A Preconditioned GMRES Method for Nonsymmetric or Indefinite Problems

DOI10.2307/2153059zbMath0766.65034OpenAlexW4237960684MaRDI QIDQ4031566

Xiao-Chuan Cai, Jin-Chao Xu

Publication date: 1 April 1993

Full work available at URL: https://doi.org/10.2307/2153059

zbMATH Keywords

domain decompositionnumerical experimentsfinite elementconjugate gradient methodpreconditionerfinite differenceGMRES methodgeneralized minimal residual methodsecond-order elliptic equationsymmetric positive definite problemsnonsymmetric or indefinite problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (20)

Multilevel preconditioning for the finite volume method ⋮ A preconditioned GMRES method ⋮ Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations ⋮ Block preconditioners for energy stable schemes of magnetohydrodynamics equations ⋮ Analysis of a preconditioned GMRES solver for a nonsymmetric SUPG discretization of the compressible Navier-Stokes equations ⋮ Two-grid IPDG discretization scheme for nonlinear elliptic PDEs ⋮ Domain Decomposition Solvers for Frequency-Domain Finite Element Equations ⋮ Two‐grid methods for time‐harmonic Maxwell equations ⋮ A convergence theory of multilevel additive Schwarz methods on unstructured meshes ⋮ Two-level additive preconditioners for edge element discretizations of time-harmonic Maxwell equations ⋮ Iterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value Problems ⋮ Preconditioned GMRES methods for discretization equation of nonsymmetric and indefinite elliptic problem ⋮ Subspace correction methods for nonsymmetric parabolic problems ⋮ A-posteriori estimates and adaptive schemes for transmission problems ⋮ A domain decomposition algorithm for general covolume methods for elliptic problems ⋮ A hybrid nonoverlapping domain decomposition scheme for advection dominated advection-diffusion problems ⋮ Optimal left and right additive Schwarz preconditioning for minimal residual methods with Euclidean and energy norms ⋮ Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids ⋮ Preconditioning by approximations of the Gram matrix for convection-diffusion equations ⋮ Convergence rate estimate for a domain decomposition method

Cites Work

• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Preconditioning and Boundary Conditions
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Domain Decomposition Algorithms for Indefinite Elliptic Problems
• A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems
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