[petsc-users] Assembling primal Schur matrix in FETI-DP method

[Thomas Witkowski]

In my current FETI-DP implementation, the solution of the Schur 
complement on the primal variables is done by an iterative solver. This 
works quite good, but for small and mid size 2D problems I would like to 
test it with direct assembling and inverting the Schur complement 
matrix. In my notation, the matrix is defined by

S_PiPi = K_PiPi - K_PiB inv(K_BB) K_BPi

"Pi" are the primal and "B" the non-primal variables. K_BB is factorized 
with a (local) direct solver (umpfack or mumps). But how can I create a 
matrix from the last expression? Is there a way to do a matrix-matrix 
multiplication in PETSc, where the first matrix is the (implicit 
defined) dense inverse of a sparse matrix, and the second matrix is a 
sparse matrix? Or is it required to extract the rows of K_BPi in some 
way and to perform than a matrix-vector multiplication with inv(K_BB)?

Thomas