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How to define a boundary condition which varies within a given domain

Posted Apr 8, 2011, 11:51 a.m. EDT Geometry, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.1 3 Replies

Chin Kin Ong
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Hi,

I am trying to solve the Poisson's Equation. To simplify the problem, it is a 1-D problem, where the domain is 0 < x < 1

the Poisson's equation defined that d^2u/dx^2 = K where K = constant.

the boundary condition which I have is u(x=0) = u0
and du/dx = 0 when x = x1

While x1 is between 0 and 1 which is yet an unknown.

Is it possible to define such a system ?

Thank you.

Best regards,
Chin Kin
3 Replies Last Post Apr 8, 2011, 4:43 p.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Apr 8, 2011, 3:42 p.m. EDT
Hi

if I count right, I find 3 DoFs and 2 boundary conditions, hence you have an infinite number of solutions and such a system cannot be solved by COMSOL as it wants a fully defined BVP, if you decide a value for your "x1", I believe it should work.

What you can do is to scan x1 from 0 to 1 (just check that if x1==0 or x1==1 you do not have a degeneracy)

--
Good luck
Ivar
Hi if I count right, I find 3 DoFs and 2 boundary conditions, hence you have an infinite number of solutions and such a system cannot be solved by COMSOL as it wants a fully defined BVP, if you decide a value for your "x1", I believe it should work. What you can do is to scan x1 from 0 to 1 (just check that if x1==0 or x1==1 you do not have a degeneracy) -- Good luck Ivar
Chin Kin Ong
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Posted: 1 decade ago Apr 8, 2011, 3:55 p.m. EDT
Hi Ivar,
Thanks for your reply. I'm sorry I missed out another boundary condition which is

u(x1) = 0

I still didn't manage to define this system.
Please help. Thanks

Best regards,
Chin Kin
Hi Ivar, Thanks for your reply. I'm sorry I missed out another boundary condition which is u(x1) = 0 I still didn't manage to define this system. Please help. Thanks Best regards, Chin Kin
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Apr 8, 2011, 4:43 p.m. EDT
Hi

Well in the new V4 COMSOL is somewhat more restrictive (if I remember right from 3.5) I see that it enforces two "zero Flux", one on each side on the external boundaries, so if I decide arbitrary to set X1=0.75 for a test and let u0 scan from -1 to 1 you get a solution per u0, as well as an unique solution on the domain 2 because you have the zero flux on the right boundary (if not defining something else).

But I'm not sure I got the full story here ;)

If you change the mesh from extremely coarse to extremely fine, you will see that the domain 2 has an unique solution for any u0, to the numerical precision via the relative mesh quality

--
Good luck
Ivar
Hi Well in the new V4 COMSOL is somewhat more restrictive (if I remember right from 3.5) I see that it enforces two "zero Flux", one on each side on the external boundaries, so if I decide arbitrary to set X1=0.75 for a test and let u0 scan from -1 to 1 you get a solution per u0, as well as an unique solution on the domain 2 because you have the zero flux on the right boundary (if not defining something else). But I'm not sure I got the full story here ;) If you change the mesh from extremely coarse to extremely fine, you will see that the domain 2 has an unique solution for any u0, to the numerical precision via the relative mesh quality -- Good luck Ivar

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