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Article
Publication date: 24 August 2010

Behnam Salimi and David R. Hayhurst

Purpose — The purpose of this paper is to seek improved solution techniques for combined boundary‐initial value problems (IVPs) associated with the time‐dependent creep…

Abstract

Purpose — The purpose of this paper is to seek improved solution techniques for combined boundary‐initial value problems (IVPs) associated with the time‐dependent creep deformation and rupture of engineering structures at high temperatures and hence to reconfigure a parallel iterative preconditioned conjugate gradient (PCG) solver and the DAMAGE XXX software, for 3‐D finite element creep continuum damage mechanics (CDM) analysis.Design/methodology/approach — The potential to speed up the computer numerical solution of the combined BV‐IVPs is addressed using parallel computers. Since the computational bottleneck is associated with the matrix solver, the parallelisation of a direct and an iterative solver has been studied. The creep deformation and rupture of a tension bar has been computed for a range of the number of degrees of freedom (ndf), and the performance of the two solvers is compared and assessed.Findings — The results show the superior scalability of the iterative solver compared to the direct solver, with larger speed‐ups gained by the PCG solver for higher degrees of freedom. Also, a new algorithm for the first trial solution of the PCG solver provides additional speed‐ups.Research limitations/implications — The results show that the ideal parallel speed‐up of the iterative solver of 16, relative to two processors, is achieved when using 32 processors for a mesh of ndf = 153,238. Originality/value — Techniques have been established in this paper for the parallelisation of CDM creep analysis software using an iterative equation solver. The significant computational speed‐ups achieved will enable the analysis of failures in weldments of industrial significance.

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Engineering Computations, vol. 27 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 5 June 2019

Gang Li, Shuo Jia and Hong-Nan Li

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of…

Abstract

Purpose

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of the solution of linear equations in each incremental step and the selected iterative algorithms.

Design/methodology/approach

First, this study employs the time complexity theory to quantitatively compare the efficiency of the Woodbury formula and the LDLT factorization method which is a commonly used method to solve linear equations. Moreover, the performance of iterative algorithms also significantly effects the efficiency of the analysis. Thus, the three-point method with a convergence order of eight is employed to solve the equilibrium equations of the nonlinear analysis method based on the Woodbury formula, aiming to improve the iterative performance of the Newton–Raphson (N–R) method.

Findings

First, the result shows that the asymptotic time complexity of the Woodbury formula is much lower than that of the LDLT factorization method when the number of inelastic degrees of freedom (IDOFs) is much less than that of DOFs, indicating that the Woodbury formula is more efficient for local nonlinear problems. Moreover, the time complexity comparison of the N–R method and the three-point method indicates that the three-point method is more efficient than the N–R method for local nonlinear problems with large-scale structures or a larger ratio of IDOFs number to the DOFs number.

Originality/value

This study theoretically evaluates the efficiency of nonlinear analysis method based on the Woodbury formula, and quantitatively shows the application condition of the comparative methods. The comparison result provides a theoretical basis for the selection of algorithms for different nonlinear problems.

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Engineering Computations, vol. 36 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 30 September 2014

Zixiang Hu, Shi Zhang, Yun Zhang, Huamin Zhou and Dequn Li

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis…

Abstract

Purpose

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

Design/methodology/approach

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

Findings

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

Originality/value

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 7 October 2013

H. Saberi Najafi and S.A. Edalatpanah

– The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.

Abstract

Purpose

The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.

Design/methodology/approach

By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated.

Findings

The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.

Research limitations/implications

Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency.

Originality/value

For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.

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Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

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Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 July 2018

Nen-Zi Wang and Hsin-Yi Chen

A cross-platform paradigm (computing model), which combines the graphical user interface of MATLAB and parallel Fortran programming, for fluid-film lubrication analysis is…

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Abstract

Purpose

A cross-platform paradigm (computing model), which combines the graphical user interface of MATLAB and parallel Fortran programming, for fluid-film lubrication analysis is proposed. The purpose of this paper is to take the advantages of effective multithreaded computing of OpenMP and MATLAB’s user-friendly interface and real-time display capability.

