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Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Aims to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end, deals with two well‐known coupled problems of computational mechanics – the fluid‐structure interaction problem and thermally‐driven flows of incompressible fluids. Demonstrates the possibility of coupling the block‐iterative loop with the nonlinearity of the problems through numerical experiments which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. Discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. Explains also the need for online synchronized communication between the different codes used as is the description of the master code which will control the overall algorithm.

The purpose of this paper is to propose a robot constant grinding force control algorithm for the impact stage and processing stage of robotic grinding.

The robot constant grinding force control algorithm is based on a grinding model and iterative algorithm. During the impact stage, active disturbance rejection control is used to plan the robotic reference contact force, and the robot speed is adjusted according to the error between the robot’s real contact force and the robot’s reference contact force. In the processing stage, an RBF neural network is used to construct a model with the robot's position offset displacement and controlled output, and the increment of control parameters is estimated according to the RBF neural network model. The error of contact force and expected force converges gradually by iterating the control parameters online continuously.

The experimental results show that the normal force overshoot of the robot based on the grinding model and iterative algorithm is small, and the processing convergence speed is fast. The error between the normal force and the expected force is mostly within ±3 N. The normal force based on the force control algorithm is more stable than the normal force based on position control, and the surface roughness of the processed workpiece has also been improved, the Ra value compared with position control has been reduced by 24.2%.

As the proposed approach obtains a constant effect in the impact stage and processing stage of robot grinding and verified by the experiment, this approach can be used for robot grinding for improved machining accuracy.

Generally, iterative methods which have some instability solutions in complex structural and non-linear mechanical problems are used to compute reliability index. The purpose of this paper is to establish a non-linear conjugate gradient (NCG) optimization algorithm to overcome instability solution of the Hasofer-Lind and Rackwitz-Fiessler (HL-RF) method in first-order reliability analysis. The NCG algorithms such as the Conjugate-Descent (CD) and the Liu-Storey (LS) are used for determining the safety index. An algorithm is found based on the new line search in the reliability analysis.

In the proposed line search for calculating the safety index, search direction is computed by using the conjugate gradient approach and the HL-RF method based on the new and pervious gradient vector of the reliability function. A simple step size is presented for the line search in the proposed algorithm, which is formulated by the Wolfe conditions based on the new and previous safety index results in the reliability analysis.

From the current work, it is concluded that the proposed NCG algorithm has more efficient, robust and appropriate convergence in comparison with the HL-RF method. The proposed methods can eliminate numerical instabilities of the HL-RF iterative algorithm in highly non-linear performance function and complicated structural limit state function. The NGC optimization is applicable to reliability analysis and it is correctly converged on the reliability index. In the NCG method, the CD algorithm is slightly more efficient than the LS algorithm.

This paper usefully shows how the HL-RF algorithm and the NCG scheme are formulated in first-order reliability analysis. The proposed algorithm is validated from six numerical and structural examples taken from the literature. The HL-RF method is not converged on several non-linear mathematic and complex structural examples, while the two proposed conjugate gradient methods are appropriately converged for all examples. The CD algorithm is converged about twice faster than the LS algorithm in most of the problems. Therefore, application of the NCG method is possible in reliability analysis.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

The purpose of this paper is to demonstrate improvement of the accuracy of electrical tomography reconstruction by incorporation of a priori knowledge into the inverse problem solution.

The fusion of two different inversion algorithms capable of real‐time operation is discussed, namely a non‐iterative monotonicity‐based approach, determining the a priori knowledge and an iterative Gauss‐Newton (GN)‐based reconstruction algorithm. Furthermore, the method is compared with the unmodified algorithms themselves by means of reconstructions from simulated inclusions at different noise levels.

The accuracy of the inverse problem reconstructions, especially at the boundary regions of the unknown inclusions, benefit from the investigations of incorporating a priori knowledge about material values and can be considerable improved. The monotonicity method itself, which has low complexity, provides remarkable reconstruction results in electrical tomography.

The paper is applied to simulated discrete two‐phase scenarios, e.g. gas/oil mixtures. In a further step the method would be tested with measured data. Moreover, investigations have to be carried out in order to make the monotonicity‐based reconstruction principle more robust against disturbing artifacts.

The fusion of the non‐iterative monotonicity‐based method with the GN‐based algorithm demonstrates a novel approach of improving the reconstruction accuracy in electrical tomography.

The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.

The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration.

The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation.

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.

This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations.

First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising.

The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem.

In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

Recent progress in element technology in large scale explicit finite element codes has opened the way for the solution of elastoplastic shell problems of unprecedented complexity. This new capability has focused attention on the numerical issues involved in the implementation of elastoplastic material models for shells, particularly when vectorizable algorithms are required for supercomputer applications. This paper reviews four algorithms currently in the literature for plane stress and shell plasticity. First, each of the four methods is described in detail. Next, an accuracy analysis is presented for each algorithm for perfectly plastic, linear kinematic hardening, and linear isotropic hardening cases. Finally, a comparison is made of the relative computational efficiency of the four algorithms, and the importance of vectorization is illustrated.

The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X.

By applying the principle of hierarchical identification and the Hermitian/skew‐Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift‐splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation.

The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms.

So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew‐Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation.

The purpose of this paper is to address the problem of polar quantization optimization. Particularly, the aim is to find the method for the optimal resolution‐constrained polar quantizer design.

The new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed.

At high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2 dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal‐to‐quantization ratio is derived.

Since circularly symmetric sources and complex presentation of signals arise in numerous applications, it can be concluded that the usage area of the suggested proposal is very wide (audio coding, image coding, spectral phase coding, synthetic aperture radars systems, coding of the discrete Fourier transform).

It should be emphasized that in contrast to earlier work, where models have been designed under high‐rate assumption, the obtained nonuniform unrestricted polar quantizer is optimal for all rates.