )
(ii) ( )
u =
∣
∂Ω
0
∇u =
∣
∂Ω
0
4 . 5
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Neumann Dirichlet
4 . 6
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Dirichlet :
Neumann :
t → ∞
4 . 7
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