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1.
Problems with conjugation conditions and their high-accuracy computational discretization algorithms
New classes of problems with discontinuous solutions are considered. The corresponding generalized problems are obtained.
Numerical schemes, which are as asymptotically accurate as similar schemes for problems with smooth solutions, are proposed
for the new classes of problems.
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 100–124, November–December, 1999. 相似文献
2.
Stefan Turek Ludmila Rivkind Jaroslav Hron Roland Glowinski 《Journal of scientific computing》2006,28(2-3):533-547
In [Turek (1996). Int. J. Numer. Meth. Fluids
22, 987–1011], we had performed numerical comparisons for different time stepping schemes for the incompressible Navier–Stokes equations. In this paper, we present the numerical analysis in the context of the Navier–Stokes equations for a modified time-stepping θ-scheme which has been recently proposed by Glowinski [Glowinski (2003). In: Ciarlet, P. G., and Lions, J. L. (eds.), Handbook of Numerical Analysis, Vol. IX, North-Holland, Amsterdam, pp. 3–1176]. Like the well-known classical Fractional-Step-θ-scheme which had been introduced by Glowinski [Glowinski (1985). In Murman, E. M. and Abarbanel, S. S. (eds.), Progress and Supercomputing in Computational Fluid Dynamics, Birkh?user, Boston MA; Bristeau et al. (1987). Comput. Phys. Rep. 6, 73–187], too, and which is still one of the most popular time stepping schemes, with or without operator splitting techniques, this new scheme consists of 3 substeps with nonequidistant substepping to build one macro time step. However, in contrast to the Fractional-Step-θ-scheme, the second substep can be formulated as an extrapolation step for previously computed data only, and the two remaining substeps look like a Backward Euler step so that no expensive operator evaluations for the right hand side vector with older solutions, as for instance in the Crank–Nicolson scheme, have to be performed. This modified scheme is implicit, strongly A-stable and second order accurate, too, which promises some advantageous behavior, particularly in implicit CFD simulations for the nonstationary Navier–Stokes equations. Representative numerical results, based on the software package FEATFLOW [Turek (2000). FEATFLOW Finite element software for the incompressible Navier–Stokes equations: User Manual, Release 1.2, University of Dortmund] are obtained for typical flow problems with benchmark character which provide a fair rating of the solution schemes, particularly in long time simulations.Dedicated to David Gottlieb on the occasion of his 60th anniversary 相似文献
3.
M. Z. Zgurovskii 《Cybernetics and Systems Analysis》2000,36(1):75-82
The paper deals with the role and place of systems analysis methods in the solution of complex problems in various spheres
of human activity in Ukraine. The social and socio-economic prerequisites for development of theory and applied methods are
being considered. The main characteristics of the problems to which these methods are applied are formulated. The hierarchy
of problems and methods used for solution of complex problems based on systems analysis methods is presented, and the main
spheres of their application in Ukraine are presented.
Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 101–109, January–February, 2000. 相似文献
4.
New optimal control problems for elliptic systems with contact conditions and nonsymmetric state operators are considered.
Existence theorems for optimal solutions are proved. High-accuracy schemes for approximating optimal controls are proposed
for the case where the set of admissible controls coincides with a complete Hilbert space.
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–85, November–December 2005. 相似文献
5.
For a vector integer quadratic programming problem, a regularizing operator is proposed that acts on a vector criterion and
transforms a possibly unstable initial problem into a series of perturbed stable problems with the same Pareto set. The technique
of ε-regularization is developed that allows replacing the considered problem by perturbed ε-stable problems.
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 128–134, March–April 2009. 相似文献
6.
High-order Compact Schemes for Nonlinear Dispersive Waves 总被引:1,自引:0,他引:1
High-order compact finite difference schemes coupled with high-order low-pass filter and the classical fourth-order Runge–Kutta
scheme are applied to simulate nonlinear dispersive wave propagation problems described the Korteweg-de Vries (KdV)-like equations,
which involve a third derivative term. Several examples such as KdV equation, and KdV-Burgers equation are presented and the
solutions obtained are compared with some other numerical methods. Computational results demonstrate that high-order compact
schemes work very well for problems involving a third derivative term. 相似文献
7.
