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Attractive inter-particle forces, such as Van Der Waals forces ( vdw ), are known to strongly influence the fluidization behavior of particles classified as Geldart C-type, and recent literature suggests that vdw forces may also become important for Geldart A and B type particles at elevated temperatures. Discrete Element Models (DEM) using a soft-sphere collision model have been developed to investigate the effects of particle–particle and particle-gas interactions on the fluidization behavior in great detail. However, it is shown that inconsistent results may be obtained with soft-sphere based DEM, depending on the numerical implementation of the vdw forces, particularly related to the calculation of the vdw forces for overlapping particles during particle collisions, as is usually done in the literature. In this work we present a new numerical approach that allows the calculation of the vdw force for particles that are in contact in a physically sound way, corresponding with theoretical arguments given by Rietema et al. (1993). We also provide a generic protocol to determine the relevant parameters based on our new approach, which will allow future work to simulate gas-solid fluidized beds with attractive inter-particle forces in a soft-sphere DEM framework.

The implicit mid-point rule is a Runge–Kutta numerical integrator for the solution of initial value problems, which possesses important properties that are relevant in micromagnetic simulations based on the Landau–Lifshitz–Gilbert equation, because it conserves the magnetization length and accurately reproduces the energy balance (i.e. preserves the geometric properties of the solution). We present an adaptive step size version of the integrator by introducing a suitable local truncation error estimator in the context of a predictor-corrector scheme. We demonstrate on a number of relevant examples that the selected step sizes in the adaptive algorithm are comparable to the widely used adaptive second-order integrators, such as the backward differentiation formula (BDF2) and the trapezoidal rule. The proposed algorithm is suitable for a wider class of non-linear problems, which are linearised by Newton’s method and require the preservation of geometric properties in the numerical solution.

E-business is as risky as any other business. The first step in risk management and risk reduction is awareness that risk exists. In today’s modern environment and Internet operations, risk management plays a critical role in protection of organizations. T...

Basketball is a sport that has a very long tradition in the territory of ex-Yugoslavia. The breakdown of the country led to a de- crease in quality of basketball in the newly created countries. The unsteadiness of quality of the teams in national leagues resulted in formation of the Regional Adriatic Basketball League (ABA) in 2001. The main goal of this research was to measure the competitive balance in ABA, Spanish (ACB) and National Basketball Association League (NBA). The competitive balance was calculated by using Ratio of Standard Deviation index (RSD) and Herfindahl-Hirschman Index (HHI).The results of RSD showed that the most equable was ABA league, then came ACB league, while the most unequable was NBA league. The calculating of HHI index gave a different result. NBA is the most equable, then comes ABA league, and the last one is ACB league, which is the most unequable according to this parameter. ABA league has less quality than ACB and NBA league, but the results show that it is competitively the most balanced league. According to the RSD rates, NBA league is the most unequable. The main reason for that is a huge number of teams taking part in the league, which causes the unequable distribution of quality players. Ac- cording to HHI, NBA is the most equable. Reason for that are different mechanisms whose goal is to reach and maintain the competitive balance.

In many European Union countries, regional and rural development strategies also include rural tourism, which helps to retain the local population, creates new jobs and contributes to the socio-economic progress of underdeveloped areas. Through specialized institutions and funds, the European Union helps and through various forms directly participates in tourism development in rural areas, and the strengthening of rural development policy has become one of the highest priorities of the European Union. Although not a member of the EU, the Republic of Serbia has defined its path of development, which implies strengthening the competitiveness and attractiveness of tourism products, taking into account new world experiences, while relying on own innovations and pre-accession EU funds. This aspect was the starting point for the development of these research and the aim of the authors was to point out one of the ways to use the excess labor force in the tourism sector, how to develop rural tourism and how to use the European funds for the development of regional tourism in the region of Vojvodina.

