Home  About us  Contact
 

Schwarz Preconditioner (schwarz + preconditioner)

Distribution by Scientific Domains
Engineering66%

Kinds of Schwarz Preconditioner

  • additive schwarz preconditioner
    		•

    Selected Abstracts

    Application of the additive Schwarz method to large scale Poisson problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2004
    K. M. Singh
    Abstract This paper presents an application of the additive Schwarz method to large scale Poisson problems on parallel computers. Domain decomposition in rectangular blocks with matching grids on a structured rectangular mesh has been used together with a stepwise approximation to approximate sloping sides and complicated geometric features. A seven-point stencil based on central difference scheme has been used for the discretization of the Laplacian for both interior and boundary grid points, and this results in a symmetric linear algebraic system for any type of boundary conditions. The preconditioned conjugate gradient method has been used as an accelerator for the additive Schwarz method, and three different methods have been assessed for the solution of subdomain problems. Numerical experiments have been performed to determine the most suitable set of subdomain solvers and the optimal accuracy of subdomain solutions; to assess the effect of different decompositions of the problem domain; and to evaluate the parallel performance of the additive Schwarz preconditioner. Application to a practical problem involving complicated geometry is presented which establishes the efficiency and robustness of the method. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    On a multilevel preconditioning module for unstructured mesh Krylov solvers: two-level Schwarz

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2002
    R. S. Tuminaro
    Abstract Multilevel methods offer the best promise to attain both fast convergence and parallel efficiency in the numerical solution of parabolic and elliptic partial differential equations. Unfortunately, they have not been widely used in part because of implementation difficulties for unstructured mesh solvers. To facilitate use, a multilevel preconditioner software module, ML, has been constructed. Several methods are provided requiring relatively modest programming effort on the part of the application developer. This report discusses the implementation of one method in the module: a two-level Krylov,Schwarz preconditioner. To illustrate the use of these methods in computational fluid dynamics (CFD) engineering applications, we present results for 2D and 3D CFD benchmark problems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A hybrid domain decomposition method based on aggregation

    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2004
    *Article first published online: 19 APR 200, Yu. Vassilevski
    Abstract A new two-level black-box preconditioner based on the hybrid domain decomposition technique is proposed and studied. The preconditioner is a combination of an additive Schwarz preconditioner and a special smoother. The smoother removes dependence of the condition number on the number of subdomains and variations of the diffusion coefficient and leaves minor sensitivity to the problem size. The algorithm is parallel and pure algebraic which makes it a convenient framework for the construction parallel black-box preconditioners on unstructured meshes. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Non-linear additive Schwarz preconditioners and application in computational fluid dynamics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002
    Xiao-Chuan Cai
    Abstract The focus of this paper is on the numerical solution of large sparse non-linear systems of algebraic equations on parallel computers. Such non-linear systems often arise from the discretization of non-linear partial differential equations, such as the Navier,Stokes equations for fluid flows, using finite element or finite difference methods. A traditional inexact Newton method, applied directly to the discretized system, does not work well when the non-linearities in the algebraic system become unbalanced. In this paper, we study some preconditioned inexact Newton algorithms, including the single-level and multilevel non-linear additive Schwarz preconditioners. Some results for solving the high Reynolds number incompressible Navier,Stokes equations are reported. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A note on the mesh independence of convergence bounds for additive Schwarz preconditioned GMRES

    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6 2008
    Xiuhong Du
    Abstract Additive Schwarz preconditioners, when including a coarse grid correction, are said to be optimal for certain discretized partial differential equations, in the sense that bounds on the convergence of iterative methods are independent of the mesh size h. Cai and Zou (Numer. Linear Algebra Appl. 2002; 9:379,397) showed with a one-dimensional example that in the absence of a coarse grid correction the usual GMRES bound has a factor of the order of . In this paper we consider the same example and show that for that example the behavior of the method is not well represented by the above-mentioned bound: We use an a posteriori bound for GMRES from (SIAM Rev. 2005; 47:247,272) and show that for that example a relevant factor is bounded by a constant. Furthermore, for a sequence of meshes, the convergence curves for that one-dimensional example, and for several two-dimensional model problems, are very close to each other; thus, the number of preconditioned GMRES iterations needed for convergence for a prescribed tolerance remains almost constant. Copyright © 2008 John Wiley & Sons, Ltd. [source]