On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids

Doklady Mathematics - Methods of nonlinear analysis and synthesis of synchronization control systems for electrical grids have been developed. The use of averaging methods and Lyapunov-type...     

Mountain Clustering on Non-Uniform Grids Using P-Trees

A new clustering technique is described, which is an improvement on the mountain method (MM) of clustering originally proposed by Yager and Filev. This new technique employs a data driven, hierarchical partitioning of the data set to be clustered, using a p-tree algorithm for spatially decomposing the data set. The centroids of data subsets in the terminal nodes of the p-tree become the set of candidate cluster centers upon which the iterative cluster center selection process of MM is applied. As the data dimension and/or the number of uniform grid lines used in Yager and Filevs original technique increases, our approach requires exponentially fewer cluster centers to be evaluated by the MM selection algorithm. Extensive sample data sets are used to illustrate the performance of this new technique.     

非定常Stokes问题的矩形Crouzeix-Raviart型各向异性非协调元变网格方法

该文给出了关于速度-压力型非定常Stokes问题的一个 矩形 Crouzeix-Raviart 型各向异性非协调有限元的变网格逼近格式.并用一些新的技巧和方法导出了各向异性网格下的有关速度和压力的最优误差估计.     

矩形网格上一类二元有理插值问题

本文首先利用Ｖａｎｄｅｒｍｏｎｄｅ矩阵得到矩形网格上二元多项式插值公式,然后利用该公式建立一类二元有理插值问题的存在性判别准则及有理插值函数的表现公式,并给出数值例子     

矩形网格上二元有理插值的存在性问题

In this paper, making use of bivariate polynomial Lagrange iterpolation formula on rectangular grids, we set up the existence criterion of bivariate rational interpolants problem and its representation formula. Numerical examples are given.     

Two Equivalent Finite Volume Schemes for Stefan Problem on Boundary-Fitted Grids: Front-Tracking and Front-Fixing Techniques

Differential Equations - We present finite-difference schemes on boundary-fitted grids for the two-dimensional Stefan problem. It is shown that the proposed numerical schemes constructed by...     

Efficient Batch Job Scheduling in Grids Using Cellular Memetic Algorithms

Computational grids are an important emerging paradigm for large-scale distributed computing. As grid systems become more wide-spread, techniques for efficiently exploiting the large amount of grid computing resources become increasingly indispensable. A key aspect in order to benefit from these resources is the scheduling of jobs to grid resources. Due to the complex nature of grid systems, the design of efficient grid schedulers becomes challenging since such schedulers have to be able to optimize many conflicting criteria in very short periods of time. This problem has been tackled in the literature by several different metaheuristics, and our main focus in this work is to develop a new highly competitive technique with respect to the existing ones. For that, we exploit the capabilities of cellular memetic algorithms (cMAs), a kind of memetic algorithm with structured population, for obtaining efficient batch schedulers for grid systems, and the obtained results will be compared versus the state of the art. A careful design of the cMA methods and operators for the problem yielded to an efficient and robust implementation. Our experimental study, based on a known static benchmark for the problem, shows that this heuristic approach is able to deliver very high quality planning of jobs to grid nodes and thus it can be used to design efficient dynamic schedulers for real grid systems. Such dynamic schedulers can be obtained by running the cMA-based scheduler in batch mode for a very short time to schedule jobs arriving in the system since the last activation of the cMA scheduler. This work has been partially funded by the Spanish MEC and FEDER under contract TIN2005-08818-C04-01 (the OPLINK project: ).     

An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing

Multigrid methods are widely used and well studied for linear solvers and preconditioners of Krylov subspace methods. The multigrid method is one of the most powerful approaches for solving large scale linear systems;however, it may show low parallel efficiency on coarse grids. There are several kinds of research on this issue. In this paper, we intend to overcome this difficulty by proposing a novel multigrid algorithm that has multiple grids on each layer.Numerical results indicate that the proposed method shows a better convergence rate compared with the existing multigrid method.     

Using Parallel Algorithms to Compute Gas-Dynamic Flows on Irregular Grids

In this article, the supersonic flow of a viscous heat-conducting gas near bodies of complex shape is simulated on a parallel computing system. Kinetically consistent difference schemes are used in the calculation, as they easily adapt to distributed-memory multiprocessor computer architectures. The parallel implementation of the kinetically consistent algorithm has been coded in the language Norma.     

An Explicit Construction for a Ramsey Problem

An explicit coloring of the edges of K_n is constructed such that every copy of K₄ has at least four colors on its edges. As n , the number of colors used is n^1/2+o(1). This improves upon the previous bound of O(n^2/3) due to Erds and Gyárfás obtained by probabilistic methods. The exponent 1/2 is optimal, since it is known that at least (n^1/2) colors are required in such a coloring.The coloring is related to constructions giving lower bounds for the multicolor Ramsey number r_k(C₄). It is more complicated however, because of restrictions imposed on interactions between color classes.* Research supported in part by NSF Grant No. DMS–9970325.     