In the numerical integration of the Landau-Lifshitz-Gilbert (LLG) equation, stiffness (stability restrictions on the time step size for explicit methods) is known to be a problem in some cases. We examine the relationship between stiffness and spatial discretization size for the LLG with exchange and magnetostatic effective fields. A maximum stable time step is found for the reversal of a single-domain spherical nanoparticle with a variety of magnetic parameters and numerical methods. From the lack of stiffness when solving a physically equivalent ODE problem, we conclude that any stability restrictions in the partial differential equation case arise from the spatial discretization rather than the underlying physics. We find that the discretization-induced stiffness increases as the mesh is refined and the damping parameter is decreased. In addition, we find that the use of the FEM/BEM method for magnetostatic calculations increases the stiffness. Finally, we observe that the use of explicit magnetostatic calculations within an otherwise implicit time integration scheme (i.e. a semi-implicit scheme) does not cause stability issues.

We present a block preconditioner for the efficient solution of the linear systems that arise when employing Newton’s method to solve monolithically-coupled large-displacement fluid–structure interaction problems in which the update of the moving fluid mesh is performed by the equations of large-displacement elasticity. Following a theoretical analysis of the preconditioner, we propose an efficient implementation that yields a solver with near-optimal computational cost, in the sense that the time for the solution of the linear systems scales approximately linearly with the number of unknowns. We evaluate the performance of the preconditioner in selected two- and three-dimensional test problems.

For transport purposes a great amount of fossil fuels is exploited which represents the biggest threat to global warming and the realization of sustainable development concept. European Union is trying to implement and plan this concept on the entire European continent. In order to manage the sustainable development strategy, it is necessary to conduct an all-inclusive analysis of the current state and depending on the results, set some goals and define the activities that will make their realization possible. This research is based on the analysis of the waterway transport on Danube River and its aim is to point out the facts, based on which it will be possible to predict further directions of sustainable transport development on the most important waterway of Europe. The research indicates the basic rules of European politics of sustainable inland waterway development. The River Danube is considered to be the backbone of water transport in Europe. It connects, via Rhine – Main Canal, Western Europe and Rotterdam harbor with the Black Sea, that is with Russia and the East. The authors also analyze the data about the use of Danube waterway for transport of goods and people. This research covered a short description of Danube, the analysis of Danube fleet, the analysis of the amount of transported goods and number of transported people as well as the analysis of load and unload of goods in Danube harbors. The research covered these points in the period starting from the year of 1950. Based on the result analysis the authors arrived at a conclusion that the use of River Danube for waterway transport purposes is unsatisfactory and that as such cannot be sustained in long term. Also, the research points to the basic European initiatives and investment projects in the field of river transport which is in implementation stage. Considering the basic regulation documents and research results, the authors present an overview of measures and suggestions for efficient management conducted so far, development of a unique information system and promotion of Danube waterway, which will lead towards long-term sustainable development transport on Danube and so it will stimulate a stable and sustainable development of all countries and regions in Europe.

We outline a new class of robust and efficient methods for solving the Navier-Stokes equations with a Boussinesq model for buoyancy driven flow. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters.

The research is done in order to describe student’s attitudes on volunteering in sport. The sample consists of 231 students from Serbia, average age 21,06±3,12years. They were from eight colleges and faculties. For nominal and ordinal variables, frequencies were determined. Many of examined students have volunteering experiences. The results confirm that students believe that we live in a society which his generally thought only to its own benefit; they think that volunteering can not solve the problems in society; that people do not have enough experience with volunteering and people do not have time to volunteering; volunteering is for young people; in their family and among friends, there are no volunteers; everyone could be volunteer only if that wishes; do not believe that volunteering is a waste of time and it helps in future career. The prevalent number of students, regardless of the Faculty which they belong, rarely volunteered in areas outside of sport. Results also shows that students from sport faculties have less experience in volunteering in sport than students from other faculties, but this difference is not dramatic.

