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How do integral equation be the boundary condition when solve PDE problem?

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Hi, everybody

The PDE problem I want to solve includes a boundary condition which is a integral equation. How to handle it?
for example:
if the problem is:
du1/dx=2*x^2+u2
du2/dx=x*u1
x(-[0,2]
the boundary conditons are :
u1(0)=1
u2(0)=2
int(u1,0,2)=10
Then the last is the especial condition want to be dealed with.

It is very possible that the results is oscillating. But it is not important. What I want to know is the way to import the integral boundary condition.

My Comsol is V4.0, the mph file with no the integral condition is attached.

Thanks in advance.

youf.


5 Replies Last Post 17 oct. 2010, 21:04 UTC−4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 16 oct. 2010, 05:17 UTC−4
Hi

have you tried to add a global equation u3=int(u1,0,2) and then force it to 10 ?

--
Good luck
Ivar
Hi have you tried to add a global equation u3=int(u1,0,2) and then force it to 10 ? -- Good luck Ivar

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Posted: 1 decade ago 16 oct. 2010, 07:01 UTC−4
Hi, Ivar

Thanks for your help!

The error of "Unknown function. - Name: Int" was obtained when I followed your advice. The error occured again when "Int" was instead by "Integral". It seems that there was no built-in "integral function" in "Global equation".

Then how to handle it?

thank you very much!

youf.
Hi, Ivar Thanks for your help! The error of "Unknown function. - Name: Int" was obtained when I followed your advice. The error occured again when "Int" was instead by "Integral". It seems that there was no built-in "integral function" in "Global equation". Then how to handle it? thank you very much! youf.

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 16 oct. 2010, 10:33 UTC−4
Hi

sorry for that int() is my shortcut for integration (Model coupling)

--
Good luck
Ivar
Hi sorry for that int() is my shortcut for integration (Model coupling) -- Good luck Ivar

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 17 oct. 2010, 06:43 UTC−4
Hi

another thing, when I see a PDE solution that is oscillating in line with the mesh, I know by experience that then the BC are overconstraine and your equation set is not correct, so I believe your example is not a coherent set of equations and BC's, there is something too much in there ;)

--
Good luck
Ivar
Hi another thing, when I see a PDE solution that is oscillating in line with the mesh, I know by experience that then the BC are overconstraine and your equation set is not correct, so I believe your example is not a coherent set of equations and BC's, there is something too much in there ;) -- Good luck Ivar

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Posted: 1 decade ago 17 oct. 2010, 21:04 UTC−4
Hi, Ivar

Thanks for your help very much!

I has tried the "integration (Model coupling)" setting, but unfortunately the satisfying result can not be obtained. I think I must tried again and the process is required for a new user of Comsol.

Thank you for testing the example. It has not real significance. What I want to know is setting the integral equation. The boundary conditions is really too many for the equations.

youf.
Hi, Ivar Thanks for your help very much! I has tried the "integration (Model coupling)" setting, but unfortunately the satisfying result can not be obtained. I think I must tried again and the process is required for a new user of Comsol. Thank you for testing the example. It has not real significance. What I want to know is setting the integral equation. The boundary conditions is really too many for the equations. youf.

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