Large scale finite element computations with GMRES-like methods on a Cray Y-MP

DOI10.1016/0168-9274(95)00021-LzbMath0855.65025OpenAlexW2102348404MaRDI QIDQ1917402

Martin B. van Gijzen

Publication date: 5 September 1996

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00021-l

zbMATH Keywords

numerical experimentspreconditioningfinite elementparallel computationGMRESconvection-diffusion equationsmatrix-vector productsvector computersDIANA codelarge non-symmetric systems

Mathematics Subject Classification ID

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) Parallel numerical computation (65Y05)

Related Items (3)

Large scale finite element computations with GMRES-like methods on a Cray Y-MP ⋮ Edge-based finite element method for shallow water equations ⋮ Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation

Uses Software

• CGS

Cites Work

• Relaxationsmethoden bester Strategie zur Lösung linearer Gleichungssysteme
• Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconitioned conjugate gradients
• An element-by-element solution algorithm for problems of structural and solid mechanics
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• A polynomial preconditioner for the GMRES algorithm
• Large scale finite element computations with GMRES-like methods on a Cray Y-MP
• An analysis of element-by-element preconditioners for nonsymmetric problems
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• GMRESR: a family of nested GMRES methods
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems

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