Dear Yuri,
The different terms are automatically added to the formulation. You can
add as many term you need with for instance
md.add_linear_generic_assembly_brick(mim, 'your term here', region)
where region is either a boundary (integration on a boundary) or a part
of the domain (integration on that part of the domain). If region is not
specified, by default the term is added on the whole domain (not the
boundary). When you add a term on a boundary you have additionnaly
access to the normal vector to the boundary with 'Normal'.
The advantage of the model object is that it gather all the variables,
it deals with Dirichlet and Neumann boundary conditions and you can use
the standard solver with it.
You can of course use lower level function of Getfem to separately make
the assembly of each matrix (in the model object, all the assemblies on
a same region are performed in a unique loop for performance reasons).
For that, you can use the assembly module (see
http://getfem.org/python/cmdref_Module%20asm.html) using also the
generic assembly, but it is a little bit more difficult to use than the
model object.
Best regards,
Yves
Le 11/10/2017 à 17:50, Yuri Kulchitsky a écrit :
Dear Yves,
First of all, thank you very much for your reply!
You're right: the placing of polynomials was not normal, I am really
grateful for that notice. However, the overall picture is basically
the same: I understand how to code one distinct term, but for now I do
not know how to combine that terms under different regions of
integration in a single equation. For example:
http://image.ibb.co/mBSUfb/La_Te_X_Example_2.png
<http://image.ibb.co/mBSUfb/La_Te_X_Example_2.png>.
Here we have basically an equation, in which a sum of an integral over
region and an integral over region's boundary is equal to other
integral over the same region.
(Actually, this situation emerges from the need to reformulate weak
form for the general linear elliptic PDE, in which there is a Hessian
in an integral over region; I know that getfem++ can operate with
Hessians, so, maybe, I should try to leave it in "as is" condition)
As I understand, I have to use the generic assembly bricks for that,
as I do not see anything comparable in the section about high-level
generic assembly procedures.
May I ask you one more question: is there any example of generic
matrix computation, when I can directly calculate the entry of the
model matrix and the right-hand side iteratively? I use the Python
interface, but any example will do. Thank you again for your time!
(p.s. Sorry, I'm sending that again since I forgot to check "reply to
all" option at the first time)
Regards,
Yuri Kulchitsky
2017-10-11 12:26 GMT+03:00 Yves Renard <[email protected]
<mailto:[email protected]>>:
Dear Yuri,
There is of course no problem to transcribe your problem into the
assembly language of Getfem. You can mixt domain and boundary
terms with no problem.
Just a question on the expression you give : some polynomials are
placed outside the integrals. Is it normal and if yes, what is the
sense of this.
Depending if you use the Matlab or Python or Scilab interface or
if you write directly your code in C++, you can find some examples
helping you to create the framework of your code in the test
directories of Getfem (see http://getfem.org/tutorial/index.html
<http://getfem.org/tutorial/index.html>)
For instance, what you denote the "implicit boundary term" can be
coded by an assembly string of the following form
"([P5(X[1],X(2]), P6(X[1],X[2]).Grad_u + l*u)*Test_lambda -
lambda*Test_u"
where 'u' and 'lambda' are the unknowns and P5, P6 functions
should be defined first (if you have an explicit expression, you
can just plug it here), and 'l' is a data that should be declared.
Regards,
Yves.
Le 10/10/2017 à 20:02, Юрий Кульчицкий a écrit :
Dear Getfem users,
I am experiencing an issue related to the problem formulation in
the case when there are both boundary integrals and usual
integrals in the 2D case.
A boundary integral arises both from adding an implicit boundary
condition using an augmented Lagrange formulation and from the
basic weak form equation. It also implies an additional unknown
(which is a corresponding multiplier) and an additional test
function.
May you point to me a way how can I formulate the problem
correctly? I would be very grateful for any help. I tried to
understand how bricks work, but so far with no success related to
different integration domains.
I also enclose the full (simplified) weak form as png image if it
would help: https://image.ibb.co/jTwUDw/La_Te_X_Example.png
<https://image.ibb.co/jTwUDw/La_Te_X_Example.png>.
Sorry if this question is too simple. I'm not quite familiar with
the library and the inner details of its FEM realization yet.
Regards,
Yuri Kulchitsky
--
Yves Renard ([email protected] <mailto:[email protected]>)
tel : (33) 04.72.43.87.08
Pole de Mathematiques, INSA-Lyon fax : (33) 04.72.43.85.29
20, rue Albert Einstein
<https://maps.google.com/?q=20,+rue+Albert+Einstein&entry=gmail&source=g>
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
<http://math.univ-lyon1.fr/%7Erenard>
---------
--
Yves Renard ([email protected]) tel : (33) 04.72.43.87.08
Pole de Mathematiques, INSA-Lyon fax : (33) 04.72.43.85.29
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
---------
