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. 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]>: > > 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) > > 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. > > 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]) 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 > > --------- > >
