Numerical Analysis and Scientific Computing Preprint Seria ILU preconditioners for non-symmetric saddle point matrices with application to the incompressible Navier-Stokes equations

ILU Preconditioners for Nonsymmetric Saddle-Point Matrices with Application to the Incompressible Navier-Stokes Equations

Motivated by the numerical solution of the linearized incompressible Navier–Stokes equations, we study threshold incomplete LU factorizations for nonsymmetric saddle-point matrices. The resulting preconditioners are used to accelerate the convergence of a Krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions. The paper presents and...

Numerical Analysis and Scientific Computing Preprint Seria LU factorizations and ILU preconditioning for stabilized discretizations of incompressible Navier-Stokes equations

Numerical Analysis and Scientific Computing Preprint Seria An algebraic solver for the Oseen problem with application to hemodynamics

The paper studies an iterative solver for algebraic problems arising in numerical simulation of blood flows. Here we focus on a numerical solver for the fluid part of otherwise coupled fluid-structure system of equations which models the hemodynamics in vessels. Application of the finite element method and semiimplicit time discretization leads to the discrete Oseen problem on every time step o...

A comparison of preconditioners for incompressible Navier-Stokes solvers

We consider solution methods for large systems of linear equations that arise from the finite element discretization of the incompressible Navier–Stokes equations. These systems are of the so-called saddle point type, which means that there is a large block of zeros on the main diagonal. To solve these types of systems efficiently, several block preconditioners have been published. These types ...

Efficient Solution of Large-Scale Saddle Point Systems Arising in Riccati-Based Boundary Feedback Stabilization of Incompressible Stokes Flow

We investigate numerical methods for solving large-scale saddle point systems which arise during the feedback control of flow problems. We focus on the instationary Stokes equations that describe instationary, incompressible flows for moderate viscosities. After a mixed finite element discretization we get a differential-algebraic system of differential index two [J. Weickert, Navier-Stokes Equ...