Application of a modified semismooth Newton method to some elasto-plastic problems

Some elasto-plasticity models with hardening are discussed and some incremental finite element methods with different time discretisation schemes are considered. The corresponding one-time-step problems lead to variational equations with various non-linear operators. Common properties of the non-linear operators are derived and consequently a general problem is formulated. The problem can be solved by Newton-like methods. First, the semismooth Newton method is analysed. The local superlinear convergence is proved in dependence on the finite element discretisation parameter. Then it is introduced a modified semismooth Newton method which contain suitable “damping” in each Newton iteration in addition. The determination of the damping coefficients uses the fact that the investigated problem can be formulated as a minimisation one. The method is globally convergent, independently on the discretisation parameter. Moreover the local superlinear convergence also holds. The influence of inexact inner solvers is also discussed. The method is illustrated on a numerical example.     

On some approaches to solve CFD problems

This paper presents two efficient methods for spatial flows calculations. In order to simulate of incompressible viscous flows, a second-order accurate scheme with an incomplete LU decomposed implicit operator is developed. The scheme is based on the method of artificial compressibility and Roe flux-difference splitting technique for the convective terms. The numerical algorithm can be used to compute both steady-state and time-dependent flow problems. The second method is developed for modeling of stationary compressible inviscid flows. This numerical algorithm is based on a simple flux-difference splitting into physical processes method and combines a multi level grid technology with a convergence acceleration procedure for internal iterations. The capabilities of the methods are illustrated by computations of steady-state flow in a rotary pump, unsteady flow over a circular cylinder and stationary subsonic flow over an ellipsoid.     

A fuzzy approach to some classification problems

An appropriate algebraic structure was previously defined which can be regarded as a possible alternative to the theory of approximate reasoning, [A. Gisolfi, Fuzzy Sets Syst. 44 , 37–43 (1992)]. In this article we aim at extending the operations of the structure in order to cope with classification problems. the theoretical aspects are emphasized in order to give an adequate background to the possible applications. After defining the basic elements and the related operations, the structure is implemented by means of Prolog. Finally the relationship between the structure and the problems of classification is discussed in some detail. © 1993 John Wiley & Sons, Inc.     

Efficient parallel solutions to some geometric problems

This paper presents new algorithms for solving some geometric problems on a shared memory parallel computer, where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location. The algorithms are quite different from known sequential algorithms, and are based on the use of a new parallel divide-and-conquer technique. One of our results is an O(log n) time, O(n) processor algorithm for the convex hull problem. Another result is an O(log n log log n) time, O(n) processor algorithm for the problem of selecting a closest pair of points among n input points.     

Ergonomics approach applied to the problems of two disabled people

Two case studies are presented to illustrate the potential of an ergonomics approach, in facilitating and widening the range of activities disabled people can perform. This approach, as illustrated here, can be used as an essential practical tool in employment rehabilitation centres and the resettlement of disabled people in open employment.     

The application of a general finite difference method to some boundary value problems

This paper presents in full a method, based on Taylor's expansion, of applying finite difference techniques to boundary value problems of complex geometry. It demonstrates both the ease with which boundary conditions are incorporated and how error analyses may be performed. A range of second and fourth order examples are presented to illustrate the versatility of the method.     

Dynamics and solutions to some control problems for water-tanksystems

We consider a tank containing a fluid. The tank is subjected to directly controlled translations and rotations. The fluid motion is described by linearized wave equations under shallow water approximations. For irrotational flows, a new variational formulation of Saint-Venant equations is proposed. This provides a simple method to establish the equations when the tank is moving. Several control configurations are studied: one and two horizontal dimensions; tank geometries (straight and nonstraight bottom, rectangular and circular shapes), tank motions (horizontal translations with and without rotations). For each configuration, we prove that the linear approximation is steady-state controllable and provide a simple and flatness-based algorithm for computing the steering open-loop control. These algorithms rely on operational calculus. They lead to second order equations in space variables whose fundamental solutions define delay operators corresponding to convolutions with compact support kernels. For each configuration, several controllability open-problems are proposed and motivated     

