Parallel Algorithms for the Generalized Stokes Problem

Abstract

The generalized Stokes problem leads, in turn, to saddle-point problems that are normally solved via an Uzawa- or projection-type method. We introduce a new approach for handling such problems in which we avoid solving the pressure unknowns first and also avoid computing orthogonal projections in the process of obtaining velocity unknowns. This approach eliminates difficult computations that are associated with problems on irregular domains. We point out similarities with the projection scheme, and show that the proposed approach provides a way of preconditioning projection methods.