In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It
adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant
reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy
for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO
and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational
cost by 20–40%, especially for problems with large fraction of constant regions. 相似文献
8.
D. R. Santos-Peñate R. Suárez-Vega P. Dorta-González 《Networks and Spatial Economics》2007,7(1):45-61
This paper summarizes some results for the leader–follower location model on networks in several scenarios. Discretization
results are considered and differences derived from the inelastic and elastic demand assumptions, as well as from the customer’s
choice rule, are emphasized. Finally, some issues for future lines of investigation are suggested. 相似文献
9.
S. Hadd A. Idrissi A. Rhandi 《Mathematics of Control, Signals, and Systems (MCSS)》2006,18(3):272-291
We investigate the infinite dimensional control linear systems with delays in the state and input. We give a new variation of constants formula when the state and control delay operators are unbounded. We prove the existence of mild and classical solutions of such systems. Our approach is based on the theory of abstract and regular linear systems introduced by Salamon (Math Syst Theor 21:147–164, 1989) and Weiss (Isr J Math 65:17–43, 1989). Finally, we apply our abstract framework to an example from population dynamics. 相似文献
10.
Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much
attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented
for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate
the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated
solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new
hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints,
a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The
proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling
mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate
the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting
Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be
statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions
with good coverage and convergence to true Pareto-optimal fronts. 相似文献
11.
Following the idea of the tailored finite point method proposed in Han and Huang (J. Comput. Math. 26:728–739, 2008) and Huang (Netw. Heterog. Media 4:91–106, 2009), a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types
of media. Stability and accuracy are analyzed and numerically verified. In particular we can obtain unconditionally stable
implicit schemes that can be solved explicitly for boundary value problems. We can also deal with the propagation of discontinuity
and highly oscillatory waves efficiently. The generalization to higher order schemes is straightforward. 相似文献
12.
M. H. Carpenter C. A. Kennedy Hester Bijl S. A. Viken Veer N. Vatsa 《Journal of scientific computing》2005,25(1):157-194
Multiple high-order time-integration schemes are used to solve stiff test problems related to the Navier–Stokes (NS) equations.
The primary objective is to determine whether high-order schemes can displace currently used second-order schemes on stiff
NS and Reynolds averaged NS (RANS) problems, for a meaningful portion of the work-precision spectrum. Implicit–Explicit (IMEX)
schemes are used on separable problems that naturally partition into stiff and nonstiff components. Non-separable problems
are solved with fully implicit schemes, oftentimes the implicit portion of an IMEX scheme. The convection–diffusion-reaction
(CDR) equations allow a term by term stiff/nonstiff partition that is often well suited for IMEX methods. Major variables
in CDR converge at near design-order rates with all formulations, including the fourth-order IMEX additive Runge–Kutta (ARK2) schemes that are susceptible to order reduction. The semi-implicit backward differentiation formulae and IMEX ARK2 schemes are of comparable efficiency. Laminar and turbulent aerodynamic applications require fully implicit schemes, as they
are not profitably partitioned. All schemes achieve design-order convergence rates on the laminar problem. The fourth-order
explicit singly diagonally implicit Runge–Kutta (ESDIRK4) scheme is more efficient than the popular second-order backward
differentiation formulae (BDF2) method. The BDF2 and fourth-order modified extended backward differentiation formulae (MEBDF4)
schemes are of comparable efficiency on the turbulent problem. High precision requirements slightly favor the MEBDF4 scheme
(greater than three significant digits). Significant order reduction plagues the ESDIRK4 scheme in the turbulent case. The
magnitude of the order reduction varies with Reynolds number. Poor performance of the high-order methods can partially be
attributed to poor solver performance. Huge time steps allowed by high-order formulations challenge the capabilities of algebraic
solver technology. 相似文献
13.
