Combination Preconditioning of saddle-point systems for positive-definiteness

Dr. Andrew Wathen

Oct. 2, 2012, 8:15 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.