Algebraic multigrid (AMG) is one of the most effective iterative methods for the solution of large, sparse linear systems obtained from the discretization of second-order scalar elliptic self-adjoint partial differential equations. It can also be used as a preconditioner for Krylov subspace methods. In this communication, we report on the design and development of a robust, effective and portable Fortran 95 implementation of the classical Ruge–Stuben AMG, which is available as package HSL_MI20 within the HSL mathematical software library. The routine can be used as a ‘black-box’ preconditioner, but it also offers the user a range of options and parameters. Proper tuning of these parameters for a particular application can significantly enhance the performance of an AMG-preconditioned Krylov solver. This is illustrated using a number of examples arising in the unstructured finite element discretization of the diffusion, the convection–diffusion, and the Stokes equations, as well as transient thermal convection problems associated with the Boussinesq approximation of the Navier–Stokes equations in 3D. Copyright © 2009 John Wiley & Sons, Ltd.

Numerical simulation of deformable objects is an important problem in biomechanical engineering and computational science. A significant class of problems in this area requires that the simulation results are presented both haptically and graphically in real time (an example being a medical training simulator based on virtual reality). In such cases various types of trade-offs between accuracy and efficiency are implemented. Numerical procedures for modelling deformable objects, with respect to their efficiency, mainly belong to the following two classes: interactive methods (that are fast but have moderate accuracy), and continuum mechanics based methods (that are accurate, but generally not fully interactive). In this paper we present a numerical method based on oriented splines for the numerical simulation of semi-deformable tubes. The numerical results demonstrate both the accuracy and the interactivity of the proposed method, making it a suitable component of complex systems for interactive virtual reality simulations of biomechanical systems.

We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditioned systems having an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. Numerical results show that the performance of the methodology is competitive with that of specialized fast iteration methods that have been developed in the context of biharmonic problems.

We examine the convergence characteristics and performance of parallelised Krylov subspace solvers applied to the linear algebraic systems that arise from low-order mixed finite element approximation of the biharmonic problem. Our strategy results in preconditioned systems that have nearly optimal eigenvalue distribution, which consists of a tightly clustered set together with a small number of outliers. We implement the preconditioner operator in a “black-box” fashion using publicly available parallelised sparse direct solvers and multigrid solvers for the discrete Dirichlet Laplacian. We present convergence and timing results that demonstrate efficiency and scalability of our strategy when implemented on contemporary computer architectures.

A preconditioning methodology for an iterative solution of discrete stress analysis problems based on a space decomposition and subspace correction framework is analysed in this paper. The principle idea of our approach is a decomposition of a global discrete system into the series of subproblems each of which correspond to the different Cartesian co-ordinates of the solution (displacement) vector. This enables us to treat the matrix subproblems in a segregated way. A host of well-established scalar solvers can be employed for the solution of subproblems. In this paper we constrain ourselves to an approximate solution using the scalar algebraic multigrid (AMG) solver, while the subspace correction is performed either in block diagonal (Jacobi) or block lower triangular (Gauss–Seidel) fashion. The preconditioning methodology is justified theoretically for the case of the block-diagonal preconditioner using Korn's inequality for estimating the ratio between the extremal eigenvalues of a preconditioned matrix. The effectiveness of the AMG-based preconditioner is tested on stress analysis 3D model problems that arise in microfabrication technology. The numerical results, which are in accordance with theoretical predictions, clearly demonstrate the superiority of a component decomposition AMG preconditioner over the standard ILU preconditioner, even for the problems with a relatively small number of degrees of freedom. Copyright © 2002 John Wiley & Sons, Ltd.

A methodology for preconditioning discrete stress analysis systems using robust scalar algebraic multigrid (AMG) solvers is evaluated in the context of problems that arise in microfabrication technology. The principle idea is to apply an AMG solver in a segregated way to the series of scalar block matrix problems corresponding to different displacement vector components, thus yielding a block diagonal AMG preconditioner. We study the component-wise AMG preconditioning in the context of the space decomposition and subspace correction framework [1]. The subspace problems are solved approximately by the scalar AMG solver and the subspace correction is performed either in block diagonal (block Jacobi) or lower triangular (block Gauss–Seidel) fashion. In our test examples we use fully unstructured grids of different sizes. The numerical experiments show robust and efficient convergence of the Krylov iterative methods with component-wise AMG preconditioning for both 2D and 3D problems. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper we present an efficient, accurate and parallelizable direct method for the solution of the (indefinite) linear algebraic systems that arise in the solution of fourth-order partial differential equations (PDEs) using mixed finite element approximations. The method is intended particularly for use when multiple right-hand sides occur, and when high accuracy is required in these solutions. The algorithm is described in some detail and its performance is illustrated through the numerical solution of a biharmonic eigenvalue problem where the smallest eigenpair is approximated using inverse iteration after discretization via the Ciarlet–Raviart mixed finite element method.

