A class of incomplete LU-factorizations with a new strategy to discard ll for large sparse systems of equations, is presented. The speciic incomplete decomposition presented in this paper allows for a user speciied number of tasks to be performed in parallel. For testing the parallel eeciency as well as the preconditioning eeciency of this decomposition a number of test problems are solved usin...

We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed method se...

Large CFD problems are often solved using iterative methods. Preconditioning is mandatory to accelerate the convergence of iterative methods. This paper presents new results using several preconditioning techniques. These preconditoners are non-standard in the CFD community. Several numerical tests were carried out for solving three-dimensional incompressible, compressible and magneto-hydrodyna...

Parallel GMRES algorithms for solution of convective transport problems on distributed memory computers are investigated in this paper. The space-time FEM stabilised by the GLS formulation is applied as the most accurate and stable. The parallel algorithms based on the domain decomposition and iterative GMRES solver are implemented in order to reduce long computing time associated with space-ti...

Steady state simulations in Computational Fluid Dynamics (CFD), which rely on implicit time integration, are not experiencing great accelerations on GPUs. Moreover, most of the reported acceleration effort concerns solving the linear system of equations while neglecting the acceleration potential of running the entire simulation on the GPU. In this paper, we present the software implementation ...

The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES...

The discrete convection-diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes. Estimates of error reduction rates for both geometric multigrid (GMG) and algebraic multigrid (AMG) are established on uniform rectangular meshes for a model problem. Our analysis shows that GMG with line Gauss-Seidel smoothing and b...

‎The global generalized minimum residual (Gl-GMRES)‎ ‎method is examined for solving the generalized Sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {A_i } XB_i = C.]‎ ‎Some new theoretical results are elaborated for‎ ‎the proposed method by employing the Schur complement‎. ‎These results can be exploited to establish new convergence properties‎ ‎of the Gl-GMRES method for solving genera...