SchurRAS: A Restricted Version of the Overlapping Schur Complement Preconditioner

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolicelliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of tr...

Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems

We present Neumann-Neumann domain decomposition preconditioners for the solution of elliptic linear quadratic optimal control problems. The preconditioner is applied to the optimality system. A Schur complement formulation is derived that reformulates the original optimality system as a system in the state and adjoint variables restricted to the subdomain boundaries. The application of the Schu...

A Spatial Domain Decomposition Method for Parabolic Optimal Control Problems ?

We present a non-overlapping spatial domain decomposition method for the solution of linear–quadratic parabolic optimal control problems. The spatial domain is decomposed into non-overlapping subdomains. The original parabolic optimal control problem is decomposed into smaller problems posed on space-time cylinder subdomains with auxiliary state and adjoint variables imposed as Dirichlet bounda...

An Acceleration Procedure for the Spectral Element Ocean Model Formulation of the Shallow Water Equations

We develop an overlapping block preconditioner based on an additive Schwarz method for preconditioning the system of equations arising from discretizing the shallow water equations using the spectral ocean element method approach. The system is complicated by being sparse, but having a very large number of nonzeroes in any row of the matrix, which is never stored. The resulting coupled system o...

A preconditioner for the Schur complement domain decomposition method