Acceleration of Convergence of Vector Sequences

Sidi, Avram; Ford, William F.; Smith, David A.

doi:10.1137/0723013

Cited by 114 publications

(88 citation statements)

References 12 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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“…Existing vector extrapolation methods can be broadly classified into two categories: polynomial methods and ε-algorithms. The first family includes three approaches: minimal polynomial extrapolation (MPE) of Cabay and Jackson [17]; reduced rank extrapolation (RRE) of Eddy [18] and Mesina [19], and the modified minimal polynomial extrapolation (MMPE) derived in [20,21,22]. The second family includes the topological ε-algorithm (TEA) and the scalar and vector ε-algorithms (SEA and VEA).We will restrict our attention to the RRE methodology in this work.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error estimation for incompressible viscous fluid with a new boundary condition

Akkad

Elkhalfi²

2018

B Soc Paran Mat

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This paper describes numerical solutions of incompressible NavierStokes equations with a new boundary condition. To solve this problem, we use the discretization by mixed finite element method. We use a vector extrapolation method for computing numerical solutions of the steady-state Navier-Stokes equations. In addition, two types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true error. A numerical experiment on the driven cavity flow is given to demonstrate the effectiveness of the vector extrapolation method. We compare the result with the solution from commercial code like ADINA system as well as with values from other simulations.

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“…The most popular vector extrapolation methods are minimal polynomial extrapolation (MPE) by Cabay and Jackson [7], reduced rank extrapolation (RRE) by Eddy [8] and Mesina [19], and modified minimal polynomial extrapolation (MMPE) due to Brezinski [3], Pugachev [20], and Sidi et al [24]. Convergence analyses of these methods can be found in [21,23,24,25] and recursive implementations are described in [3,9,17]. When applied to linearly generated vector sequences, the MPE and RRE methods are mathematically equivalent to the FOM and GMRES Krylov subspace methods, respectively, for the iterative solution of linear systems of equations; see [22].…”

Section: Tsvd Introduce the Singular Value Decompositionmentioning

confidence: 99%

Vector extrapolation enhanced TSVD for linear discrete ill-posed problems

2008

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Abstract. The truncated singular value decomposition (TSVD) is a popular solution method for small to moderately sized linear ill-posed problems. The truncation index can be thought of as a regularization parameter; its value affects the quality of the computed approximate solution. The choice of a suitable value of the truncation index generally is important, but can be difficult without auxiliary information about the problem being solved. This paper describes how vector extrapolation methods can be combined with TSVD, and illustrates that the determination of the proper value of the truncation index is less critical for the combined extrapolation-TSVD method than for TSVD alone. The numerical performance of the combined method suggests a new way to determine the truncation index.

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Acceleration of Convergence of Vector Sequences

Cited by 114 publications

References 12 publications

Partitioned Simulation of Fluid-Structure Interaction

Partitioned Simulation of Fluid-Structure Interaction

A posteriori error estimation for incompressible viscous fluid with a new boundary condition

Vector extrapolation enhanced TSVD for linear discrete ill-posed problems

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