5.6.2 Parallel Schur complement CG

If the matrix in (5.1) is symmetric and positive definite the proper Schur complement is also symmetric and positive definite. Then we can solve II) in Alg. 5.19 iteratively via the CG method.


Exercise 14:

Write the parallel Schur complement CG and focus your attention on on the matrix-times-vector multiplication.

Several techniques for preconditioning the Schur complement, i.e. approximating the Schur complement, have been developed, see e.g., [Dry84,BPS89,TCK92]. One approach using BEM (Boundary element method) and multigrid methods can be found in [CKL96].