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre–Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite–element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite–element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non–convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator.

Razvoj informacionih tehnologija danas dovodi do kontradiktornosti u poslovnoj filozofiji koja se suocava sa dva suprotna procesa, globalizacijom i individualizacijom. Rast tržista, raznolikost potrosaca i heterogenost njihovih potreba i želja predstavlja stalan izazov za proizvođace, kao i konstantnu potrebu za kreiranjem novog tržisnog nastupa.Razvoj informacionih tehnologija (IT) je omogucio stvaranje softvera, koji podržavaju proces kreiranja proizvoda po željama kupaca preko Interneta. Pomocu modula, koji kupci sami biraju, ovi softveri komponuju proizvod koji je korisnik zamislio. Ovakav oblik masovne kastomizacije se zove ekastomizacija i podrazumeva da je barem jedan od tri elementasubjekti na tržistu, proizvod ili proces, digitalan. Rezultati istraživanja ovoga rada govore o prednosti i manama implementiranja modela masovne kastomizacije na domacem tržistu kao i mogucnostima interneta u implementaciji masovne kastimerizacije.

SUMMARY We present a numerical method for the monolithic discretisation of the Boussinesq system in three spatial dimensions. The key ingredients of the proposed methodology are the finite element discretisation of the spatial part of the problem using unstructured tetrahedral meshes, an implicit time integrator, based on adaptive predictor–corrector scheme (the explicit second-order Adams–Bashforth method with the implicit stabilised trapezoid rule), and a new preconditioned Krylov subspace solver for the resulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh–Benard convection. Copyright © 2013 John Wiley & Sons, Ltd.

The Navier-Stokes equations represent a mathematical model of incompressible fluid flow. To obtain a unique solution, these need to be supplemented by a physically relevant set of boundary conditions (BCs). These BCs, such as natural outflow, no-slip, no-penetration, can be easily imposed within the finite element setting in the case of straight boundaries that are aligned with the Cartesian axes. When more general domains are considered, as in many realistic industrial applications, one practical way of imposing BCs is with Lagrange multipliers. This procedure leads to an augmented linear system at the discrete level. In this paper we discuss efficient preconditioning of such systems.

A partitioning algorithm for solving tridiagonal system of linear equations which is suitable for implementation on multiprocessor systems with small to moderate number of processors is described in this paper. The method is based on decomposing a matrix of order n×n into p partitions of size n×k, where n=pk. The fundamental idea of the proposed algorithm is that the elimination is performed using alternatively superdiagonal and subdiagonal elements, contrary to the Gaussian elimination which uses main diagonal elements. Performance results obtained when the proposed algorithm is implemented on the p-processor orthogonal and linear arrays, both of MIMD type, are presented.

The finite-element-based solution of partial differential equations often requires the solution of large systems of linear equations. Krylov subspace methods are efficient solvers when combined with effective preconditioners. We consider block preconditioners that are applicable to problems that have different types of degree of freedom (e.g., velocity and pressure in a fluid simulation). We discuss the development of an object-oriented parallel block preconditioning framework within oomph-lib, the object-oriented, multi-physics, finite-element library, available as open-source software at http://www.oomph-lib.org. We demonstrate the performance of this framework for problems from non-linear elasticity, fluid mechanics, and fluid-structure interaction.

A fast and efficient parallel algorithm for tridiagonal matrix inversion is presented. The algorithm is based on partitioning and reordering the initial tridiagonal matrix which allows us to parallelize it efficiently. The algorithm is implemented on a linear processor array. For interprocessor communication we consider three types of network components: dual-port RAM, FIFO RAM and a router. We derive the performances of the algorithm and the system which relates to the number of calculation steps, speedup and efficiency. The obtained results show that the method is highly valuable.