Hi Robert,
I see. Thanks for pointing this out. I'll see whether I can make my problem more suitable for the FEM. :)
Ben
On Monday, April 1, 2013 10:23:33 PM UTC+1, Robert Cimrman wrote:Hi Ben,
On 04/01/2013 01:17 PM, Ben Derrett wrote:
> Hello Vladimir and Robert,
>
> Vladimir: Thanks. In the problem I'm considering, the NBC is of the form
> \nabla V\cdot n = V^N (i.e. without the M). This complicates things a
> little -- see attached pdf.
Looking at the pdf, I second Vladimir's question/objection :) Usually, one
deals with the boundary integral \int_\Gamma p (M \cdot \nabla V) \cdot n in
one of the three ways:
- it is zero on the Dirichlet boundary part, as p is zero there (the test function)
- it is zero, because the flux (M \cdot \nabla V) \cdot n is zero
- if the flux is non-zero, then "(M \cdot \nabla V) \cdot n" is replaced in the
integral by the given value.
So the question is, why "M" disappeared from you condition \nabla V \cdot n =
-1, and how to reintroduce it :)
> Robert: Yes, that sounds like a good name. I've attached a pdf describing a
> demo problem which -- I think -- requires a term of this type. If I've got
> my calculations correct, you'll be able to test the new term against the
> analytical solution.
If the above does not apply to your case (which I doubt), we can try adding
this term, but caution is required - the FE solution V lives in a function
space, that does not have IMHO a well defined gradient on the boundary. We have
used terms like that in the past in some numerical tests, and their accuracy
was atrocious.
r.
> Thanks once again,
> Ben
>
> On Friday, March 29, 2013 3:16:15 PM UTC, Robert Cimrman wrote:
>>
>> Hello Ben,
>>
>> On 03/29/2013 03:35 PM, Ben Derrett wrote:
>>> Hello,
>>>
>>> In the weak formulation of my problem (a 2D diffusion problem), I have
>> the
>>> term
>>>
>>> \int_{\Gamma^N} p\nabla V\cdot M n
>>>
>>> where \Gamma^N is region where Neumann BC is applied, p is a test
>> function,
>>> V is the unknown function, M is a 2x2 matrix and n is the normal vector.
>>> Has an SfePy term been written corresponding to this?
>>
>> I do not think so. However it should not be difficult to add it - could
>> you
>> provide an example file using a term like that, so that I could test the
>> possible implementation. It should run without the non-existing term.
>> Also,
>> what name would you propose? dw_surface_s_grad_s_n??
>>
>>> Alternatively, is there a SfePy term corresponding to the integral
>>>
>>> \int_{\Gamma^N} p\nabla V\cdot q,
>>>
>>> where q is a vector? I saw the term dw_surface_lcouple, but it doesn't
>> seem
>>> to support the weak evaluation mode.
>>
>> As above, but I assume that having the above term would suffice, right?
>>