Solving Schemes for Computational Magneto-Aerodynamics

The electromagnetic force introduces a new physics dimension for enhancing aerodynamic performance of aerospace vehicles. In order to simulate interdisciplinary phenomena, the Navier–Stokes and Maxwell equations in the time domain must be integrated on a common frame of reference. For a wide range of applications from subsonic unmanned vehicles to hypersonic flight control, the resultant nonlinear partial differential equations offer a formidable challenge for numerical analysis. The experience and physical insight using the approximate Riemann and compact-differencing formulation as well as several temporal discritizations will be shared. The most recent development and advancement in numerical procedures for solving this system of governing equations are delineated     

Problems of discrete optimization: Challenges and main approaches to solve them

This paper briefly reviews the current state of the art in the field of discrete optimization problems. Emphasis is on the generalization of the experience gained at the V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine in research and development of solution methods and software for various classes of complicated discrete programming problems. The study was partially sponsored by the grant UKM2-2812-KV-06 (SRDF Cooperative Grants Program). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–25, July–August 2006.     

Fuzzy classification maximum likelihood algorithms for mixed-Weibull distributions

In this paper we propose an efficient algorithm based on Yang’s (Fuzzy Sets Syst 57:365–337, 1993) concept, namely the fuzzy classification maximum likelihood (FCML) algorithm, to estimate the mixed-Weibull parameters. Compared with EM and Jiang and Murthy (IEEE Trans Reliab 44:477–488, 1995) methods, the proposed FCML algorithm presents better accuracy. Thus, we recommend FCML as another acceptable method for estimating the mixed-Weibull parameters.     

Structural models of algorithms in problems of applied programming. I. Formal algorithmic structures

A structural approach to modelling algorithms is proposed. The concept of an algorithmic structure with operations over algorithms is introduced. Models of algorithms constructed from algorithmic structures reflect aspects of algorithm representation and execution. Examples of structural and path models of algorithms are considered. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–14, May-June 2009.     

Memory-based neuro-fuzzy system for interpolation of reflection coefficients of printing inks

The problem of interpolation of a two-dimensional function on a nonuniform axial rectangular grid is considered. To solve the problem, a memory-based neuro-fuzzy system is proposed. This system is computationally simple and provides a high-quality interpolation. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–11, September–October 2008.     

Applications of hybrid optimization techniques for model updating of rotor shafts

This paper presents an approach by combining the genetic algorithm (GA) with simulated annealing (SA) algorithm for enhancing finite element (FE) model updating. The proposed algorithm has been applied to two typical rotor shafts to test the superiority of the technique. It also gives a detailed comparison of the natural frequencies and frequency response functions (FRFs) obtained from experimental modal testing, the initial FE model and FE models updated by GA, SA, and combination of GA and SA (GA–SA). The results concluded that the GA, SA, and GA–SA are powerful optimization techniques which can be successfully applied to FE model updating, but the appropriate choice of the updating parameters and objective function is of great importance in the iterative process. Generally, the natural frequencies and FRFs obtained from FE model updated by GA–SA show the best agreement with experiments than those obtained from the initial FE model and FE models updated by GA and SA independently.     

Sorting-based localization and stable computation of zeros of a polynomial. II

The stability of a sorting-based scheme for identifying polynomial zeros under coefficient perturbation is discussed. A method is proposed for simultaneous reconstruction (with a logarithmic estimate of time complexity) of the coefficients of an arbitrary polynomial from the values of its zeros. The method of identification of polynomial zeros is based on the operator of localization of extremal elements of a numerical sequence after its preliminary sorting. The method is extended to pattern recognition. Part I of this article is published in No. 1 (2007). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 161–174, March–April 2007.     

Structural models of algorithms in problems of applied programming. II. Structural-algorithmic approach to software simulation

Relations existing between algorithms that are variously represented and are performed on various execution units are formalized. The process of software development is considered in the context of development and transformation of models. Possible applications of the structural-algorithmic approach are analyzed in various aspects of applied programming. Problems of analyzing algorithms in the context of execution of programs on computers are formulated. Part I of this article is published in No. 3 (2009). Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 49–56, July–August 2009.     

Localization of edges in graph models of two-level algorithms

Multidimensional computational models of two-level algorithms are introduced and investigated. Transformations of graph models of the algorithms are developed, which allow one to obtain modified models without global edges. The modified graph models can be transformed by the well-known transformation and mapping procedures into one-, two-, and three-dimensional array processors without global interconnections. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 63–71, November–December, 1999.     

