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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.

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.

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.

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.

The paper analyses the preconditioning of non‐linear nonsymmetric equations with approximations of the discrete Laplace operator. The test problems are non‐linear 2‐D elliptic equations that describe natural convection, Darcy flow, in a porous medium. The standard second order accurate finite difference scheme is used to discretize the models’ equations. The discrete approximations are solved with a double iterative process using the Newton method as outer iteration and the preconditioned generalised conjugate gradient (PGCG) methods as inner iteration. Three PGCG algorithms, CGN, CGS and GMRES, are tested. The preconditioning with discrete Laplace operator approximations consists of replacing the solving of the equation with the preconditioner by a few iterations of an appropriate iterative scheme. Two iterative algorithms are tested: incomplete Cholesky (IC) and multigrid (MG). The numerical results show that MG preconditioning leads to mesh independence. CGS is the most robust algorithm but its efficiency is lower than that of GMRES.

Aims to apply the generalized minimal residual (GMRES) algorithm combined with the fast Fourier transform (FFT) technique to solve dense matrix equations from the mixed potential integral equation (MPIE) when the planar microstrip circuits are analyzed.

To enhance the computational efficiency of the GMRES‐FFT algorithm, the multifrontal method is first employed to precondition the matrix equations since their condition numbers can be improved.

The numerical calculations show that the proposed preconditioned GMRES‐FFT algorithm can converge nearly 30 times faster than the conventional one for the analysis of microstrip circuits. Some typical microstrip discontinuities are analyzed and the good results demonstrate the validity of the proposed algorithm.

In the future, some more efficient preconditioning techniques will be found for the mixed potential integral equation (MPIE) when the planar microstrip circuits are analyzed.

This paper is concerned with the numerical solution of multi‐dimensional convection dominated convection‐diffusion problems. These problems are characterized by a large parameter, K, multiplying the convection terms. The goal of this work is the development and analysis of effective preconditioners for iteratively solving the large system of linear equations arising from various finite element and finite difference discretizations with grid size h. When centered finite difference schemes and standard Galerkin finite element methods are used, h must be related to K by the stability constraint, Kh ≤ C₀, where the constant C₀ is sufficiently small. A class of preconditioners is developed that significantly reduces the condition number for large K and small h. Furthermore, these preconditioners are inexpensive to implement and well suited for parallel computation. It is shown that under suitable assumptions, the number of iterations remains bounded as h ↓0 with K fixed and, at worst, grows slowly as K ↓ ∞. Numerical results are presented illustrating the theory. It is also shown how to apply the theoretical results to more general convection‐diffusion problems and alternative discretizations (including streamline diffusion methods) that remain stable as Kh ↓ ∞.

The purpose of this paper is to investigate and analyze the efficiency and stability of the implementation of the Crout version of ILU (ILUC) preconditioning on fast‐multipole method (FMM) for solving large‐scale dense complex linear systems arising from electromagnetic open perfect electrical conductor (PEC).

The FMM is employed to reduce the computational complexity of the matrix‐vector product and the memory requirement of the impedance matrix. The numerical examples are initially solved by the quasi‐minimal residual (QMR) method with ILUC preconditioning. In order to fully investigate the performance of ILUC in connection with other iterative solvers, a case is also solved by bi‐conjugate gradient solver and conjugate gradient squared solver with ILUC preconditioning.

The solutions show that the ILUC preconditioner is stable and significantly improves the performance of the QMR solver on large ill‐conditioned open PEC problems compared to using ILU(0) and threshold‐based ILU (ILUT) preconditioners. It dramatically decreases the number of iterations required for convergence and consequently reduces the total CPU solving time with a reasonable overhead in memory.

The preconditioning scheme can be applied to large ill‐conditioned open PEC problems to effectively speed up the overall electromagnetic simulation progress while maintaining the computational complexity of FMM. More complex structures including wire‐PEC junctions and microstrip arrays may be addressed in future work.

The performance of ILUC has been previously reported only on preconditioning sparse linear systems, in which the ILU preconditioner is constructed by the ILUC of the coefficient matrix (e.g. matrix arised from two‐dimensional finite element convection‐diffusion problem) and subsequently applied to the same sparse linear systems; so it is important to report its performance on the dense complex linear systems that arised from open PEC electromagnetic problems. In contrast, the preconditioner is constructed upon the near‐field matrix of the FMM and subsequently applied to the whole dense linear system. The comparison of its performance against the diagonal, ILU(0) and ILUT precoditioners is also presented.

The aim of this paper is to accelerate the convergence of iterative methods on ill‐conditioned linear systems of equations.

First a brief numerical analysis is given of left preconditioners on ill‐conditioned linear systems of equations. From this result, it is deduced that a double preconditioning approach may be better. Then, a double preconditioner based on an iterative diagonal scaling method and an incomplete factorization method is proposed. The efficiency of this approach is illustrated on two finite element models produced by computational electromagnetism.

The double preconditioning approach is efficient for 2D and 3D finite element problems. The bi‐conjugate gradient algorithm always converges when it is double preconditioned. This is not the case when a simple incomplete factorization method is applied. Furthermore, when the two preconditioning techniques lead to the convergence of the iterative solving method, the double preconditioner significantly reduces the number of iterations in comparison with the simple preconditioner. On the proposed 2D problem, the speed‐up is between 6 and 32. On the proposed 3D problem, the speed‐up is between 13 and 20. Finally, the approach seems to reduce the growth of the condition number when higher‐order finite elements are used.

The paper proposes a particular double preconditioning approach which can be applied to any invertible linear system of equations. A numerical evaluation on a singular linear system is also provided but no proof or analysis of stability is given for this case.

