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Reference point in PDE mode

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Hello I am working with Comsol 3.5 in the PDE mode. I have defined subdomain. I would like to know how to create a reference point linked to one (or several) of the boundaries of the subdomain thanks to equations so that i can define the boundary conditions on this reference point (and not directly on the boundaries).

Thanks a lot !

6 Replies Last Post Oct 5, 2010, 10:25 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Oct 2, 2010, 7:44 a.m. EDT
Hi

The peinciple of COMSOL is to set BC's on the boundaries, so I do not understand really what you want to do.

If it's that you have some parameters or variables that you want to use to define your BC, then define these parameters or these variables, and use them in the BC definition.

--
Good luck
Ivar
Hi The peinciple of COMSOL is to set BC's on the boundaries, so I do not understand really what you want to do. If it's that you have some parameters or variables that you want to use to define your BC, then define these parameters or these variables, and use them in the BC definition. -- Good luck Ivar

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Posted: 1 decade ago Oct 2, 2010, 8:21 a.m. EDT
In the attached file you will find a figure illustrating what i exactly want to do :

The whole problem is defined by 3 subdomains on which there are 3 differents subdomain-settings. The point is that i would like to introduce coupling between points 1,3,5 and coupling between 2,4,6. So i wonder if i can define 2 reference points RP1 and RP2 and define a "link" between 1,3,5 and RP1 and an other "link" between 2,4,6 and RP2.

Maybe it is posible to define coupling equations between the different boundaries, but i don't know how to do it.

Tanks !
In the attached file you will find a figure illustrating what i exactly want to do : The whole problem is defined by 3 subdomains on which there are 3 differents subdomain-settings. The point is that i would like to introduce coupling between points 1,3,5 and coupling between 2,4,6. So i wonder if i can define 2 reference points RP1 and RP2 and define a "link" between 1,3,5 and RP1 and an other "link" between 2,4,6 and RP2. Maybe it is posible to define coupling equations between the different boundaries, but i don't know how to do it. Tanks !


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

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Posted: 1 decade ago Oct 3, 2010, 2:42 a.m. EDT
Hi
you have to better define what you mean by "link", in principle this is possible for most cases, via coupling variables, predefined BC's or weak constraints all depends what kind of physics you have (and via the weak constraints you have mono and bidirectional links)

--
Good luck
Ivar
Hi you have to better define what you mean by "link", in principle this is possible for most cases, via coupling variables, predefined BC's or weak constraints all depends what kind of physics you have (and via the weak constraints you have mono and bidirectional links) -- Good luck Ivar

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Posted: 1 decade ago Oct 4, 2010, 3:36 p.m. EDT
Let's imagine that my problem is made of 2 variables u and v. On boundaries 1,3,5 i want to set u(1)=v(1)= u(3)=v(3)= u(5)=v(5)=0.

Then on boundaries 2,4,6 i want to set u(2)=u(4)=(6)=C ; where C is a constant that I impose.
So there is no difficulty for this.

And I want v(2)=v(4)=v(6) but I don't now how to impose this equality.

Do I have to define a coupling variable w, so that I will set v(2)=v(4)=v(6)=w (where w is free) ?

Thanks
Let's imagine that my problem is made of 2 variables u and v. On boundaries 1,3,5 i want to set u(1)=v(1)= u(3)=v(3)= u(5)=v(5)=0. Then on boundaries 2,4,6 i want to set u(2)=u(4)=(6)=C ; where C is a constant that I impose. So there is no difficulty for this. And I want v(2)=v(4)=v(6) but I don't now how to impose this equality. Do I have to define a coupling variable w, so that I will set v(2)=v(4)=v(6)=w (where w is free) ? Thanks

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Posted: 1 decade ago Oct 5, 2010, 1:15 a.m. EDT
Hey
Your problem is not a "well posed pde problem but look like a "control problem" that comsol cannot solve directly [ they are harder to solve too] .

beware, too, it is also possible that your problem is not well posed and dont have a proper solution but without knowng anyting of it i will assume it is well posed.

Tere is a ton of bibliography on how to solve these "control" problems for they are very important in practice. [ for example your boundary condition could express the fact that you want equal temperature on several faces of an object to control differential stress but that you dont really care about the value of its temperature...

Usually the way you solve them is by finding a functionnal that will be for example minimum when your "control" boundary condition v(2)=v(4)=v(6) is met
the test function are the set of then NON UNIQUE solution of your PDE with your other standard BC.
You can also for some problem find an iterative problem where each step is made of one set of classical pde with its "normal BC" that converge toward the solution of your problem.... it really depends on the specific of your problem here.

I am not sure if Comsol can resolve this problem alone but it is possible that with matlab it can provide some input, at least IF your PDE are linear [ because then you can use a few exact solution to describe the full set of solutions...

Not sure if I am clear but in short my advice will be

1 make sure your problem has really a solution

2 look at bigraphy on control which is very large

and
3 from there make your choice.but again comsol is designed to resolve "straight pde problem" you will have to do more to resolve your problem.

JF
Hey Your problem is not a "well posed pde problem but look like a "control problem" that comsol cannot solve directly [ they are harder to solve too] . beware, too, it is also possible that your problem is not well posed and dont have a proper solution but without knowng anyting of it i will assume it is well posed. Tere is a ton of bibliography on how to solve these "control" problems for they are very important in practice. [ for example your boundary condition could express the fact that you want equal temperature on several faces of an object to control differential stress but that you dont really care about the value of its temperature... Usually the way you solve them is by finding a functionnal that will be for example minimum when your "control" boundary condition v(2)=v(4)=v(6) is met the test function are the set of then NON UNIQUE solution of your PDE with your other standard BC. You can also for some problem find an iterative problem where each step is made of one set of classical pde with its "normal BC" that converge toward the solution of your problem.... it really depends on the specific of your problem here. I am not sure if Comsol can resolve this problem alone but it is possible that with matlab it can provide some input, at least IF your PDE are linear [ because then you can use a few exact solution to describe the full set of solutions... Not sure if I am clear but in short my advice will be 1 make sure your problem has really a solution 2 look at bigraphy on control which is very large and 3 from there make your choice.but again comsol is designed to resolve "straight pde problem" you will have to do more to resolve your problem. JF

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Posted: 1 decade ago Oct 5, 2010, 10:25 a.m. EDT
Hi,

I've managed to do what i want, using integration coupling variables,

Thanks for your time !
Hi, I've managed to do what i want, using integration coupling variables, Thanks for your time !

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