共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, the -stability of the first order fully discrete Galerkin finite element methods for the Boussinesq equations with smooth and non-smooth initial data is presented. The finite element spatial discretization for the Boussinesq equations is based on the mixed finite element method, and the temporal treatments of the spatial discrete Boussinesq equations include the implicit scheme, the semi-implicit scheme, the implicit/explicit scheme and the explicit scheme. The -stability results of the above numerical schemes are established. Firstly, we prove that the implicit and semi-implicit schemes are the -unconditional stable. Then we show that the implicit/explicit scheme is -almost unconditional stable with the initial data that belong to and , and the similar results are obtained for the semi-implicit/explicit scheme in the case of the initial data that belong to . Furthermore, we show that the explicit scheme is the -conditional stable. Finally, some numerical examples are provided to verify the established theoretical findings and confirm the corresponding stability analysis of the different numerical schemes. 相似文献
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Yanli Ren Shuozhong Wang Xinpeng Zhang 《Computers & Mathematics with Applications》2013,65(9):1403-1412
Parallel key-insulated encryption (PKIE) usually allows two independent helper keys to be alternately used in temporary secret key update operations. At least half of temporary secret keys would be exposed and at least half of ciphertexts could be decrypted if one of the helper keys is exposed. In this paper, we propose a new PKIE scheme with helper keys, where . If one of the helper keys is exposed, only temporary secret keys would be exposed and ciphertexts could be decrypted, so the new PKIE scheme can greatly decrease loss due to key-exposure. The scheme is provably secure without random oracles based on a bilinear group of composite order. Most important, the scheme is practical and much more efficient than the extended ones from the previous PKIE schemes. 相似文献
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In this paper, four alternating direction implicit (ADI) schemes are presented for solving two-dimensional cubic nonlinear Schrödinger equations. Firstly, we give a Crank–Nicolson ADI scheme and a linearized ADI scheme both with accuracy , with the same method, use fourth-order Padé compact difference approximation for the spatial discretization; two HOC-ADI schemes with accuracy are given. The two linearized ADI schemes apply extrapolation technique to the real coefficient of the nonlinear term to avoid iterating to solve. Unconditionally stable character is verified by linear Fourier analysis. The solution procedure consists of a number of tridiagonal matrix equations which make the computation cost effective. Numerical experiments are conducted to demonstrate the efficiency and accuracy, and linearized ADI schemes show less computational cost. All schemes given in this paper also can be used for two-dimensional linear Schrödinger equations. 相似文献
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《Journal of Parallel and Distributed Computing》2004,64(11):1286-1296
In this paper, we investigate the star graph with faulty vertices and/or edges from the graph theoretic point of view. We show that between every pair of vertices with different colors in a bicoloring of , , there is a fault-free path of length at least , and there is a path of length at least joining a pair of vertices with the same color, when the number of faulty elements is or less. Here, is the number of faulty vertices. , , with at most faulty elements has a fault-free cycle of length at least unless the number of faulty elements are and all the faulty elements are edges incident to a common vertex. It is also shown that , , is strongly hamiltonian-laceable if the number of faulty elements is or less and the number of faulty vertices is one or less. 相似文献
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Yongge Tian 《Computers & Mathematics with Applications》2011,61(6):1493-1501
Let and be two linear matrix expressions, and denote by and the collections of the two matrix expressions when and run over the corresponding matrix spaces. In this paper, we study relationships between the two matrix sets and , as well as the two sets and , by using some rank formulas for matrices. In particular, we give necessary and sufficient conditions for the two matrix set inclusions and to hold. We also use the results obtained to characterize relations of solutions of some linear matrix equations. 相似文献
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In this paper, we execute elementary row and column operations on the partitioned matrix into to compute generalized inverse of a given complex matrix , where is a matrix such that and . The total number of multiplications and divisions operations is and the upper bound of is less than when . A numerical example is shown to illustrate that this method is correct. 相似文献
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The number of states in a deterministic finite automaton (DFA) recognizing the language , where is regular language recognized by an -state DFA, and is a constant, is shown to be at most and at least in the worst case, for every and for every alphabet of at least six letters. Thus, the state complexity of is . In the case the corresponding state complexity function for is determined as with the lower bound witnessed by automata over a four-letter alphabet. The nondeterministic state complexity of is demonstrated to be . This bound is shown to be tight over a two-letter alphabet. 相似文献
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Alireza Rahimi Abbas Kasaeipoor Ali Amiri Mohammad Hossein Doranehgard Emad Hasani Malekshah Lioua Kolsi 《Computers & Mathematics with Applications》2018,75(5):1795-1813
In the present study, the three-dimensional natural convection and entropy generation in a cuboid enclosure included with various discrete active walls is analyzed using lattice Boltzmann method. The enclosure is filled with CuO–water nanofluid. To predict thermo-physical properties, dynamic viscosity and thermal conductivity, of CuO–water nanofluid, the KKL model is applied to consider the effect of Brownian motion on nanofluid properties. In lattice Boltzmann simulation, two different MRT models are used to solve the problem. The D3Q7-MRT model is used to solve the temperature filed, and the D3Q19 is employed to solve the fluid flow of natural convection within the enclosure. The influences of different Rayleigh numbers and solid volume fractions and four different arrangements of discrete active walls on the fluid flow, heat transfer, total entropy generation, local heat transfer irreversibility and local fluid friction irreversibility are presented comprehensively. 相似文献