A generalized two-sweep shift splitting method for non-Hermitian positive definite linear systems

In this paper, based on the shift splitting of the coefficient matrix, a generalized two-sweep shift splitting (GTSS) method is introduced to solve the non-Hermitian positive definite linear systems. Theoretical analysis shows that the GTSS method is convergent to the unique solution of the linear systems under a loose restriction on the iteration parameter. Numerical experiments are reported to the efficiency of the GTSS method

Augmented interface systems for the Darcy-Stokes problem

In this paper we study interface equations associated to the Darcy-Stokes problem using the classical Steklov-Poincaré approach and a new one called augmented. We compare these two families of methods and characterize at the discrete level suitable preconditioners with additive and multiplicative structures. Finally, we present some numerical results to assess their behavior in presence of small physical parameters

Augmented Interface Systems for the Darcy-Stokes Problem

In this paper we study interface equations associated to the Darcy-Stokes problem using the classical Steklov-Poincaré approach and a new one called augmented. We compare these two families of methods and characterize at the discrete level suitable preconditioners with additive and multiplicative structures. Finally, we present some numerical results to assess their behavior in presence of small physical parameters

Numerical Approximation of Filtration Processes through Porous Media

In this thesis, we studied numerical methods for the coupling of free fluid flow with porous medium flow. The free fluid flow is modelled by the Stokes equations while the flow in the porous medium is modelled by Darcy’s law. Appropriate conditions are imposed at the interface between the two regions. The weak formulation of the problem is based on mixed-formulation for Stokes and on a primal-mixed formulation for Darcy equation, incorporating in a natural way the interface conditions. The finite element discretization of the problem leads to large, sparse and ill-conditioned algebraic system to be solved for velocities in both domains, Stokes pressure and piezometric head in porous domain. The system is reduced to interface systems for the normal velocity and piezometric head by a Schur complement approach. We present numerical results for several solution methods based on different preconditioning techniques for the solution of the interface systems. We study the effectiveness of the preconditioners with respect to mesh refinement and physical parameters. An application to cross-flow membranes has been considered. Finally, we also assess the numerical accuracy of an uncoupled algorithm for transient problem, which uses different time steps in the Stokes and in the Darcy domains

A GENERALIZATION OF THE HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION

This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting iteration for solving positive definite, non-Hermitian linear systems. It is shown that the new scheme has some advantages over the standard HSS method, and can be used as an effective preconditioner for certain linear systems in saddle point form. Numerical experiments using discretizations of incompressible flow problems demonstrate the effectiveness of the generalized HSS preconditioner