On an alternative approach to stress constraints relaxation in topology optimization 总被引:5,自引:4,他引:1
Matteo Bruggi 《Structural and Multidisciplinary Optimization》2008,36(2):125-141
The paper deals with the imposition of local stress constraints in topology optimization. The aim of the work is to analyze
the performances of an alternative methodology to the ε-relaxation introduced in Cheng and Guo (Struct Optim 13:258–266, 1997), which handles the well-known stress singularity problem. The proposed methodology consists in introducing, in the SIMP
law used to apply stress constraints, suitable penalty exponents that are different from those that interpolate stiffness
parameters. The approach is similar to the classical one because its main effect is to produce a relaxation of the stress
constraints, but it is different in terms of convergence features. The technique is compared with the classical one in the
context of stress-constrained minimum-weight topology optimization. Firstly, the problem is studied in a modified truss design
framework, where the arising of the singularity phenomenon can be easily shown analytically. Afterwards, the analysis is extended
to its natural context of topology bidimensional problems. 相似文献
14.
A. F. Gainutdinova 《Cybernetics and Systems Analysis》1999,35(5):836-840
A new SIMD-model of parallel computations is proposed, in which the processors are interconnected by a controlled tree-like
communication circuit. For the problems considered, an architecture is proposed that is more effective than that for well-known
models.
Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 175–180, September–October, 1999. 相似文献
15.
A new method of genetic programming, named chemical genetic programming (CGP), which enables evolutionary optimization of the mapping from genotypic strings to phenotypic trees is proposed. A cell
is evolved which includes a DNA string that codes the fundamental mapping from the DNA code to computational functionality.
Genetic modification of a cell's DNA allows the DNA code and the genotype-to-phenotype translation to coevolve. Building an
optimal translation table enhances evolution within a population while maintaining the necessary diversity to explore the
entire search space.
This work was presented in part at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30,
2004 相似文献
16.
The problems of robust l
2−l
∞ and H
∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The
filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov
stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters
guaranteeing a prescribed l
2−l
∞ or H
∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient
interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less
conservative than earlier results. 相似文献
17.
Wei-Guo Zhang Wei-Lin Xiao Ying-Luo Wang 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2009,13(6):627-633
This paper deals with the portfolio selection problem when the returns of assets obey LR-type possibility distributions and there exist the limits on holdings. A new possibilistic mean–variance model to portfolio
selection is proposed based on the definitions of the possibilistic return and possibilistic risk, which can better integrate
an uncertain decision environment with vagueness and ambiguity. This possibilistic mean–variance model can be regarded as
extensions of conventional probabilistic mean–variance methodology and previous possibilistic approaches since it contains
less parameter and has a more extensive application. A numerical example of a possibilistic fuzzy portfolio selection problem
is given to illustrate our proposed effective means and approaches.
This project was supported by NCET (No.06-0749) and The National Natural Science Foundation of China (No.70571024). 相似文献
18.
Directional selectivity to local visual stimuli appears in various levels of the visual pathway, being in the retina very
conspicuous. Neurophysiology suggests that directionality (as well as other local and quasi-global filtering properties) are
based in the space–time interactions of processes with different “memory” (latency). We draw inspiration from the corresponding
underlying biological mechanisms to propose two general schemes for directionality computation in nets, compatible with other
space–time filtering properties. First, a connectivistic mechanism based on bipolar–amacrine–ganglion cell interaction is
proposed, by formalizing the classical proposals of early vision neurophysiologists. Second, inspired initially in the more
recently described intrinsic directionality of amacrines, novel schemes are proposed where directionality appear as the computing
consequence of adding memory to spatial filtering structures. The mathematical formulations are achieved by means of Newton
Filters and Hermite Functionals. 相似文献
19.
In this work a new class of numerical methods for the BGK model of kinetic equations is presented. In principle, schemes of
any order of accuracy in both space and time can be constructed with this technique. The methods proposed are based on an
explicit–implicit time discretization. In particular the convective terms are treated explicitly, while the source terms are
implicit. In this fashion even problems with infinite stiffness can be integrated with relatively large time steps. The conservation
properties of the schemes are investigated. Numerical results are shown for schemes of order 1, 2 and 5 in space, and up to
third-order accurate in time. 相似文献