Re: [Getfem-users] coupling PDEs with linear terms

[Alice Nicolas]

I tried to implement coupled PDEs using the add_explicit_matrix brick:
 Eq(1): Laplacian(u)=p
 Eq (2): Laplacian(p)=x
u(0)=p(0)=0, u(1)=1/120, p(1)=1/6
 Although the program does work, it does not give the right solution.

I guess, I do not write correctly the tangent system. May I ask to one 
of you a critical eye on the part of code below? This would be of real help.
Thanks in advance.

Alice Nicolas

#evaluate the boundary conditions
gul = mfp.eval('0.')
gur=mfp.eval('1./120')
gpl = mfp.eval('0.')
gpr=mfp.eval('1./6')

# interpolate the source terms
fp = mfrhsp.eval('-x[0]')

# model
md = gf.Model('real')

# add variables and datas to model
md.add_fem_variable('u', mfu)
md.add_fem_variable('p', mfp)
md.add_initialized_fem_data('fp', mfrhsp, fp) # volumic source term

md.add_initialized_fem_data('gul', mfu, gul) # Dirichlet condition on u 
(left)
md.add_initialized_fem_data('gur', mfu, gur)# Dirichlet condition on u 
(right)
md.add_initialized_fem_data('gpl', mfp, gpl) # Dirichlet condition on p 
(left)
md.add_initialized_fem_data('gpr', mfp, gpr)# Dirichlet condition on p 
(right)

# brick the problem
md.add_Laplacian_brick(mim, 'u')
md.add_Laplacian_brick(mim, 'p')
md.add_source_term_brick(mim, 'p', 'fp') # volumic source term in Eq. 2
B=gf.Spmat('identity',mfu.nbdof()) #add the coupling term in Eq. 1
md.add_explicit_matrix('u','p',B)

# Dirichlet conditions
md.add_Dirichlet_condition_with_penalization(mim, 'u', 
dirichlet_coefficient, left, 'gul')
md.add_Dirichlet_condition_with_penalization(mim, 'u', 
dirichlet_coefficient, right, 'gur')
md.add_Dirichlet_condition_with_penalization(mim, 'p', 
dirichlet_coefficient, left, 'gpl')
md.add_Dirichlet_condition_with_penalization(mim, 'p', 
dirichlet_coefficient, right, 'gpr')

# assembly of the linear system and solve.
md.solve()


Le 07/06/2011 13:21, Yves Renard a écrit :
> On lundi 6 juin 2011, Alice Nicolas wrote:
> > Dear getfem users,
> >
> > I have a very beginner's question.
> > I am trying to solve a system of 2 PDE (variables u and p) that are
> > coupled through linear terms. As a crude example, Eq(1): Laplacian(u)=p,
> > Eq (2): Laplacian(p)=x, and boundary conditions.
> > I figured out that I need to add an explicit term to the tangent system
> > in order to account for the linear term -p in Eq (1). Is it the correct
> > way of tackling this problem? Would someone have some example of
> > programming such coupling of PDE (or of the declaration of the matrix
> > and the use of the add_explicit_matrix brick in case I am correct)?
> >
> > Thank you very much for your invaluable help!!
> > Best regards,
> > Alice Nicolas
> This is indeed the simplest mean to perform a coupling. The other mean is to
> write a new brick, but this not possible for the moment directly with the
> matlab/scilab/python interface.
>
> Yves.


--
________________________________
Alice Nicolas
Laboratoire des Technologies de la Microelectronique
17 av des martyrs, 38054 Grenoble cedex, France
tel: 33 (0)4 38 78 94 04
fax: 33 (0)4 38 78 58 92
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