Repository logo

Browsing by Subject "GMRES"

Filter results by typing the first few letters
Now showing 1 - 3 of 3
  • thumbnail.journal.alt
    Item type:Thesis, Access status: Open Access ,
    Biblioteka numeryczna do rozwiązywania algebraicznych układów równań liniowych metodami iteracyjnymi
    (Data obrony: 2020-05-21) Rębisz, Dariusz
    Wydział Fizyki i Informatyki Stosowanej
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Efficient simulations of large-scale convective heat transfer problems
    (Wydawnictwa AGH, 2021) Goik, Damian; Banaś, Krzysztof; Bielański, Jan Gustaw; Chłoń, Kazimierz
    We describe an approach for efficient solution of large-scale convective heat transfer problems that are formulated as coupled unsteady heat conduction and incompressible fluid-flow equations. The original problem is discretized over time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid-flow problem uses Picard’s iterations to solve the arising nonlinear equations. Both problems (the heat transfer and Navier–Stokes equations) give rise to large sparse systems of linear equations. The systems are solved by using an iterative GMRES solver with suitable preconditioning. For the incompressible flow equations, we employ a special preconditioner that is based on an algebraic multigrid (AMG) technique. This paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned – especially for ill-conditioned systems that arise from discretizations of incompressible Navier–Stokes equations. We describe a parallel implementation of the solver using MPI and elements from the PETSC library. The scalability of the solver is favorably compared with other methods, such as direct solvers and the standard GMRES method with ILU preconditioning.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    ILU preconditioning based on the FAPINV algorithm
    (2015) Salkuyeh, Davod Khojasteh; Rafiei, Amin; Roohani, Hadi
    A technique for computing an ILU preconditioner based on the factored approximate inverse (FAPINV) algorithm is presented. We show that this algorithm is well-defined for H-matrices. Moreover, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Numerical experiments on some test matrices are given to show the efficiency of the new ILU preconditioner.