The paper presents a new preconditioning technique based on the combination of two very simple and elementary methods: a diagonal scaling method and an incomplete factorization process. Acceleration obtained from this approach is quite impressive.

The purpose of this paper is to achieve an understanding of the challenges and preconditions for inter-organizational collaborative project practices in industrial engineering projects. A framework for identifying the challenges and preconditions for inter-organizational collaboration is presented.

The adopted research method is qualitative, and empirical data were collected from the industrial engineering project sector in Finland. The literature related to industrial engineering projects and inter-organizational collaborative project management practices is summarized, informing the qualitative design of the study.

By analyzing empirical data from industrial engineering projects, the challenges for inter-organizational collaboration are identified in each industrial engineering project stage. A framework of preconditions for inter-organizational collaboration is identified, in which investors are advised to pay attention when deciding on the use of collaborative project management methods.

The findings of this study help practitioners deal effectively with mechanisms aimed at fostering and hindering inter-organizational collaborative practices. The identified preconditions for inter-organizational collaboration provide support for decision-making in every phase of an engineering project and can be used as guidelines throughout the process.

Inter-organizational collaborative project management practices have recently been attracting attention in the industrial engineering project setting. This research is an attempt to identify the underlying forces supporting and preventing inter-organizational collaboration in industrial engineering projects. This study offers a framework that can help academics and project management practitioners deal with the challenges affecting inter-organizational collaboration at each project stage and consider preconditions for inter-organizational collaboration in industrial engineering project settings.

The purpose of this paper is to propose novel factored approximate sparse inverse schemes and multi-level methods for the solution of large sparse linear systems.

The main motive for the derivation of the various generic preconditioning schemes lies to the efficiency and effectiveness of factored preconditioning schemes in conjunction with Krylov subspace iterative methods as well as multi-level techniques for solving various model problems. Factored approximate inverses, namely, Generic Factored Approximate Sparse Inverse, require less fill-in and are computed faster due to the reduced number of nonzero elements. A modified column wise approach, namely, Modified Generic Factored Approximate Sparse Inverse, is also proposed to further enhance performance. The multi-level approximate inverse scheme, namely, Multi-level Algebraic Recursive Generic Approximate Inverse Solver, utilizes a multi-level hierarchy formed using Block Independent Set reordering scheme and an approximation of the Schur complement that results in the solution of reduced order linear systems thus enhancing performance and convergence behavior. Moreover, a theoretical estimate for the quality of the multi-level approximate inverse is also provided.

Application of the proposed schemes to various model problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than results by other researchers for some of the model problems.

Further enhancements are investigated for the proposed factored approximate inverse schemes as well as the multi-level techniques to improve quality of the schemes. Furthermore, the proposed schemes rely on the definition of multiple parameters that for some problems require thorough testing, thus adaptive techniques to define the values of the various parameters are currently under research. Moreover, parallel schemes will be investigated.

The proposed approximate inverse preconditioning schemes as well as multi-level schemes are efficient computational methods that are valuable for computer scientists and for scientists and engineers in engineering computations.

The purpose of this chapter is to determine the basic preconditions to information economy’s formation in modern Russia.

The methodology of the research includes the method of comparative analysis, which is used for comparing the values of the indicators of informatization of Russia’s socio-economic system to the indicators of other countries, and the method of trend analysis, which is used for determining the growth rate of these indicators in Russia.

The authors study the dynamics of the values of the indicators of information economy in Russia in 2008-2017 and determine three basic preconditions to the formation of information economy in modern Russia. The first precondition is related to the necessary normative and legal provision of information economy that determines the course at its formation. The second one is related to the readiness of infrastructural provision (mobile communications, the Internet, the system of e-commerce, and online payments) for formation of information economy. The third precondition is vivid progress in informatization of the socio-economic system, as a result of which Russia exceeds the average global level.

It is concluded that Russia has quickly implemented the strategy of modernization of the socio-economic system, creating a platform for formation of information economy.

Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as adaptive cross approximation (ACA) with generalized minimal residual (GMRES) is introduced to develop the high performance BEM (HPBEM). It is found that for slender beams, the stress analysis using iterative solver GMRES will difficult to converge. For the analysis of slender beams and thin structures, to enhance the efficiency of GMRES solver becomes a key problem in the development of the HPBEM. The purpose of this paper is study on the preconditioning method to solve this convergence problem, and it is started from the 2D BE analysis of slender beams.

The conventional sparse approximate inverse (SAI) based on adjacent nodes is modified to that based on adjacent nodes along the boundary line. In addition, the authors proposed a dual node variable merging (DNVM) preprocessing for slender thin-plate beams. As benchmark problems, the pure bending of thin-plate beam and the local stress analysis (LSA) of real thin-plate cantilever beam are applied to verify the effect of these two preconditioning method.

For the LSA of real thin-plate cantilever beams, as GMRES (m) without preconditioning applied, it is difficult to converge provided the length to height ratio greater than 50. Even with the preconditioner SAI or DNVM, it is also difficult to obtain the converged results. For the slender real beams, the iteration of GMRES (m) with SAI or DNVM stopped at wrong deformation state, and the computation failed. By changing zero initial solution to the analytical displacement solution of conventional beam theory, GMRES (m) with SAI or DNVM will not be stopped at wrong deformation state, but the stress error is still difficult to converge. However, by GMRES (m) combined with both SAI and DNVM preconditioning, the computation efficiency enhanced significantly.

This paper presents two preconditioners: DNVM and a modified SAI based on adjacent nodes along the boundary line of slender thin-plate beam. In the LSA, by using GMRES (m) combined with both DNVM and SAI, the computation efficiency enhanced significantly. It provides a reference for the further development of the 3D HPBEM in the LSA of real beam, plate and shell structures.