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hi, anyone can help me on application of Boundary condition in 3D Fem
Wed, 2008-10-22 07:17 - sameer2008
hi i am solving 3D heat diffusion equation could you tell me the process of boundary condition application in the main problem. i want to use mixed boundary condition that is robin boundary condition. how the boundary condition will effect the system stiffness and the mass matrix? or plz tell me some good books' name from where i can get some idea.
plz plz plz
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Re: Robin boundary condition
I assume that you're talking about the transient heat conduction equation in a solid. In that case, a Robin boundary condition that has no time dependence will affect only the stiffness matrix and the load vector.
To get an idea of a potential derivation, see my notes at http://en.wikiversity.org/wiki/Nonlinear_finite_elements/Solution_of_heat_equation#Robin_boundary_conditions
For more background on the notation etc. see http://en.wikiversity.org/wiki/Nonlinear_finite_elements Section 2 Part 3.
-- Biswajit
Dear Dr. Biswajit, thanx
Dear Dr. Biswajit,
thanx for answering me. see in my case, i am giving input in a single surface elemen (tetrahedron) and that is temperature. except that surface input element every one has zero temperatue and trying to fing temperature distribution over the doamin. and for this i want to use robin-boundary condition. i have calculated the stiffness and the mass matrices and confused on boundary conditions as there every thing are unknown except the source oistion term.
plz suggest me
Re: Robin boundary conditions
Not sure what you're saying. Let me try to parse your comment.
1) " i am giving input in a single surface elemen (tetrahedron) and that is temperature"
So you have temperature boundary conditions (Dirichlet, I presume). Are the temperatures time dependent? Is time dependence at all relevant to your problem?
2) "except that surface input element every one has zero temperatue"
So all interior nodes have zero temperature? Only the surface nodes have nonzero T?
3) " trying to fing temperature distribution over the doamin"
So you're trying to find the distribution of T in the body after time t given some T_b over three boundary nodes. Is that correct?
4) " and for this i want to use robin-boundary condition"
Why do you need to use Robin boundary conditions? What are your Robin boundary conditions?
5) " confused on boundary conditions as there every thing are unknown except the source oistion term"
I don't know what "oistion" means. Are you saying that there are sources on the boundary? You don't need to specify the temperature on the portion of the boundary with Robin boundary conditions. You can solve for those. But you will need T bcs on at least some part of the boundary so the matrix to ne nonsingular.
To see how Robin boundary conditions are formulated see the Wikiversity page that I pointed to you last time. Were you able to understand that? If not, you can ask some specific questions on that.
-- Biswajit
anyway thanx
anyway thanx
1. all surface (except one)
1. all surface (except one) elements and all interior elements has zero temperature (initially). i want to solve time independent heat equation thats why robin boundary condition.
2. input is in only four nodes ( surface element) ( one element has four nodes for tetrahedron);Or it can be only surface three nodes
3. oistion==position ( it will be position , sorry for typos )
4. in Our case the input is in only boundary single element ( basically it is point heat source)
In robin boundary condition how i will get the nornal derivative .(is it zero? as we have defined all boundary nodes has zero tempetature initially).
plz suggest the possible idea
Re: More on Robin BCs
Based on your comment:
1) Since you're dealing with a time-independent problem, you should not have a mass matrix at all.
2) Do you have the equation for the Robin BC that you are using? Without that equation It's hard to say exactly how your problem should be solved.
3) My notes on Wikiversity show how to deal with the normal derivative. Perhaps that's confusing you. Note that (Grad T) . n is the same as dT/dn (if that's the point of confusion).
4) dT/dn = 0 implies no flux.
5) You can't apply both Robin BCs (a combination of T and dT/dn) and Dirichlet BCs (fixed T) at the the same boundary nodes at the same time. It's either one or the other.
Not to belabour the point, but note that Robin BCs have the form A T + B dT/dn = C, where A, B, C are parameters that are given. If C = 0, then dT/dn = A/B T. If T = 0, then dT/dn = C/B. If dT/dn = 0 then T = C/A.
Good luck in your quest.
-- Biswajit