### Simulate Poisson equation: What is the appropriate boundary condition that does not effect the diffusion of the solution outside the simulation domain?

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Dear all

I am looking for an appropriate boundary condition that does not effect the solution when it is close to the boundary. As you know, the either the Dirichlet BC or Neumann BC affect the value as set precise value or add flux in or out.

If you have any idea, please let me know.

Thank you very much

Best regards

I am looking for an appropriate boundary condition that does not effect the solution when it is close to the boundary. As you know, the either the Dirichlet BC or Neumann BC affect the value as set precise value or add flux in or out.

If you have any idea, please let me know.

Thank you very much

Best regards

Community: FEniCS Project

I don't think you can include a boundary condition that does not affect the domain, rather, you can have a problem that does not get affected much by the boundary condition. You do so by decreasing the diffusion coefficient a lot in the vicinity of the boundary, compared to the value in the rest of the domain.

written
5 months ago by
Miguel

For wave equations there are some absorbing boundary conditions (PML, Gaussian taper, etc) used for this purpose. I don't know if for Poisson/Diffusion equations exist something similar, but maybe a fast search of "absorbing boundary conditions (or artificial boundary conditions) for diffusion equation" can give you more information

written
5 months ago by
Hernán Mella

### 1 Answer

0

Thank you all. I found an interesting discussion about this problem.

Link: https://scicomp.stackexchange.com/questions/5471/open-boundary-conditions-with-the-advection-diffusion-equation

The paper mentioned in the discussion is Griffiths 1997 - THE ‘NO BOUNDARY CONDITION’ OUTFLOW BOUNDARY CONDITION.

Link: https://scicomp.stackexchange.com/questions/5471/open-boundary-conditions-with-the-advection-diffusion-equation

The paper mentioned in the discussion is Griffiths 1997 - THE ‘NO BOUNDARY CONDITION’ OUTFLOW BOUNDARY CONDITION.

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