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Article
Publication date: 16 July 2019

Chih-Hao Chen and Siva Nadarajah

This paper aims to present a dynamically adjusted deflated restarting procedure for the generalized conjugate residual method with an inner orthogonalization (GCRO) method.

Abstract

Purpose

This paper aims to present a dynamically adjusted deflated restarting procedure for the generalized conjugate residual method with an inner orthogonalization (GCRO) method.

Design/methodology/approach

The proposed method uses a GCR solver for the outer iteration and the generalized minimal residual (GMRES) with deflated restarting in the inner iteration. Approximate eigenpairs are evaluated at the end of each inner GMRES restart cycle. The approach determines the number of vectors to be deflated from the spectrum based on the number of negative Ritz values, k∗.

Findings

The authors show that the approach restores convergence to cases where GMRES with restart failed and compare the approach against standard GMRES with restarts and deflated restarting. Efficiency is demonstrated for a 2D NACA 0012 airfoil and a 3D common research model wing. In addition, numerical experiments confirm the scalability of the solver.

Originality/value

This paper proposes an extension of dynamic deflated restarting into the traditional GCRO method to improve convergence performance with a significant reduction in the memory usage. The novel deflation strategy involves selecting the number of deflated vectors per restart cycle based on the number of negative harmonic Ritz eigenpairs and defaulting to standard restarted GMRES within the inner loop if none, and restricts the deflated vectors to the smallest eigenvalues present in the modified Hessenberg matrix.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 1989

Mingwu Yuan, Pu Chen, Shanji Xiong, Yuanneng Li and Edward L. Wilson

The advantages of a direct superposition of the Ritz vector in dynamic response analysis (developed by Wilson, Yuan, and Dickens in 1982 and termed the WYD method) are that: no…

Abstract

The advantages of a direct superposition of the Ritz vector in dynamic response analysis (developed by Wilson, Yuan, and Dickens in 1982 and termed the WYD method) are that: no iteration is involved; the method is at least four times faster than the subspace iteration method; and fewer Ritz vectors are necessary for the mode superposition of dynamic response analysis than exact eigenvectors are used. The major purpose of this paper is to illustrate that the WYD method can also be used as a general approximate algorithm to calculate eigenvalues and eigenvectors. The WYD and Lanczos algorithms are very similar and a formula that relates the two is given in this paper. Although the exact algebraic value of only a single eigenvector of a multi‐eigenvalue can be calculated using either the WYD or Lanczos methods, an artificial round‐off is presented that can be used to solve the eigenvalue problem. A method of estimating the error introduced by the WYD method is also developed. A dynamic substructuring technique, based on the WYD method, and which assumes that the connectivities on the interfaces among the substructures need not be considered is also presented.

Details

Engineering Computations, vol. 6 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 April 1987

P. Léger and E.L. Wilson

The evaluation of linear dynamic response analysis of large structures by vector superposition requires, in its traditional formulation, the solution of a large and expensive…

187

Abstract

The evaluation of linear dynamic response analysis of large structures by vector superposition requires, in its traditional formulation, the solution of a large and expensive eigenvalue problem. A method of solution based on a Ritz transformation to a reduced system of generalized coordinates using load dependent vectors generated from the spatial distribution of the dynamic loads is shown to maintain the high expected accuracy of modern computer analysis and significantly reduces the execution time over eigensolution procedures. New computational variants to generate load dependent vectors are presented and error norms are developed to control the convergence characteristics of load dependent Ritz solutions. Numerical applications on simple structural systems are used to show the relative efficiency of the proposed solution procedures.

Details

Engineering Computations, vol. 4 no. 4
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 March 1991

MINGWU YUAN, SHANJI XIONG and XIAOHONG CHEN

An exact multiple‐level dynamic substructure technique was developed by a combination of WYD algorithm and static multiple‐level substructuring technique. This method is…

Abstract

An exact multiple‐level dynamic substructure technique was developed by a combination of WYD algorithm and static multiple‐level substructuring technique. This method is essentially different from the traditional mode component synthesis. The eigenvalues and eigenvectors created by the method are the eigenpairs for the whole structure and not for the components of structure. On the other hand, the dynamic response by using mode superposition can also be implemented in substructure level. This algorithm actually is an exact substructuring technique which means that substructuring itself did not introduce any additional error except the round‐off when a structure was split into some arbitrary subdomains and the error of WYD or mode superposition themselves. It is no longer necessary to assume any connective condition on the interface between substructures. This method makes the capacity of dynamic analysis of a structural analysis program unlimited. It is especially attractive for the programs on microcomputers. Of course, the method leads to a frequent I/O for a subsequent search of the files from each substructure. It is time consuming compared to the mode component synthesis. But the potential still exists to improve the efficiency by using parallel computation on concurrent computers. In this paper the theory and procedure of the algorithm are presented.

