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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The purpose of this paper is to show how simulation of the flow of particulates and fluids using discrete element modelling (DEM) and smoothed particle dynamics (SPH) particle methods, offer opportunities for better understanding the dynamics of flow processes.

DEM and SPH methods are demonstrated in a broad range of computationally‐demanding applications including comminution, biomedical, geophysical extreme flow events (risk/disaster modelling), eating of food by humans and elite water‐based sports.

DEM is ideally suited to predicting industrial and geophysical applications where collisions between particles are the dominant physics. SPH is highly suited to multi‐physics fluid flow applications in industrial, biophysical and geophysical applications. The advantages and disadvantages of these particle methods are discussed.

Research results are limited by the numerical resolution that can currently be afforded.

The paper demonstrates the use of particle‐based computational methods in a series of high value applications. Enterprises that share interests in these applications will benefit in their product and service development by adopting these methods.

The ability to model disasters provides governments and companies with the opportunity and obligation to use these to render knowable disasters which were previously considered unknowable. The ability to predict the breakdown of food during eating opens up opportunities for the design of superior performing foods with lower salt, sugar and fat that can directly contribute to improved health outcomes and can influence government food regulatory policy.

The paper extends the scale and range of modelling of particle methods for demanding leading‐edge problems, of practical interest in engineering and applied sciences.

Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finite‐difference operator‐splitting method, a version of the known SIMPLEC‐like method on a staggered grid, is described. Appropriate theoretical results are presented. The method has second‐order accuracy in space, conserving mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to 401 × 321 grid points, at sequentially halved time steps to ensure grid‐independent results. Three types of flow are shown to exist at Re = 500: a steady‐state unstable flow and two which are transient, fully periodic and asymmetric about the centre line but mirror symmetric to each other. Discrete frequency spectra of drag and lift coefficients are presented.

This paper is devoted to the topic of how mathematics might be more efficiently used in educational administration. The position taken here is that mathematics is a branch of philosophy whose subject matter is a set of abstract entities and identified operational rules. It is a vocabulary of symbols that can be used to label objects and, more importantly, a set of grammatical rules for using the vocabulary. The paper begins with a review of some recent developments reported in the social science literature on the uses of mathematics in political science, sociology and economics, and ends with some illustrations of how these developments could lead to similar applications in both the practice and theory domains of educational administration.

This paper aims to provide a well-behaved nonlinear scheme and accelerating iteration for the nonlinear convection diffusion equation with fundamental properties illustrated.

A nonlinear finite difference scheme is studied with fully implicit (FI) discretization used to acquire accurate simulation. A Picard–Newton (PN) iteration with a quadratic convergent ratio is designed to realize fast solution. Theoretical analysis is performed using the discrete function analysis technique. By adopting a novel induction hypothesis reasoning technique, the L^∞ (H¹) convergence of the scheme is proved despite the difficulty because of the combination of conservative diffusion and convection operator. Other properties are established consequently. Furthermore, the algorithm is extended from first-order temporal accuracy to second-order temporal accuracy.

Theoretical analysis shows that each of the two FI schemes is stable, its solution exists uniquely and has second-order spatial and first/second-order temporal accuracy. The corresponding PN iteration has the same order of accuracy and quadratic convergent speed. Numerical tests verify the conclusions and demonstrate the high accuracy and efficiency of the algorithms. Remarkable acceleration is gained.

The numerical method provides theoretical and technical support to accelerate resolving convection diffusion, non-equilibrium radiation diffusion and radiation transport problems.

The FI schemes and iterations for the convection diffusion problem are proposed with their properties rigorously analyzed. The induction hypothesis reasoning method here differs with those for linearization schemes and is applicable to other nonlinear problems.

Presents the scientific methodology from the enlarged cybernetical perspective that recognizes the anisotropy of time, the probabilistic character of natural laws, and the entry that the incomplete determinism in Nature opens to the occurrence of innovation, growth, organization, teleology communication, control, contest and freedom. The new tier to the methodological edifice that cybernetics provides stands on the earlier tiers, which go back to the Ionians (c. 500 BC). However, the new insights reveal flaws in the earlier tiers, and their removal strengthens the entire edifice. The new concepts of teleological activity and contest allow the clear demarcation of the military sciences as those whose subject matter is teleological activity involving contest. The paramount question “what ought to be done”, outside the empirical realm, is embraced by the scientific methodology. It also embraces the cognitive sciences that ask how the human mind is able to discover, and how the sequence of discoveries might converge to a true description of reality.