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Comparison of linear system solvers applied to diffusion-type finite element equations. (English) Zbl 0647.65018

Various iterative methods for solving the linear systems associated with finite element approximations to self-adjoint elliptic differential operators are compared based on their performance on serial and parallel machines. The methods studied are all preconditioned conjugate gradient methods, differing only in the choice of preconditioner. The preconditioners considered arise from diagonal scaling, incomplete Cholesky decomposition, hierarchical basis functions, and a Neumann- Dirichlet domain decomposition technique. The hierarchical basis function idea is shown to be especially effective on both serial and parallel architectures.
Reviewer: A.Greenbaum

MSC:

65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65Y05 Parallel numerical computation

Software:

LINPACK
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Full Text: DOI EuDML

References:

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