Search

In this paper, several local and parallel finite element algorithms are proposed and analyzed for the 2D/3D stationary inductionless incompressible magnetohydrodynamic (MHD) equations. The core concept is to guarantee the charge-conservation property by choosing mixed finite element spaces in H 0 (div , Ω) × L 0 2 (Ω) to approximate (J , ϕ) , meantime combining the idea of domain decomposition method to realize parallel operation. The characteristic of the proposed algorithms is that the computational complexity is greatly reduced while ensuring the accuracy of the numerical simulation. With the local a prior estimate as the technical means of theoretical analysis, we give the error estimates of the algorithms. Finally, several numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we have designed a simple method for the inverse scattering problem of stratified ocean waveguide. The simple approach applies the bisection technique in parallel to estimate the boundaries of inhomogeneous media from the received partial data. In addition, the algorithm only involves the matrix–vector operations and possesses the optimal computation complexity in both two and three dimensions. In practice, it is easy to carry out, robust against noise and capable of reconstructing the penetrable obstacles of different locations and shapes. We can consider the simple method as a direct and straightforward process to supply satisfactory initial positions for the implementation of any existing more refined but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers. [ABSTRACT FROM AUTHOR]

Abstract: Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods I, Numer. Math. 56 (1989) 157–177; O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods II, SIAM J. Numer. Anal. 27 (1990) 1569–1590] on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant in the so-called strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. More precisely, the value of the upper bound for is a part of the construction of various multilevel extensions of the related two-level methods. In this paper algebraic two-level and multilevel preconditioning algorithms for second-order elliptic boundary value problems are constructed, where the discretization is done using Rannacher–Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The proposed variants of the hierarchical two-level basis are first introduced in a rather general setting. Then, the parameters involved are studied and optimized. The major contribution of the paper is the derived estimates of the constant in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver. [Copyright &y& Elsevier]

In this paper, we present two novel symbolic computational algorithms to solve periodic pentadiagonal (PP) linear systems. These two algorithms are based on a special matrix decomposition and the use of any fast pentadiagonal linear solver, respectively. Some numerical examples are given in order to demonstrate the performance of the proposed algorithms and their competitiveness with existing algorithms. All of the experiments are performed on a computer workstation with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]

Abstract: Frequent itemset mining from data streams is an important data mining problem with broad applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. However, it is also a difficult problem due to the unbounded, high-speed and continuous characteristics of streaming data. Therefore, extracting frequent itemsets from more recent data can enhance the analysis of stream data. In this paper, we propose an efficient algorithm, called Max-FISM (Maximal-Frequent Itemsets Mining), for mining recent maximal frequent itemsets from a high-speed stream of transactions within a sliding window. According to our algorithm, whenever a new transaction is inserted in the current window only its maximum itemset should be inserted into a prefix tree-based summary data structure called Max-Set for maintaining the number of independent appearance of each transaction in the current window. Finally, the set of recent maximal frequent itemsets is obtained from the current Max-Set. Experimental studies show that the proposed Max-FISM algorithm is highly efficient in terms of memory and time complexity for mining recent maximal frequent itemsets over high-speed data streams. [Copyright &y& Elsevier]

Abstract: Having been widely used in a VoIP system, the ITU-T G.729 standard is of high computational complexity, a heavy load for a real-time operation on a low-end smart phone or other embedded devices even with the G.729A standard. In this paper, there are three methods proposed for an efficient complexity reduction of G.729A, i.e., a combined local optimal pulse method, employed to search an algebraic codebook, a discontinuous pitch estimation, used to analyze the open-loop pitch, and the hybrid two-stage vector quantization (HTVQ), assigned to quantize the line spectral frequency (LSF) coefficients. It is validated by experimental results that the improved version of G.729A can be easily implemented on a smart phone (312 MHz CPU, 64 MB RAM) in real-time operation. In total 80.94% of computational load can be thus eliminated in comparison with the G.729A and a satisfactory speech quality is maintained as intended, an excellent efficiency demonstration by the methods proposed. [Copyright &y& Elsevier]