Barriers to student computer usage: staff and student perceptions

Ensuring that all graduates are able to exploit new technologies is a primary goal of all UK universities and a variety of assumptions have underpinned policies designed to promote this goal. This paper explores some of these assumptions through the findings of a longitudinal study involving a cohort of over 800 university students. The study adopted a student perspective to examine the factors affecting their use of computers over a three year period. Unsurprisingly, the results indicated that situational factors (e.g. access, training and time) influence the extent to which students use computers, but a disparity was found in the importance attributed to these factors by the academic staff, who focused on the needs of their department, and by the students, who focused on their individual needs. Results suggest that increased attention to a student perspective may lead to improved strategic planning in students' use of computers.     

C-calculus: An elementary approach to some problems in pattern recognition

This work utilizes the concept of “Composite set” (C-set) and of the related C-calculus to study some standard problems of pattern analysis and general processing of signals. After some basic definitions and notations about composite sets are briefly stipulated, it is shown how a family of C-sets can be associated with a digitized picture. Each element in the family conveys partial information about the picture itself, yet it is possible to combine the various contributions from each C-set in such a way as to completely retrieve the image. Conditions that guarantee such “convergence” are theoretically investigated: the cases of nonconvergence are also proved to be of some interest.

C-calculus is concretely applied to the extraction of significant regions in a digitized picture, of contours, etc. An application to texture discrimination and analysis is also outlined.     

A new front updating solution applied to some engineering problems

Summary An automatic mesh generation dealing with domains of an arbitrary shape could be realized by an advancing front method. The mesh generator based on this method creates triangle elements inside a domain starting with the polygonal (polyhedral in 3D) discretisation of its border. In this paper an original algorithm for the front updating procedures as a part of the mesh generator is presented. The proposed algorithm provides an efficient mesh generation procedure. It has been verified on the various domains with complex geometry and with nonuniform distribution of edge nodes such as the discretisation of the switched reluctance motor and power cable configuration, respectively. The related finite element calculations are carried out.     

Uniform approach for solving some classical problems on a lineararray

It is shown that a number of classical problems from linear algebra and graph theory, including instances of the algebraic path problem, matrix multiplication, matrix triangularization, and matrix transpose, can be solved using the same basic recurrence. A simple mapping of the recurrence onto a unidirectional linear array is discussed. Qualitative advantages to programming linear arrays using this approach include uniformity of design, simplicity of programming, and scalability to larger problems. The major disadvantage is that the resulting algorithms are not necessarily optimal     

Statement and solution of some problems on a mathematical safe

The problem on a mathematical safe is formulated and studied in terms of graph theory. The cases of simplest digraphs such as paths, contours, and doubly connected components are analyzed. A number of statements on the existence of solutions to these problems are proved. The results obtained are extended to the case of corresponding nondirected graphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–14, May–June 2006.     

Algorithms for some graph problems on a distributed computational model

This paper presents distributed algorithms for some graph problems on a network model of computation. These graph problems include breadth-first and breadth-depth searches of graphs, recognition of directed acyclic graphs and strong connectedness, finding weights of all the shortest paths from a single source to all other nodes in a weighted directed acyclic graph, and analyzing activity networks. The results of computations (i.e., the outputs) of all the algorithms but the algorithm for recognition of directed acyclic graphs are available in a distributed manner. For algorithms in such a computational model, two types of complexity measures are important. One is the time complexity and the other is the message or communication complexity. Both of these complexities are obtained for each of the aforesaid distributed algorithms.     

Algorithms for some maximization scheduling problems on a single machine

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT _j and for the problem of maximizing the number of tardy jobs 1‖maxΣU _j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT _j is polynomially solvable. For several special cases of problem 1‖maxΣT _j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.