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The purpose of this paper is to obtain an iterative algorithm to find the solution of the coupled Sylvester-like matrix equations.

In this work, the matrix form of the conjugate direction (CD) algorithm to find the solution X of the coupled Sylvester-like matrix equations:

It is proven that the algorithm converges to the solution within a finite number of iterations in the absence of round-off errors. Finally, four numerical examples were used to test the proficiency and convergence of the established algorithm.

The numerical examples have led the author to believe that the generalized CD (GCD) algorithm is efficient and it converges more rapidly in comparison with the CGNR and CGNE algorithms.

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.

Virtual assembly process plays an important role in assembly design of complex product and is typically time- and resource-intensive. This paper aims to investigate a dynamic assembly simplification approach in order to demonstrate and interact with virtual assembly process of complex product in real time.

The proposed approach regards the virtual assembly process of complex product as an incremental growth process of dynamic assembly. During the growth process, the current-assembled-state assembly model is simplified with appearance preserved by detecting and removing its invisible features, and the to-be-assembled components are simplified with assembly features preserved using conjugated subgraphs matching method based on an improved subgraph isomorphism algorithm.

The dynamic assembly simplification approach is applied successfully to reduce the complexity of computer aided design models during the virtual assembly process and it is proved by several cases.

A new assembly features definition is proposed based on the notion of “conjugation” to assist the assembly features recognition, which is a main step of the dynamic assembly simplification and has been translated into conjugated subgraphs matching problem. And an improved subgraph isomorphism algorithm is presented to address this problem.

The purpose of this paper is to develop a counter-extrapolation approach for computational heat and mass transfer with the interfacial discontinuity considered at conjugate interfaces.

By applying finite-difference approximations for the interfacial gradients along the local normal direction, the conjugate system can be simplified to the Dirichlet boundary problems for individual domains. A suitable method for the Dirichlet boundary value condition can then be used. The lattice Boltzmann method has been used to demonstrate the method. The model has been carefully validated by comparing the simulation results and theoretical solutions for steady and unsteady systems with flat or circular interfaces. Furthermore, the cooling process of a hot cylinder in a cold flow, which involves unsteady flow and heat transfer across a curved interface, has been simulated as an example to illustrate the practical usefulness of this model.

Good agreement has been observed in comparisons of simulations and theoretical solutions. The convergence and stability of the method have also been examined and satisfactory results have been obtained. Results of the cylinder cooling process show that a surface insulation layer can effectively reduce the heat transfer process and slow down the cooling process.

This method possesses several technical advantages, including the simple and straightforward algorithm, and accurate representation of the interface geometry. The basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems with interface discontinuity.

The purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.

Conjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.

A conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.

The proposed algorithm is a new approach that will not either submitted or publish somewhere.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

As well known, in the finite element method, the calculation and the location of the elements of the matrix C of the coefficients requires a lot of calculation times and memory employment especially for 3D problems. Besides, once the matrix C is properly filled, the solution of the system of linear equations is computationally expensive.

The paper consists of two parts. In the first part, to quickly calculate and store only the non‐null terms of the matrix of the system, a geometrical analysis on three‐dimensional domains has been carried out. The second part of the paper deals with the solution of the system of linear equations and proposes a procedure for increasing the solution speed: the traditional method of the conjugate gradient is hybridized with an adequate genetic algorithm (Genetic Conjugate Gradient).

The proposed geometrical procedure allows us to calculate the non‐null terms and their location within the matrix C by simple recursive formulas. The results concerning the genetic conjugate gradient show that the convergence to the solution of the linear system is obtained in a much smaller number iterations and the calculation time is also significantly decreased.

The approach proposed to analyze the geometrical space has been turned out to be very useful in terms of memory saving and computational cost. The genetic conjugate gradient is an original hybrid method to solve large scale problems quicker than the traditional conjugate gradient. An application of the method has been shown for current fields generated by grounding electrodes.

The purpose of this paper is to present a novel gradient‐based iterative algorithm for the joint diagonalization of a set of real symmetric matrices. The approximate joint diagonalization of a set of matrices is an important tool for solving stochastic linear equations. As an application, reliability analysis of structures by using the stochastic finite element analysis based on the joint diagonalization approach is also introduced in this paper, and it provides useful references to practical engineers.

By starting with a least squares (LS) criterion, the authors obtain a classical nonlinear cost‐function and transfer the joint diagonalization problem into a least squares like minimization problem. A gradient method for minimizing such a cost function is derived and tested against other techniques in engineering applications.

A novel approach is presented for joint diagonalization for a set of real symmetric matrices. The new algorithm works on the numerical gradient base, and solves the problem with iterations. Demonstrated by examples, the new algorithm shows the merits of simplicity, effectiveness, and computational efficiency.

A novel algorithm for joint diagonalization of real symmetric matrices is presented in this paper. The new algorithm is based on the least squares criterion, and it iteratively searches for the optimal transformation matrix based on the gradient of the cost function, which can be computed in a closed form. Numerical examples show that the new algorithm is efficient and robust. The new algorithm is applied in conjunction with stochastic finite element methods, and very promising results are observed which match very well with the Monte Carlo method, but with higher computational efficiency. The new method is also tested in the context of structural reliability analysis. The reliability index obtained with the joint diagonalization approach is compared with the conventional Hasofer Lind algorithm, and again good agreement is achieved.

Many a times, the information about the boundary heat flux is obtained only through inverse approach by locating the thermocouple or temperature sensor in accessible boundary. Most of the work reported in literature for the estimation of unknown parameters is based on heat conduction model. Inverse approach using conjugate heat transfer is found inadequate in literature. Therefore, the purpose of the paper is to develop a 3D conjugate heat transfer model without model reduction for the estimation of heat flux and heat transfer coefficient from the measured temperatures.

A 3 D conjugate fin heat transfer model is solved using commercial software for the known boundary conditions. Navier–Stokes equation is solved to obtain the necessary temperature distribution of the fin. Later, the complete model is replaced with neural network to expedite the computations of the forward problem. For the inverse approach, genetic algorithm (GA) and particle swarm optimization (PSO) are applied to estimate the unknown parameters. Eventually, a hybrid algorithm is proposed by combining PSO with Broyden–Fletcher–Goldfarb–Shanno (BFGS) method that outperforms GA and PSO.

The authors demonstrate that the evolutionary algorithms can be used to obtain accurate results from simulated measurements. Efficacy of the hybrid algorithm is established using real time measurements. The hybrid algorithm (PSO-BFGS) is more efficient in the estimation of unknown parameters for experimentally measured temperature data compared to GA and PSO algorithms.

Surrogate model using ANN based on computational fluid dynamics simulations and in-house steady state fin experiments to estimate the heat flux and heat transfer coefficient separately using GA, PSO and PSO-BFGS.