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

[Domenico Notaro]

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