In Robin boundary condition, the derivative of the dependent variable is given as a function of the dependent variable on the boundary. Can boundary element method (BEM) handle Robin boundary conditions? If yes, please refer me some published work. Thanks in advance for your kind help.
Hi Santosh,
yes, BEM can handle Robin-type boundary condition. The standard scheme of the BEM is like:
[H]{u}=[G]{q}
and the robin boundary condtion is of the form:
uj+\alpha qj+ \beta =0 . (subindex j makes reference to a node)
then, you can sum columns of the system and elimiate unknows:
[ Hij+ (1/\alpha + \beta)Gij ] uj = 0
Hope the asnwer is usefull for you.
Regards,
Antonio.
There is no inherent limitiation in the BE method preventing Robin conditions. See e.g. A Gentle Introduction to the Boundary Element Method in Matlab/Freemat which can be found on this site.
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Hi Santosh
Are you using a specific piece of software that can handle BEM or are you setting it up yourself in e.g. MATLAB?
Hi Santosh,
yes, BEM can handle Robin-type boundary condition. The standard scheme of the BEM is like:
[H]{u}=[G]{q}
and the robin boundary condtion is of the form:
uj+\alpha qj+ \beta =0 . (subindex j makes reference to a node)
then, you can sum columns of the system and elimiate unknows:
[ Hij+ (1/\alpha + \beta)Gij ] uj = 0
Hope the asnwer is usefull for you.
Regards,
Antonio.
Dear René Christensen, I want to write my own code using MATLAB. Thank you Antonio for your kind answer.
Hi Santosh,
You could consider using OpenBEM then (http://www.openbem.dk/people.html), since most of the work is already done for you. It is made by my former PhD supervisors with contributions from their students throughout the years. It probably has a steep learning curve, but perhaps you could use it as is, or at least find inspiration in it.
Another site for inspiration: http://www.boundary-element-method.com/laplace/ where code is available.
Best regards
René
Thanks Rene for the link to my website www.boundary-element-method.com.
I have always thought that this boundary condition issue was one of the missing links in the BEM -particulary the direct BEM. I have generally tried to work with a more general type of boundary condition than the one used here. That is
a(p) \phi(p) + b(p) d\phi(p)/dn = f(p)
which also allows for switches netween Dirichlet and Neumann. I have developed a method for this which links to LU factorisation and I use it in the spreadsheet (Excel) demo below.
http://www.boundary-element-method.com/Excel_VBA/LIBEM2.xlsm
If the question group are interested I would be interested that this would become a project on researchgate
Note that this is a project
https://www.researchgate.net/project/Extending-the-boundary-element-method-to-the-generalised-Robin-boundary-condition
I thing that all problems concerning the Robin boundary condition are expained in the previous letters
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