Design/methodology/approach

A validation of computing performance of MATLAB and Fortran coding for solving two simple sliders by iterative solution methods is conducted. The online display of the particles’ search process is incorporated in the MATLAB coding, and the execution of the air foil bearing optimum design is conducted by using OpenMP multithreaded computing in the background. The optimization analysis is conducted by particle swarm optimization method for an air foil bearing design.

Findings

It is found that the MATLAB programs require prolonged execution times than those by using Fortran computing in iterative methods. The execution time of the air foil bearing optimum design is significantly minimized by using the OpenMP computing. As a result, the cross-platform paradigm can provide a useful graphical user interface. And very little code rewritting of the original numerical models is required, which is usually optimized for either serial or parallel computing.

Research limitations/implications

Iterative methods are commonly applied in fluid-film lubrication analyses. In this study, iterative methods are used as the solution methods, which may not be an effective way to compute in the MATLAB’s setting.

Originality/value

In this study, a cross-platform paradigm consisting of a standalone MATLAB and Fortran codes is proposed. The approach combines the best of the two paradigms and each coding can be modified or maintained independently for different applications.

Details

Industrial Lubrication and Tribology, vol. 70 no. 6
Type: Research Article
ISSN: 0036-8792

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Article
Publication date: 3 October 2016

Zhen Sun and Zilong Zou

The purpose of this paper is to present a practical and efficient iterative method for predicting vehicle-induced response of bridge.

Abstract

Purpose

The purpose of this paper is to present a practical and efficient iterative method for predicting vehicle-induced response of bridge.

Design/methodology/approach

The vehicle-bridge interaction (VBI) problem is generalized mathematically and a computational algorithm for VBI is proposed. This method rests on an iterative procedure, which utilizes the whole interaction process for iteration. By this means, vehicle and bridge become totally uncoupled and are only linked by the contact force history. This method provides flexibility to choose simplified or refined vehicle and bridge models for the VBI problem, as well as open options for different commercial FEM software without specialized codes.

Findings

The method is verified through two numerical examples. The first example uses a simple 1D beam bridge model, which illustrates the procedure of this method and demonstrates its fast convergence in several iterations. The second example employs a realistic full 3D finite element bridge model, which shows that the method easily connects complex FEM bridge models in ABAQUS with a calibrated vehicle model in Matlab. The dynamic response of the bridge is reliably calculated within only a few iterations.

Originality/value

The proposed iterative method separates vehicle and bridge into independent subsystems in the computational process, thus providing more flexibility to utilize commercial FEM softwares. Its efficiency is realized through choosing the whole interaction force process for iteration, which considerably reduces the iteration steps.

Details

Engineering Computations, vol. 33 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 March 1992

J. FRÖHLICH and R. PEYRET

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the…

Abstract

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 30 September 2014

Zixiang Hu, Zhenmin Wang, Shi Zhang, Yun Zhang and Huamin Zhou

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD)…

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Abstract

Purpose

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.

Design/methodology/approach

To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.

Findings

Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.

Originality/value

The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 March 2017

Oleg M. Alifanov

The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author…

Abstract

Purpose

The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author and his colleagues to the solution to ill-posed inverse heat transfer problems (IHTPs) with their possible extension to a wider class of inverse problems of mathematical physics and, most importantly, to show the wide possibilities of this methodology by examples of aerospace applications. In this regard, this study can be seen as a continuation of those applications that were discussed in the lecture.

Design/methodology/approach

The application of the inverse method was pre-tested with experimental investigations on a special test equipment in laboratory conditions. In these studies, the author used the solution to the nonlinear inverse problem in the conjugate (conductive and convective) statement. The corresponding iterative algorithm has been developed and tested by a numerical and experimental way.

Findings

It can be stated that the theory and methodology of solving IHTPs combined with experimental simulation of thermal conditions is an effective tool for various fundamental and applied research and development in the field of heat and mass transfer.

Originality/value

With the help of the developed methods of inverse problems, the investigation was conducted for a porous cooling with a gaseous coolant for heat protection of the re-entry vehicle in the natural environment of hypersonic flight. Moreover, the analysis showed that the inverse methods can make a useful contribution to the study of heat transfer at the surface of a solid body under the influence of the hypersonic heterogeneous (dusty) gas stream and in many other aerospace applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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