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The advantages of using a multi‐CPU concurrent computer in solving a steady state free surface seepage problem are studied. The underlying computational task is the solution of a large set of linear equations with a projection operation numerous times. In the study, both Jacobi and SOR iteration methods with projection in a modified alternating iteration scheme are used to solve the problem with varied number of nodes (CPUs) and the timing results are compared between a 32 node Hypercube Concurrent Computer and a VAX 11/780 (single CPU). In addition, the performance and the feasibility of the Hypercube Concurrent Computer are discussed by comparing with the number of nodes used and with the VAX 11/780.

An iteration technique has been developed based on the Mickens iteration method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced.

In this paper, the truncated terms of the Fourier series have been used and utilized in every step of the iteration.

The obtained results are valid for whole ranges of vibration amplitude of the oscillations. The approximated results are compared with existing and corresponding numerical (considered to be exact) results which show excellent agreement. The error analysis has been carried out and shown acceptable results for the proposed iteration technique.

Effectiveness of the proposed iteration technique is found in comparison with other existing methods. The method is demonstrated by examples.

Addresses problems in mechanics and physics involving two or more coupled variables of different nature, or a number of distinct domains which interact. For these kinds of problems, considers numerical solution by the coupling of operators appertaining to the individual participating phenomena, or defined in the domains. Reviews the co‐operation of distinct discretized operators in connection with the integration of temporal evolution processes, and the iterative treatment of stationary equations of state. The specification of subtasks complies with the demand for an independent treatment on different processing units arising in parallel computation. Physical subtasks refer to problems of different field variables interacting on the continuum level; their number is usually small. Fine granularity may be achieved by separating the problem region into subdomains which communicate via the boundaries. In multiphysics simulations operators are preferably combined such that subdomains are processed in parallel on different units, while physical phenomena are processed sequentially in the subdomain.

The purpose of this paper is to present research into reducing the aircraft design cycle period, by reducing the necessary number of design cycle iterations. The design cycle period is one of the main characteristics of the design process and design cycle iterations play a major role in the design cycle period.

To achieve the above‐mentioned goal, the paper presents a mathematical model of iterations for the aircraft design process. This model describes the design coupled tasks as a discrete‐linear time invariant dynamic system. This model also helps identify tasks which are the most important for generating iterations. This new method basically helps break information cycles that create iterations among important tasks.

Studies conducted on a general aviation (GA) airplane (FAJR‐3) design process show the success of the suggested approach. This procedure eventually leads to an expedited convergence rate for the design iterations. That is, through proper breaking of information cycles, the convergence rate of the most dominant design mode could be increased by up to 31 percent. The process also leads to decoupling of the so‐called “coupled parts of design process,” which in turn leads to a more modular design with relatively easier management.

This method offers a new way of managing aircraft design processes while having to deal with constraints such as time and resources. The approach could be easily implemented as it manages any complex design‐process based on its resemblance to a dynamic system. The method can also be used as a component of an Integrated Airframe Design (IAD), as a tool for “Cycle time reduction”.

The advantage of this new approach, over other existing ones, lies in its ability to distinguish the important information cycles in a systematic manner. This helps to break the design process in a way that guarantees the increase in convergence speed of the whole design process.

The purpose of this paper is to apply the variational iterations method to solve two difference types such as the modified Boussinesq (MB) and seven‐order Sawada‐Kotara (sSK) equations and to compare this method with that obtained previously by Adomian decomposition.

The variational iteration method is used for finding the solution of the MB and sSK equations. The solution obtained is an infinite power series for appropriate initial condition. The numerical results obtain for nth approximation and compare with the known analytical solutions; the results show that an excellent approximation to the actual solution of the equations was achieved by using only three iterations.

The comparison demonstrates that the two obtained solutions are an excellent agreement. The numerical results calculated show that this method, variational iteration method, can be readily implemented to this type of nonlinear equation and excellent accuracy can be achieved. The results of variation iteration method confirm the correctness of those obtained by means of Adomian decomposition method.

The results presented in this paper show that the variational iteration method is a powerful mathematical tool for solving the MB and the sSK equations; it is also a promising method for solving other nonlinear equations.

This paper aims to provide a well-behaved nonlinear scheme and accelerating iteration for the nonlinear convection diffusion equation with fundamental properties illustrated.

A nonlinear finite difference scheme is studied with fully implicit (FI) discretization used to acquire accurate simulation. A Picard–Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis reasoning technique, the L^∞ (H¹) convergence of the scheme is proved despite the difficulty because of the combination of conservative diffusion and convection operator. Other properties are established consequently. Furthermore, the algorithm is extended from first-order temporal accuracy to second-order temporal accuracy.

