A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations

DOI10.1007/BF02521112zbMath0829.65035OpenAlexW2074605507MaRDI QIDQ1895913

Rudnei Dias da Cunha, T. R. Hopkins

Publication date: 25 January 1996

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02521112

zbMATH Keywords

preconditioningparallel implementationrestartnonsymmetric systemconvection- diffusion equationsfive-point finite difference approximationsGMRES\((c)\) method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (11)

A parallel Navier–Stokes solver for the rotating flow problem ⋮ Stabilized Finite Element Formulation and High-Performance Solver for Slightly Compressible Navier–Stokes Equations ⋮ Hybrid grid-particle methods and penalization: a Sherman-Morrison-Woodbury approach to compute 3D viscous flows using FFT ⋮ Iterative local solvers for distributed Krylov-Schwarz method applied to convection-diffusion problems ⋮ Analysis of locally-aligned and non-aligned discretisation schemes for reactor-scale tokamak edge turbulence simulations ⋮ Performance evaluation of OpenMP-based algorithms for handling Kronecker descriptors ⋮ GMRES algorithms over 35 years ⋮ A hybrid GMRES/LS-Arnoldi method to accelerate the parallel solution of linear systems ⋮ Varying the \(s\) in your \(s\)-step GMRES ⋮ An implicit pseudo-spectral multi-domain method for the simulation of incompressible flows ⋮ Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations

Uses Software

• PVM
• PIM

Cites Work

• Approximating the inverse of a matrix for use in iterative algorithms on vector processors
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• A data parallel finite element method for computational fluid dynamics on the Connection Machine system
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Parallel Triangular System Solving on a Mesh Network of Transputers
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory
• Parallelizable restarted iterative methods for nonsymmetric linear systems. II: parallel implementation
• α-GMRES: A new parallelizable iterative solver for large sparse non-symmetric linear systems arising from CFD
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