Combination Preconditioning of saddle-point systems for positive-definiteness

Dr. Andrew Wathen

Oct. 2, 2012, 10:15 a.m. S2 416

There are by now several examples of preconditioners for
saddle-point systems which destroy symmetry but preserve
self-adjointness in non-standard inner products. The method
of Bramble and Pasciak was the earliest of these. We will
describe how combining examples of this structure allow the
construction of preconditioned matrices which are self adjoint
and positive definite and allow rapid linear system solution by
the Conjugate Gradient method in the appropriate inner product.