Conjugate Grids for Unconstrained Optimisation

Several recent papers have proposed the use of grids for solving unconstrained optimisation problems. Grid-based methods typically generate a sequence of grid local minimisers which converges to stationary points under mild conditions.In this paper the location and number of grid local minimisers is calculated for strictly convex quadratic functions in two dimensions with certain types of grids. These calculations show it is possible to construct a grid with an arbitrary number of grid local minimisers. The furthest of these can be an arbitrary distance from the quadratic's minimiser. These results have important implications for the design of practical grid-based algorithms.Grids based on conjugate directions do not suffer from these problems. For such grids only the grid points closest (depending on the choice of metric) to the minimiser are grid local minimisers. Furthermore, conjugate grids are shown to be reasonably stable under mild perturbations so that in practice, only approximately conjugate grids are required.     

地形构造中地震波传播的非对称交错网格模拟

提出了一种新的三维空间对称交错网格差分方法,模拟地形构造中弹性波传播过程．通过具有二阶时间精度和四阶空间精度的不规则网格差分算子用来近似一阶弹性波动方程,引入附加差分公式解决非均匀交错网格的不对称问题．该方法无需在精细网格和粗糙网格间进行插值,所有网格点上的计算在同一次空间迭代中完成．使用精细不规则网格处理海底粗糙界面、 断层和空间界面等复杂几何构造, 理论分析和数值算例表明, 该方法不但节省了大量内存和计算时间, 而且具有令人满意的稳定性和精度．在模拟地形构造中地震波传播时,该方法比常规方法效率更高．     

A Finite Difference Scheme for a Semiconductor Device Problem on Grids with Local Refinement in Time and Space

The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. A finite difference scheme for simulating transient behaviors of a semiconductor device on grids with local refinement in time and space is constructed and studied. Error analysis is presented and is illustrated by numerical examples.     

Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors

In this article, we introduce two versions of nonsmooth extension of Abadie constraint qualification in terms of convexifactors and Clarke subdifferential and employ the weaker one to develop new necessary Karush–Kuhn–Tucker type optimality conditions for optimistic bilevel programming problem with convex lower-level problem, using an upper estimate of Clarke subdifferential of value function in variational analysis and the concept of convexifactor.     

Using Homogeneous Weights for Approximating the Partial Cover Problem

In this paper we consider the natural generalizations of two fundamental problems, the Set-Cover problem and the Min-Knapsack problem. We are given a hypergraph, each vertex of which has a nonnegative weight, and each edge of which has a nonnegative length. For a given threshold , our objective is to find a subset of the vertices with minimum total cost, such that at least a length of of the edges is covered. This problem is called the partial set cover problem. We present an O(|V|² + |H|)-time, Δ_E-approximation algorithm for this problem, where Δ_E ≥ 2 is an upper bound on the edge cardinality of the hypergraph and |H| is the size of the hypergraph (i.e., the sum of all its edges cardinalities). The special case where Δ_E = 2 is called the partial vertex cover problem. For this problem a 2-approximation was previously known, however, the time complexity of our solution, i.e., O(|V|²), is a dramatic improvement.We show that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation. Now, using the local-ratio technique, it is sufficient to repeatedly subtract a homogeneous weight function from the given weight function.     

Load Balancing for Adaptively Refined Grids

The solution of partial differential equations on a parallel computer is usually done by a data parallel approach. The grid is partitioned and mapped onto the processors. However, partitioning of unstructured meshes and adaptively refined meshes in general is an NP‐hard problem and heuristics are needed. In this paper a parallelisable and cheap method based on space‐filling curves is analysed. Quasi‐optimal estimates are derived for partitions of adaptively refined grids.     

On the Inverse Problem for Robust Capture Zone Construction

An interception problem with variable velocities and variable lateral acceleration boundaries is considered. Two problems, inverse to constructing the capture zone for a given linear strategy, are formulated. In the first (weak) formulation, a linear strategy is derived forcing its capture zone to contain a given set. In the second (strong) formulation, the capture zone of such a linear strategy is forced to coincide with a given set. A step-by-step algorithm, solving these problems, is derived. This algorithm is based on a detailed differential-geometrical analysis of the capture zone boundary. Illustrative examples are presented.     

An Iterative Construction Heuristic for the Ore Selection Problem

The ore selection problem involves choosing a processing option for a number of mining blocks that maximises the expected payoff for a given level of financial risk. An innovative neighbourhood search heuristic is proposed for the ore selection problem. This iterative construction heuristic employs a stochastic demolition and reconstruction strategy. Computational experiments with this heuristic for two ore selection problem instances, one involving 2,500 blocks and the other involving 78,000 blocks, are given. These problem instances are made publicly available for use by future workers. Our computational experiments indicate that the proposed heuristic produces better quality solutions faster than a relay hybrid (constructive-simulated annealing) heuristic.     

Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors

The paper is devoted to the applications of convexifactors to bilevel programming problem. Here we have defined ∂ ^∗-convex, ∂ ^∗-pseudoconvex and ∂ ^∗-quasiconvex bifunctions in terms of convexifactors on the lines of Dutta and Chandra (Optimization 53:77–94, 2004) and Li and Zhang (J. Opt. Theory Appl. 131:429–452, 2006). We derive sufficient optimality conditions for the bilevel programming problem by using these functions, and we establish various duality results by associating the given problem with two dual problems, namely Wolfe type dual and Mond–Weir type dual.