On block minimal residual methods

Bouyouli, R.; Jbilou, Khalide; Messaoudi, Ali; Sadok, H.

doi:10.1016/j.aml.2006.04.009

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Cited by 5 publications

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“…where A is an n × n real large and sparse matrix, B and X are n × s rectangular matrices with s>n. For nonsymmetric problems, some block Krylov subspace methods have been developed these last years; see [3,9,12,14] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

New convergence results on the global GMRES method for diagonalizable matrices

Bellalij¹,

Jbilou²,

Sadok³

2008

Journal of Computational and Applied Mathematics

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Section: Introductionmentioning

confidence: 99%

New convergence results on the global GMRES method for diagonalizable matrices

Bellalij¹,

Jbilou²,

Sadok³

2008

Journal of Computational and Applied Mathematics

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A solver combining reduced basis and convergence acceleration with applications to non‐linear elasticity

Cadou

Potier‐Ferry²

2009

Numer Methods Biomed Eng

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SUMMARYAn iterative solver is proposed to solve the family of linear equations arising from the numerical computation of non-linear problems. This solver relies on two quantities coming from previous steps of the computations: the preconditioning matrix is a matrix that has been factorized at an earlier step and previously computed vectors yield a reduced basis. The principle is to define an increment in two sub-steps. In the first sub-step, only the projection of the unknown on a reduced subspace is incremented and the projection of the equation on the reduced subspace is satisfied exactly. In the second sub-step, the full equation is solved approximately with the help of the preconditioner. Last, the convergence of the sequences is accelerated by a well-known method, the modified minimal polynomial extrapolation. This algorithm assessed by classical benchmarks coming from shell buckling analysis. Finally, its insertion in path following techniques is discussed. This leads to non-linear solvers with few matrix factorizations and few iterations.

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