To day they no sparse static condensation in FreeFem++
in fact you want to eliminate of internal dof of the formulation.
Il is not to hard of code with the HashMatrix, it is the same ShurComplement.cpp algorithm of plugin
but the result is a sparse matrix (ie. a hash matrix in freefem++)
the only difficulty is to compute
I given numbering of Schur complement I[i] is the index in A of the i in S if I[i] >=0
the matrix A is split in 4 blocks [[AII,AIJ],[AJI, AJJ]] where
J = index not in I, AII = A(I,I),
S = AII - AIJ AJJ^-1 AJI
but le matrix AJJ^-1 is a diagonal block matrix
if we get the correct numbering J. (ie. we get a numbering by connect component
of the graphe G_A defined by A (ie i,j a link if a_ij is non zero) restricted on J. ).
then S is Sparse matrix.
If you are able to code this you are well come.
F. Hecht.