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

[Barry Smith]

http://www.mcs.anl.gov/petsc/documentation/faq.html#schurcomplement


On Nov 18, 2011, at 7:02 AM, Thomas Witkowski wrote:

> 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