Quelques EDP simples r´esolues avec FreeFem++, Astuces et Trucs

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algorithm We use the following fix point method : let be, k = 0, Ω k = Ω. First step, we forgot the Neumann BC and we solve the problem : Find p in V = H 1 (Ω k ), such p = y on Γ k b et on Γk f � Ω k ∇p∇p′ = 0, ∀p ′ ∈ V with p ′ = 0 on Γ k b ∪ Γk f With the residual of the Neumann boundary condition we build a domain transformation F(x, y) = [x, y − v(x)] where v is solution of : v ∈ V , such than v = 0 on Γ k a (bottom) � Ω k ∇v∇v′ = � Γ k f ( ∂p ∂n − q K nx)v ′ , ∀v ′ ∈ V with v ′ = 0 sur Γ k a remark : we can use the previous equation to evaluate � Γ k ∂p ∂n v′ = − � ∇p∇v′ Ωk Journée Gamni, IHP, 23 sept. 2005 16
The new domain is : Ω k+1 = F(Ω k ) Warning if is the movement is too large we can have triangle overlapping. problem Pp(p,pp,solver=CG) = int2d(Th)( dx(p)*dx(pp)+dy(p)*dy(pp)) + on(b,f,p=y) ; problem Pv(v,vv,solver=CG) = int2d(Th)( dx(v)*dx(vv)+dy(v)*dy(vv)) + on (a, v=0) + int1d(Th,f)(vv*((Q/K)*N.y)) + wdpdn[] ) ; while(errv>1e-6) { j++ ; Pp ; wdpdn[] = A*p[] ; wdpdn[] = wdpdn[].*onfree[] ; wdpdn[] = -wdpdn[] ; // hack Pv ; errv=int1d(Th,f)(v*v) ; coef = 1 ; // Here french cooking if overlapping see the example Th=movemesh(Th,[x,y-coef*v]) ; // deformation } file:///Users/hecht/Desktop/ffday Journée Gamni, IHP, 23 sept. 2005 17
Page 1 and 2: Quelques EDP simples résolues avec
Page 3 and 4: HISTORIQUE Idée suivre le cours de
Page 5 and 6: The main characteristics of FreeFem
Page 7 and 8: The main characteristics of FreeFem
Page 9 and 10: trouver u solution de Equation de l
Page 11 and 12: Equation de la chaleur/ table de co
Page 13 and 14: Equation de la chaleur avec de matr
Page 15: Un problème de nappe phréatique T
Page 19 and 20: Inequation Variationnelle mesh Th=s
Page 21 and 22: Aii=A.diag ; // get the diagonal of
Page 23 and 24: Methode de Joint Methode de joint ,
Page 25 and 26: Methode de Joint macro defspace(i)
Page 27 and 28: Methode de Joint lh[]=0 ; varf vDD(

Quelques EDP simples r´esolues avec FreeFem++, Astuces et Trucs

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