neumann and dirichlet at the same time

Numerical methods and mathematical models of Elmer
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Takala
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Joined: 23 Aug 2009, 23:59

neumann and dirichlet at the same time

Post by Takala »

Hi,

I'm trying to solve the conductivity of a domain by nonlinearly iterating "Static current conduction" -equation.
so the eq. is: div( sigma(u) * grad (u) ) = 0,
where sigma is the conductivity and is dependent on the potential u.

Now, I want to add constraints u=someFunction(y) and du/dx=someOtherFunction(y) on one boundary. I believe this requires Neumann and Dirichlet at the same time. Is this possible to do in the sif somehow?

Please give comments on the solving method as well.

cheers,

Eelis
raback
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Re: neumann and dirichlet at the same time

Post by raback »

Hi Eelis

Dirichlet always overrides the Neumann. The strategy here would be to set both conditions on the given boundary and use conditional Dirichlet condition to deactivate the Dirichlet on parts of the boundary. For example,

Code: Select all

Potential = 0.0
Potential Condition = Variable Coordinate 1
  Real MATC "tx-1"
would set the potential only for x>1using the sign of the expression. Elsewhere the matrix is intact and the Neumaan prevails. (this assumes that the DefaultDirichlet condition setting is used. I don't remember if that's the case also with StatCurrentSolve).

-Peter
Takala
Posts: 184
Joined: 23 Aug 2009, 23:59

Re: neumann and dirichlet at the same time

Post by Takala »

raback wrote:Hi Eelis

Dirichlet always overrides the Neumann. The strategy here would be to set both conditions on the given boundary and use conditional Dirichlet condition to deactivate the Dirichlet on parts of the boundary. For example,

Code: Select all

Potential = 0.0
Potential Condition = Variable Coordinate 1
  Real MATC "tx-1"
would set the potential only for x>1using the sign of the expression. Elsewhere the matrix is intact and the Neumaan prevails. (this assumes that the DefaultDirichlet condition setting is used. I don't remember if that's the case also with StatCurrentSolve).

-Peter
Thanks for the reply.

So it is not possible to put constraints u=something and du/dx=something at the same time? If it is not possible through the sif file would it be possible to hack somehow? I know this is not something that one would normally need, but I need to solve something that is not real. I need to imitate 3D resistive block with 2D domain, and that is why I need to fix the current and the potential at the same time.

/Eelis
raback
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Re: neumann and dirichlet at the same time

Post by raback »

Well, this would overdetermine the problem (you may check this rather easily in 1D). You could let the conductivity be a variable which leads to an inverse problem though. And probably not what you want either.
Takala
Posts: 184
Joined: 23 Aug 2009, 23:59

Re: neumann and dirichlet at the same time

Post by Takala »

Yes, you are right.

Would you have an idea how this problem could be solved?
I tried to do a coupled system iteration between the eqns. div( sigma * grad (u) ) = 0 and div( sigma * E ) = 0, where potential u is variable in the first one and sigma is variable in the second one. But this hasn't been converging...

/Eelis
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