Formalization of interrelations between operators and data within the framework of an extended algebra of algorithms

A system of algorithmic algebras is considered whose basic concepts are newly interpreted to formalize the interrelation between operators and data of such a system. A modified formal instrument is constructed that extends the possibilities of design and transformation of regular schemes of algorithms. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 170–182, November–December 2008.     

An approach to the parallel solution of a high-dimensional basic flow problem

The body of mathematics of modified systems of algorithmic algebras (SAA-M) is used to formalize the Edmonds–Karp algorithm of finding the maximum flow in a network. With allowance made for the distributed system features that are usually used for solving complicated problems, optimization criteria are formulated and used to obtain parallel SAA-M-schemes. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 146–152, March–April 2009.     

Direct methods of solving systems of linear algebraic ef ions with complex a-matrices

Algorithms of computer algebra are proposed for solving systems of linear algebraic equations with complex á- matrices. An analysis of roundoff errors for the computational schemes considered is given. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 144–156, March–April, 2000.     

Means of supporting the solution of differential equations in problem of supply-and-demand macroanalysis

This paper deals with models of demand-supply problems. A scheme of virtually organized computer support of the solution of such problems is discussed. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 174–183, July–August, 1999.     

Stability of bundles of dynamic systems and related problems

Solutions of a generalization of classical stability problems of linear systems are considered from a unified viewpoint of computational complexity. The stability problems are solved for bundles (generally speaking, continual) that are given by the degree of the characteristic polynomial and domain of admissible values of parameters. The stability criteria of the objects considered are proposed, which are based on the classical results obtained for linear systems. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 17–22, September–October, 1999.     

Inference of structures of models of probabilistic dependences from statistical data

Problems of reconstruction of structures of probabilistic dependence models in the class of directed (oriented) acyclic graphs (DAGs) and mono-flow graphs are considered. (Mono-flow graphs form a subclass of DAGs in which the cycles with one collider are prohibited.) The technique of induced (provoked) dependences is investigated and its application to the identification of structures of models is shown. The algorithm “Collifinder-M” is developed that identifies all collider variables (i.e., solves an intermediate problem of reconstruction of the structure of a mono-flow model). It is shown that a generalization of the technique of induced dependences makes it possible to strengthen well-known rules of identification of orientation of edges in a DAG model. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 19–31, November–December 2005.     

Approximation Algorithms for 3D Orthogonal Knapsack

We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is either forbidden or permitted, and we wish to maximize the total profit. Since this optimization problem is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms for the non-rotational scenario with approximation ratios 9 ε and 8 ε , as well as an algorithm with approximation ratio 7 ε that uses more sophisticated techniques; these are the smallest approximation ratios known for this problem. Furthermore, we show how the used techniques can be adapted to the case where rotation by 90° either around the z-axis or around all axes is permitted, where we obtain algorithms with approximation ratios 6 ε and 5 ε , respectively. Finally our methods yield a 3D generalization of a packability criterion and a strip packing algorithm with absolute approximation ratio 29/4, improving the previously best known result of 45/4.     

Methods of constructing Bayesian networks based on scoring functions

Available methods of constructing Bayesian networks with the use of scoring functions are analyzed. The Cooper-Herskovits and MDL functions are described in detail and used to compare algorithms of constructing Bayesian networks. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 81–88, March–April 2008.     

A fast cellular method of matrix multiplication

This paper proposes a cellular method of matrix multiplication. The method reduces the multiplicative and additive complexities of well-known matrix multiplication algorithms by 12.5%. The computational complexities of cellular analogs of such algorithms are estimated. A fast cellular analog is presented whose multiplicative and additive complexities are equal to ≈0.382n³ multiplications and ≈1.147n³ additions, respectively, where n is the order of the matrices being multiplied. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 55–59, May–June 2008.     

Complexity of the problem of verifying the coordination mechanism in a system of software support of network collaboration

The problem of verifying the coordination mechanism in a system of software support of network collaboration is considered. This problem is demonstrated to be similar to the agent verification problem. It is proved that the problem of verifying the coordination mechanism is co-complete. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 15–19, July–August 2008.     

Comparison of the Prim-Dijkstra and kraskal algorithms on an associative parallel processor

With the help of a model of an associative parallel processor with vertical processing (STAR computer), Prim-Dijkstra and Kraskal algorithms for finding a minimal spanning tree of an undirected graph represented in the form of a list of edges and their weights are compared. A relatively simple representation of the Prim-Dijkstra algorithm is constructed in which the initial node is taken into account. The Kraskal algorithm is also presented and the possibility of eliminating the stage of preliminary sorting of edges by their weights is shown. Translated from Kibernetika i Sistemnyi Analiz, No. 2. pp. 19–27, March–April, 2000.