Details

Engineering Computations, vol. 8 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1987

K. Ritz

A model for a symmetric three‐layer configuration is developed. This model refers to Cu/Invar/Cu (CIC) laminates. Calculated values for the coefficient of thermal expansion (CTE…

Abstract

A model for a symmetric three‐layer configuration is developed. This model refers to Cu/Invar/Cu (CIC) laminates. Calculated values for the coefficient of thermal expansion (CTE) are compared with literature values. The model is then extended to symmetric CIC‐Metalcore boards and its prediction is compared with experimental results. Shearing of FR‐4 is discussed.

Details

Circuit World, vol. 13 no. 4
Type: Research Article
ISSN: 0305-6120

Article
Publication date: 9 April 2020

Dragan D. Milašinović, Petar Marić, Žarko Živanov and Miroslav Hajduković

The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the…

Abstract

Purpose

The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.

Design/methodology/approach

The inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.

Findings

Inelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.

Originality/value

This paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure

Article
Publication date: 1 April 1988

K. Ritz

A method is shown which allows evaluation of production tolerances for high speed PCBs (microstrip, stripline) in order to maintain the impedance Z within a specified range.

Abstract

A method is shown which allows evaluation of production tolerances for high speed PCBs (microstrip, stripline) in order to maintain the impedance Z within a specified range.

Details

Circuit World, vol. 15 no. 1
Type: Research Article
ISSN: 0305-6120

Article
Publication date: 16 April 2018

Xuanhua Fan, Keying Wang and Shifu Xiao

As a practical engineering method, earthquake response spectra play an important role in seismic hazard assessment and in seismic design of structures. However, the computing…

Abstract

Purpose

As a practical engineering method, earthquake response spectra play an important role in seismic hazard assessment and in seismic design of structures. However, the computing scale and the efficiency of commercial software restricted the solution of complex structures. There is a clear need of developing large-scale and highly efficient finite element procedures for response spectrum analysis.

Design/methodology/approach

In this paper, the kernel theories for earthquake response spectra are deduced and the corresponding parallel solution flow via the modal superposition method is presented. Based on the algorithm and the parallel data structure of JAUMIN framework, a parallel finite element (FE) solution module is established. Using the solution procedure on a supercomputer equipped with up to thousands of processors, the correctness and parallel scalability of the algorithm are evaluated via numerical experiments of typical engineering examples.

Findings

The results show that the solution module has the same precision as the commercial FE software ANSYS; the maximum solution scale achieves 154 million degrees of freedom (DOFs) with a favorable parallel computing efficiency, going far beyond the computing ability of the commercial FE software.

Originality/value

The solution scale in this paper is very challenging for the large-scale parallel computing of structural dynamics and will promote the dynamic analysis ability of complex facilities greatly.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Book part
Publication date: 28 April 2021

Stefan Razinskas

Successful teams tend to be highly cohesive and team cohesion to be particularly helpful in allowing teams and their members to sustain their success even in the most challenging…

Abstract

Successful teams tend to be highly cohesive and team cohesion to be particularly helpful in allowing teams and their members to sustain their success even in the most challenging times. One disillusioning consequence of this reciprocity between cohesion and performance would suggest that failures made by teams and/or their members likely jeopardize their success by preventing them from capitalizing on such virtuous circles associated with team cohesion. Yet, many teams uphold their performance despite the failures they have to cope with, suggesting that the potential vicious circles can be overcome. This chapter aims at illuminating the vicious and virtuous circles associated with team cohesion that are induced by either collective failures of teams or individual failures of their members. It therefore offers a multilevel perspective not only on the emergence and diffusion of failures at the individual and team levels, but also on the critical role that team cohesion plays for a team’s (dys)functional coping across these levels. It is theorized that collective failures triggered exogenously can help build team cohesion, and that whether endogenously-triggered collective failures bring about the vicious or the virtuous circles of team cohesion depends on whether the individual failures developing into collective failures are triggered endogenously or exogenously. The implications of this conceptual work are discussed in light of the literatures on error/failure management and group cohesiveness.

Details

Work Life After Failure?: How Employees Bounce Back, Learn, and Recover from Work-Related Setbacks
Type: Book
ISBN: 978-1-83867-519-6

Keywords

Article
Publication date: 1 February 1990

The fifth in the series of Printed Circuit World Conventions is being held in Glasgow, Scotland, from 12—15 June 1990. It is organised by the UK Printed Circuit World Convention…

Abstract

The fifth in the series of Printed Circuit World Conventions is being held in Glasgow, Scotland, from 12—15 June 1990. It is organised by the UK Printed Circuit World Convention Committee under the direction of the co‐sponsors: EIPC (Europe), IMF (UK), IPC (USA), JPCA (Japan) and PCIF (UK).

Details

Circuit World, vol. 16 no. 3
Type: Research Article
ISSN: 0305-6120

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