Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithme

Brezinski, Claude

doi:10.1007/bf02575753

Cited by 108 publications

(105 citation statements)

References 19 publications

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“…Vector extrapolation methods can be classified into two families. The first family contains the minimal polynomial extrapolation (MPE) method [31], the reduced rank extrapolation (RRE) method [58,133] and the modified minimal polynomial extrapolation (MMPE) method [21,157,174]. The second class includes the topological -algorithm (TEA) [21] and the scalar and vector -algorithm (SEA and VEA) [202].…”

Section: Implicit Couplingmentioning

confidence: 99%

Partitioned Simulation of Fluid-Structure Interaction

Degroote¹

2013

Arch Computat Methods Eng

123

107

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In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss-Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.

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Section: Implicit Couplingmentioning

confidence: 99%

Partitioned Simulation of Fluid-Structure Interaction

Degroote¹

2013

Arch Computat Methods Eng

123

107

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“…As far as we know, various kinds of vector extrapolation methods have been discussed in SIAM Review [33]. For example, the polynomial-type vector extrapolation methods which include the minimal polynomial extrapolation (MPE) of Cabay and Jackson [34], and the epsilon vector extrapolation methods which utilize the scalar and vector epsilon methods of Wynn [35,36], and the topological epsilon method of Brezinski [37].…”

Section: Accelerated Two-level Multigrid Methodsmentioning

confidence: 99%

An Accelerated Two-level Multigrid Method for Markov Chains

2015

J Appl Computat Math

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Based on the quadratic extrapolation method and its generalization, this paper presents an accelerated two-level multigrid method for speeding up the numerical computation of the stationary probability vector of an irreducible Markov chain. It shows how to combine these vector extrapolation methods with the two-level multigrid method on the coarse level in detail. Numerical results on two Markov chain problems are provided to illustrate the effectiveness of our proposed method in terms of reducing the iteration counts and computing time.

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“…As the previous example indicates, most interest arising from practical applications centres may be accelerated by the use of the functional s-algorithm [Brezinski, 1975]. For the case of The denominator polynomial q[n/ 2 kl(.A) is given by the same formula (2.5), but with …”

Section: A=d-l-umentioning

confidence: 99%