Theoretical analysis shows that each of the two FI schemes is stable, its solution exists uniquely and has second-order spatial and first/second-order temporal accuracy. The corresponding PN iteration has the same order of accuracy and quadratic convergent speed. Numerical tests verify the conclusions and demonstrate the high accuracy and efficiency of the algorithms. Remarkable acceleration is gained.

The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems.

The FI schemes and iterations for the convection diffusion problem are proposed with their properties rigorously analyzed. The induction hypothesis reasoning method here differs with those for linearization schemes and is applicable to other nonlinear problems.

This paper aims to accelerate the iteration convergence for elliptic fluid flow problems, so that an under‐relaxation factor control method is developed.

There should be an optimal under‐relaxation factor that can result in the equivalence of the global residual norms of momentum equation u and momentum equation v. The two residual norms of the momentum equations will be equivalent through controlling the velocity under‐relaxation factors, and then the iteration convergence can be accelerated. Two expressions (α=(α⁰)^βγ and α=(α⁰)^(1/β)γ) are proposed to adjust the values of under‐relaxation factors for every n iterations.

From the five preliminary computations it is found that the value of γ can be larger than 1 and of n can be less than 5 for an open system, and the value of γ should be less than 1 and that of n should be larger than 10 for a closed system. These two pairs of parameters are then used in another five examples. It is found that the saving in CPU times is at least 43.9 percent for the closed system and 67.5 percent for the open system.

When the Re or Ra of the two‐dimensional problems are low, this control method is feasible. More research work is needed in order to apply it in three‐dimensional or high Re or Ra problems.

This method is helpful for the acceleration of iteration convergence in simple problems, and is a preparation for the advanced research in complicated problems.

The interval multi-objective optimization problems (IMOPs) are universal and vital uncertain optimization problems. In this study, an interval multi-objective grey wolf optimization algorithm (GWO) based on fuzzy system is proposed to solve IMOPs effectively.

First, the classical genetic operators are embedded into the interval multi-objective GWO as local search strategies, which effectively balanced the global search ability and local development ability. Second, by constructing a fuzzy system, an effective local search activation mechanism is proposed to save computing resources as much as possible while ensuring the performance of the algorithm. The fuzzy system takes hypervolume, imprecision and number of iterations as inputs and outputs the activation index, local population size and maximum number of iterations. Then, the fuzzy inference rules are defined. It uses the activation index to determine whether to activate the local search process and sets the population size and the maximum number of iterations in the process.

The experimental results show that the proposed algorithm achieves optimal hypervolume results on 9 of the 10 benchmark test problems. The imprecision achieved on 8 test problems is significantly better than other algorithms. This means that the proposed algorithm has better performance than the commonly used interval multi-objective evolutionary algorithms. Moreover, through experiments show that the local search activation mechanism based on fuzzy system proposed in this study can effectively ensure that the local search is activated reasonably in the whole algorithm process, and reasonably allocate computing resources by adaptively setting the population size and maximum number of iterations in the local search process.

This study proposes an Interval multi-objective GWO, which could effectively balance the global search ability and local development ability. Then an effective local search activation mechanism is developed by using fuzzy inference system. It closely combines global optimization with local search, which improves the performance of the algorithm and saves computing resources.

Traditional parallel methods for structural design, as well as modern preconditioned iterative linear solvers, do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design, specifically trusses. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design updates. These rules can be applied serially, periodically, or concurrently, and Jacobi or Gauss‐Seidel style updating can be done. These options are compared with respect to convergence, speed, and stability for an example, problem of combined sizing and topology design of truss domain structures. The central theme of the paper is that the cellular automaton paradigm is tantamount to classical block Jacobi or block Gauss‐Seidel iteration, and consequently the performance of a cellular automaton can be rigorously analyzed and predicted.

The purpose of this paper is to test the capability of a new population‐based optimization algorithm for solving an NP‐hard problem, called “Multiple Knapsack Problem”, or MKP.

Here, the intelligent water drops (IWD) algorithm, which is a population‐based optimization algorithm, is modified to include a suitable local heuristic for the MKP. Then, the proposed algorithm is used to solve the MKP.

The proposed IWD algorithm for the MKP is tested by standard problems and the results demonstrate that the proposed IWD‐MKP algorithm is trustable and promising in finding the optimal or near‐optimal solutions. It is proved that the IWD algorithm has the property of the convergence in value.

This paper introduces the new optimization algorithm, IWD, to be used for the first time for the MKP and shows that the IWD is applicable for this NP‐hard problem. This research paves the way to modify the IWD for other optimization problems. Moreover, it opens the way to get possibly better results by modifying the proposed IWD‐MKP algorithm.