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Abstract: This paper follows our earlier work on axisymmetric flows [1–4] where algorithms, theories, experiments, simulations, applications, and validations were presented. Here we study the effectiveness and efficiency of explicit front tracking by comparing the L 1-error for spherical shock refraction simulations with and without tracking. We find that front tracking reduces the level of mesh refinement needed to achieve a specified error tolerance by a significant factor compared to corresponding methods without tracking, thus substantially reducing the computational time as well as memory usage for simulations with contacts or material interfaces. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an algorithm for solving the obstacle problem. We try tofind the approximated region of the contact in the obstacle problem by iteration. Numerical examples are given for the obstacle problem for a membrane and the elastic-plastic torsion problem. [Copyright &y& Elsevier]

Abstract: This paper proves the convergence of some generalized Schwarz algorithms for solvingthe obstacle problems with a T-monotone operator. Numerical results show that the generalized Schwarz algorithms converge faster than the classical Schwarz algorithms. [Copyright &y& Elsevier]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [Copyright &y& Elsevier]

Most collision detection algorithms are ones of a discrete type which utilize convexity and local coherence to verify the closest points. However, the incremental algorithms have such critical drawbacks like failure to detect high-speed collisions and dependence on the time complexity on the time step size of animation. In this paper, in order to find a new method which can resolve the drawbacks, we are concerned with a more restricted but nontrivial version of the problem: given a fixed infinite plane H and a moving convex polyhedron P, compute their collision time. Our algorithm utilizes the spherical extreme vertex diagram that is the embedding of the dual graph P onto the Gauss sphere. Exploiting the diagram, we are able to efficiently compute the sequence of the extreme vertices vis, i = 1, …, m and find the time interval [ti, ti+1] during which vi is the extreme vertex of P. With the sequences of the consecutive time intervals and extreme vertices, we construct a distance function between P and H. Hence, we can compute their collision time within a given tolerance by applying the interval Newton method to the distance function. Moreover, the total time complexity is independent of the time step size of animation. [Copyright &y& Elsevier]

Mathematical essence and structures of the feedforward neural networks are investigated in this paper. The interpolation mechanisms of the feedforward neural networks are explored. For example, the well-known result, namely, that a neural network is an universal approximator, can be concluded naturally from the interpolative representations. Finally, the learning algorithms of the feedforward neural networks are discussed. [Copyright &y& Elsevier]

This paper presents some new techniques in designing finite-difference domain decomposition algorithm for the heat equation. The basic procedure is to define the finite-difference schemes at the interface grid points with smaller time step Δt = SHAPE="SOL" ALIGN="C" STYLE="S">Δtm (m is a positive integer) by Saul''yev asymmetric schemes. The algorithm can increase the stability bounds of the classical explicit method by 2m times, and the prior error estimates for the numerical solutions are obtained for some algorithms when m = 2 or m = 3. Numerical experiments on stability and accuracy are also presented. [Copyright &y& Elsevier]

Let CSRnxn={A=(aij)∊Rnxn|aij=an+1−j, i,j=1,2…, n} In this paper, we mainly discuss solving the following problems. PROBLEM Io Given X, B ∊ Rnxm Find A ∊ CSRn×n such that AX = B. PROBLEM I. Given X, B ∊ Rn×m. Find A ∊ CSRn×n such that ∥AX−B∥=min.PROBLEM II. Given A` ∊ Rn×n. Find A* ∊ SE such that where ∥ · ∥ is the Frobenius norm, and SE is the solution set of Problem I or I0.The expressions of the general solution of Problems I and 10 have been derived. The sufficient and necessary conditions for the solvability of Problem I0 have been provided. The numerical algorithm to find the optimal approximate solution and some numerical experiments have been given. [Copyright &y& Elsevier]

In this paper, we combine the new trust region subproblem proposed in [1] with the nonmonotone technique to propose a new algorithm for unconstrained optimization—the nonmonotone adaptive trust region method. The local and global convergence properties of the nonmonotone adaptive trust region method are proved. Its efficiency is tested by numerical results. [Copyright &y& Elsevier]