Abstract: This paper proposed an improved version of the Particle Swarm Optimization (PSO) approach to solve Traveling Salesman Problems (TSP). This evolutionary algorithm includes two phases. The first phase includes Fuzzy -Means clustering, a rule-based route permutation, a random swap strategy and a cluster merge procedure. This approach firstly generates an initial non-crossing route, such that the TSP can be solved more efficiently by the proposed PSO algorithm. The use of sub-cluster also reduces the complexity and achieves better performance for problems with a large number of cities. The proposed Genetic-based PSO procedure is then applied to solve the TSP with better efficiency in the second phase. The proposed Genetic-based PSO procedure is applied to TSPs with better efficiency. Fixed runtime performance was used to demonstrate the efficiency of the proposed algorithm for the cases with a large number of cities. [Copyright &y& Elsevier]

Abstract: This paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable. We mainly evaluate the system reliability that units of data can be sent from the source to the sink under both time threshold and budget . In particular, the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time. A simple algorithm is proposed to generate all lower boundary points for (), and the system reliability can then be computed in terms of such points by utilizing a union of subsets. Computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently. [Copyright &y& Elsevier]

Abstract: Two-terminal reliability, which is defined as the probability that there exists at least one path from source node to sink node, is an important performance measure in network system. However, it is well known that the complexity of exact two-terminal reliability evaluation is NP-hard. This paper considers a bounding algorithm for computing two-terminal reliability based on decomposition technique originally used in computing multi-state reliability. Compared with traditional bounding algorithms, the proposed algorithm requires neither all MPs/MCs to be enumerated in advance, nor all arcs to have the same state probabilities. It can sequentially improve the quality of approximation according to a predetermined value . Especially, it may be an exact algorithm if it runs into completion. An example shows that the proposed algorithm is practical and effective. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the fractal properties of the generalized Chaikin corner-cutting subdivision scheme with two arbitrary parameters. On the basis of the discussion of limit points on the limit curve, the fractal range of the scheme is obtained and illustrated. The results obtained suggest a clear direction for generating fractal curves by using this scheme. Two fractal examples and their complexity evaluation results obtained by using the box dimension are given. [Copyright &y& Elsevier]

Abstract: Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability results related to two implementations of the Richardson Extrapolation (Active Richardson Extrapolation and Passive Richardson Extrapolation) are formulated and proved in this paper. An advanced atmospheric chemistry scheme, which is commonly used in many well-known operational environmental models, is applied in a long sequence of experiments in order to demonstrate the fact that [(a)] it is indeed possible to improve the accuracy of the numerical results when the Richardson Extrapolation is used (also when very difficult, badly scaled and stiff non-linear systems of ODEs are to be treated), [(b)] the computations can become unstable when the combination of the Trapezoidal Rule and the Active Richardson Extrapolation is used, [(c)] the application of the Active Richardson Extrapolation with the Backward Euler Formula is leading to a stable computational process, [(d)] experiments with different algorithms for solving linear systems of algebraic equations are very useful in the efforts to select the most suitable approach for the particular problems solved and [(e)] the computational cost of the Richardson Extrapolation is much less than that of the underlying numerical method when a prescribed accuracy has to be achieved. [Copyright &y& Elsevier]

Abstract: In this paper, an inversion algorithm for a banded matrix is presented. The twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the decomposition, as is shown with the analysis of computing complexity and the numerical experiments. [Copyright &y& Elsevier]

Abstract: In a communication network it is desirable that all pairs of nodes can exchange messages at the same time. But under the capacity constraints on nodes or links this desired property may not be satisfied; only some node pairs can communicate with each other while the rest have to be blocked. A natural question is what is the maximum number of node pairs that can communicate synchronously with the load restriction? In this paper, we first show that the problem is NP-complete. Then we present two approximation algorithms for the problems under the node load constraint and the link load constraint, respectively. [Copyright &y& Elsevier]