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Re: [Getfem-users] interface condition question

 From: Jehanzeb Hameed Subject: Re: [Getfem-users] interface condition question Date: Tue, 14 Jul 2009 18:41:44 -0500

```Hello,

I am trying to use the approach in inter_element.cc . I have a
triangle mesh of a circle. The interface between the domains is also a
circle.

as I want to calculate the jump in the normal direction for a vector
variable. However, it seems something is amiss in calculation of
normals. E.g. the code

cout << "convex = " << cv1 << " face = " << f1<< " normal = "<<
pgt1->normals()[f1] << " points = ";
for (bgeot::size_type pt = 0;pt <  3; ++pt) {
}

gives output,

convex = 0    face = 1       normal = [-1, 0]         points = [-0.5,
0.866025][-0.288353, 0.385477][1.77042e-12, 1]

As can be seen, the normal is calculated incorrectly. Can someone

I also wanted to discuss my approach to the problem, and was wondering
if its the best one. I have a system with a vector and a scalar
variable. I could see two ways to go about it in getfem.

1) Use bricks

2) Form my own system, with a fem having 3 (2 for vector, 1 for
scalar) degree of freedom's per vertex. This requires using
generic_assembly.

3) Use 2 fems, one for vector, one for scalar, form 4 matrices using
generic_assembly, then add these into one big matrix.

I followed approach 2. I wanted to impose dirichlet conditions
strongly (i.e. use "getfem::assembling_Dirichlet_condition"), and I
couldnt see how I could do this with approach 1 and 3 above. It seems
I have to use a dirichlet condition brick, which uses lagrange
multipliers to enforce dirichlet conditions. Am I right, i.e. if I
want to use strong dirichlet conditions, then using approch 2 is the
way to go ?

So far, I have been able to get my approach working without the jump
condition. Now I want to incorporate the jump condition, but  thats
presenting some issues. Will it be possible for someone (e.g Yves or
Ronan or anyone else) to look into my code  if I am still unable to
get this to work?

Thanks,
-Jehanzeb

On Sun, Jul 12, 2009 at 6:20 AM, Renard Yves<address@hidden> wrote:
>
> Jehanzeb Hameed <address@hidden> a écrit :
>
>> Hello,
>>
>> I am now comfortable enough with getfem to start attacking the
>> interface problem, thanks to help from this list. In the code for
>> getfem++/contrib/inter_element_test, there is piece of code which I
>> cant fully understand, and I havent been able to figure it from the
>> documentation. The relevant lines of code are:
>>
>>    const base_matrix& B = ctx1.B();
>>    gmm::mult(B, pgt1->normals()[f1], up);
>>    scalar_type norm = gmm::vect_norm2(up);
>>    scalar_type J = ctx1.J() * norm;
>>
>> What is the matrix B? Also, does J give the determinant of Jacobian
>> transformation for the face (if so, why)?
>
> B is the transpose of the inverse of the gradient of the geometric
> transformation (pseudo-inverse if the element have a lower dimension than
> the mesh) see the documentation pages
>
>
>
> ctx1.J() is the jacobian of the transformation of the whole element.
> Multiplied by the norm of the normal to the face, it gives the jacobian of
> the transformation of the face, yes.
>
>>
>> Also, on a related note, I am planning to use the technique in this
>> file to implement the jump integral. Yves mentioned the method in
>> crack.cc, which uses mortars and some sort of constraints matrix,
>> which I havent looked into yet. Is there a reason to prefer one of the
>> two approaches?
>
> It depends of what you need to do. If you have a single mesh with to regions
> and a discontinuity between the two regions, the faster is probably the
> method used in crack.cc.
>
>
> Regards,
>
> Yves.
>
>
>
>>
>> Thanks,
>> -Jehanzeb
>>
>>
>>>
>>> Hello,
>>>
>>> it was not fully straightforward but you can find an example in:
>>> getfem++/contrib/inter_element_test,
>>> if you have matching meshes on the interface. If not it is certainly
>>> possible but I am not the expert to explain how to do.
>>>
>>> I hope it helps,
>>> Best regards,
>>> Ronan
>>>
>>> Jehanzeb Hameed a écrit :
>>>>
>>>> Hello,
>>>>
>>>> I am investigating the possibility of using getfem for implementing a
>>>> 2 domain problem, with an interface between the domains. I want to use
>>>> continuous lagrange elements on each domain, and a jump condition at
>>>> the interface. The jump condition will take the form (u_1 - u_2, v_1 -
>>>> v_2), where u_1 and v_1 and test and trial functions for domain 1, and
>>>> u_2 and v_2 are test and trial functions for domain 2.  The integral
>>>> (u_1 - u_2, v_1 - v_2) is only over the interface between the domains.
>>>>
>>>> Can this be done relatively easily in getfem?
>>>>
>>>> Thanks,
>>>> -Jehanzeb
>>>>
>>>> _______________________________________________
>>>> Getfem-users mailing list
>>>> https://mail.gna.org/listinfo/getfem-users
>>>>
>>>
>>>
>>
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