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...

Many interesting areas of current industry work deal with non-linear coupled systems of partial differential equations. We examine iterative methods for the solution of a model two-dimensional coupled system based on a linearized form of the two carrier drift-diffusion equations from semiconductor modeling. Discretizing this model system yields a large non-symmetric indefinite sparse matrix. To...

ILU smoothers are good smoothers for linear multigrid methods. In this paper, a new ILU smoother for the incompressible Navier-Stokes equations, called CILU (Collective ILU), is designed, based on r-transformations. Existing ILU decompositions factorize the matrix with real elements. In CILU the elements of the matrix that is factorized are submatrices, corresponding to the set of physical vari...

Linear systems which originate from the simulation of wave propagation phenomena can be very difficult to solve by iterative methods. These systems are typically complex valued and they tend to be highly indefinite, which renders the standard ILU-based preconditioners ineffective. This paper presents a study of ways to enhance standard preconditioners by altering the diagonal by imaginary shift...

The scalability and robustness of a class of non-overlapping domain decomposition preconditioners using 2-way nested dissection reordering is studied. In particular, three methods are considered: a nested symmetric successive over-relaxation (NSSOR), a nested version of modified ILU with rowsum constraint (NMILUR), and nested filtering factorization (NFF). The NMILUR preconditioner is exact wit...

ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that maintains this important stability property. Even better, TPILU(k) preconditioning produces an answer that is bit-compatible with the sequential ILU(k) prec...

Two methods for solving the generalized Stokes problems that occur in viscous, incompressible ows are described and tested. Both are based on some type of linear algebraic orthogonaliza-tion process. The rst, EMGS, is a preconditioner derived from an incomplete Gram{Schmidt factorization, and it is proven to exist whenever the matrix being preconditioned can be factored using Gaussian eliminati...

Numerical simulations of unsteady three-dimensional compressible flow problems require the solution of large, sparse, nonlinear systems of equations arising from the discretization of Euler or Navier-Stokes equations on unstructured, possibly dynamic, meshes. In this paper we study a highly parallel, scalable, and robust nonlinear iterative method based on the Defect Correction method (DeC), th...

This paper deals with the iterative solution of large sparse symmetric positive definite systems. We investigate preconditioning techniques of the two-level type that are based on a block factorization of the system matrix. Whereas the basic scheme assumes an exact inversion of the submatrix related to the first block of unknowns, we analyze the effect of using an approximate inverse instead. W...

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...