[Getfem-users] [SOLVED] Assembly of rectangular matrix: order of trial and test FE spaces

[Domenico Notaro]

OK, hence the following statement should be valid:

If one wants to implement a matrix 
   A(i,j)   i=1,...,mf_p.nb_dof(), j=1,...,mf_u.nb_dof() 
He has to "invert" the order of basis function within the assembly: 
   assem("M$1(#1,#2)+=comp(Base(#2).Base(#1));");
as a consequence of the generic FEM relation A(i,j) = a(Base^j, Base^i), being 
a(.,.) the bilinear form associated to A.


Thank you so much,
Domenico 
________________________________________
Da: Yves Renard <address@hidden>
Inviato: domenica 8 novembre 2015 18.52
A: Domenico Notaro
Cc: getfem-users
Oggetto: Re: [Getfem-users] Assembly of rectangular matrix: order of trial and  
test FE spaces

Dear Domenico,

You can of course obtain the transposed matrix. In fact just by interverting 
the terms in the assembly string:

generic_assembly assem("M$1(#1,#2)+=comp(Base(#2).vGrad(#1))(:,:,i,i);");
assem.push_mi(mim);
assem.push_mf(mf_u);
assem.push_mf(mf_p);
assem.push_mat(M);
assem.assembly(rg);

Yves.



----- Mail original -----
De: "Domenico Notaro" <address@hidden>
À: "yves renard" <address@hidden>
Cc: "getfem-users" <address@hidden>
Envoyé: Dimanche 8 Novembre 2015 18:08:54
Objet: Re: [Getfem-users] Assembly of rectangular matrix: order of trial and    
test FE spaces

Dear Professor Renard,


thank you for your prompt reply. Actually, the solution you suggest me was 
exactly my first attempt (a), apart from a stupid typing error (obviously it 
was "vBase().Normal()"-->"vGrad()"!).

But this assembly routine returns a mf_u.nb_dof() x mf_p.nb_dof() matrix while 
I need the transposed... That's why I arrived to option (b), since I thought 
the dimensions of output matrix follow from the order of mesh_fem pushes.

Finally, if I have understood you correctly, in the main file I have to:
- define a blank transposed matrix: sparse_matrix_type D(mf_u.nb_dof(), 
mf_p.nb_dof());
- call the assembly routine (a) over this matrix D
- use gmm::transposed(D) every time I need the matrix D=\int DIV(u).q
And I am supposed to do the same for every rectangular matrix assembly?


Best regards,
Domenico

________________________________________
Da: Yves Renard <address@hidden>
Inviato: domenica 8 novembre 2015 17.19
A: Domenico Notaro
Cc: getfem-users
Oggetto: Re: [Getfem-users] Assembly of rectangular matrix: order of trial and  
test FE spaces

Dear Domenico,

The assembly in the low-level generic assembly should be

generic_assembly assem("M$1(#1,#2)+=comp(vGrad(#1).Base(#2))(:,i,i,:);");
assem.push_mi(mim);
assem.push_mf(mf_u);
assem.push_mf(mf_p);
assem.push_mat(M);
assem.assembly(rg);

(You have it in getfem_assembling.h for instance at lines 769 (asm_stokes_B).

Note that you can obtain this also with the high-level generic assembly with an 
assembly string of the form "Div_Test_u*Test_p".

Yves.

----- Mail original -----
De: "Domenico Notaro" <address@hidden>
À: "getfem-users" <address@hidden>
Envoyé: Samedi 7 Novembre 2015 12:45:32
Objet: [Getfem-users] Assembly of rectangular matrix: order of trial and        
test FE spaces

Dear GetFEM users,







I would like to have a double-check on a very basic issue, that is the order of 
trial and test spaces in rectangular matrix assembly.





In particular, which of the following assembly routines returns the matrix


$ M = \int DIV(u).q $


where u is the trial mf_u function and q is the test mf_p function?




(a)


generic_assembly 
assem("M$1(#1,#2)+=comp(vBase(#1).Normal().Base(#2))(:,i,i,:);");
assem.push_mi(mim);
assem.push_mf(mf_u);
assem.push_mf(mf_p);
assem.push_mat(M);
assem.assembly(rg);


(b)




generic_assembly 
assem("M$1(#2,#1)+=comp(vBase(#2).Normal().Base(#1))(:,i,i,:);");
assem.push_mi(mim);
assem.push_mf(mf_p);


assem.push_mf(mf_u);
assem.push_mat(M);
assem.assembly(rg);




(c)


generic_assembly 
assem("M$1(#1,#2)+=comp(Base(#1).vBase(#2).Normal())(:,:,i,i);");
assem.push_mi(mim);
assem.push_mf(mf_p);


assem.push_mf(mf_u);
assem.push_mat(M);
assem.assembly(rg);





I want to build a matrix M with mf_p.nb_dof() rows and mf_u.nb_dof() columns 
(i.e. in the main file I have " sparse_matrix_type M(mf_p.nb_dof(), 
mf_u.nb_dof()); ")










Thank you in advance,

Domenico

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