Search results

The purpose of this paper is to deal with the study of free convection magnetohydrodynamic (MHD) boundary layer flow of an incompressible viscoelastic fluid along an inclined moving plate and heat transfer characteristics with prescribed quadratic power-law surface temperature.

The governing partial differential equations are transformed into non-dimensional, non-linear coupled ordinary differential equations which are solved numerically by robust Galerkin finite element method.

Numerical results for the dimensionless velocity and temperature profiles are displayed graphically for various physical parameters such as viscoelasticity, Prandtl number, angle of inclination parameter, magnetic and buoyancy parameter. The local Nusselt number is found to be the decreasing function of magnetic field parameter whereas it increases with increasing values of Prandtl number, viscoelastic parameter and buoyancy parameter.

The present problem finds significant applications in MHD power generators, cooling of nuclear reactors, thin film solar energy collector devices.

The objective of this work is to analyze the heat transfer of convective MHD viscoelastic fluid along a moving inclined plate with quadratic power law surface temperature. An extensively validated, highly efficient, variation finite element code is used to study this problem. The results are validated and demonstrated graphically.

The purpose of this paper is to put forward the lubrication model of oil bearing and enrich the design theory under the condition of mixed lubrication.

A mixed lubrication model of bilayer porous bearing is established. The effects of the working conditions on the lubrication performance and seepage behavior were analyzed.

Results show that the oil film pressure mainly occurs in the bearing convergence zone and contact pressure mainly occurs near the minimum film thickness. The oil infiltrates into the porous matrix in the contact area and precipitates out to the friction surface at the inlet of the contact area. The oil seepage velocity and dynamic pressure effect at the friction interface can be improved by reasonably matching the load and speed. With the decrease of the external load or increase of the rotating speed, the lubrication performance becomes well.

This study provides a reference for the design and application of oil bearing under harsh working conditions.

The purpose of this paper is to introduce a new method called simultaneous elimination and back-substitution method (SEBSM) to solve a system of linear equations as a new finite element method (FEM) solver.

In this paper, a new technique assembling the global stiffness matrix will be proposed and meanwhile the direct method SEBSM will be applied to solve the equations formed in FEM.

The SEBSM solver for FEM with the present assembling technique has distinct advantages in both computational time and memory space occupation over the conventional methods, such as the Gauss elimination and LU decomposition methods.

The developed solver requires less memory space no matter the coefficient matrix is a typical sparse matrix or not, and it is applicable to both symmetric and unsymmetrical linear systems of equations. The processes of assembling matrix and dealing with constraints are straightforward, so it is convenient for coding. Compared to the previous solvers, the proposed solver has favorable universality and good performances.

The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.

In first step, time derivative is discretised by forward difference method. Then, quasi-linearisation process is used to tackle the non-linearity in the equation. Finally, fully discretisation by differential quadrature method (DQM) leads to a system of linear equations which is solved by Gauss-elimination method.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than (Dehghan and Shokri, 2009; Pekmen and Tezer-Sezgin, 2012) by choosing less number of grid points and big time step length. Also, the scheme can be extended for multidimensional problems.

The Lanczos method with the Golub and Kahan bidiagonalization algorithm is used to solve non‐symmetric diagonal dominant simultaneous equations. The method is very suitable for sparse matrix and vector computer. The problem with loss of orthogonal property is dealt with by restating the iteration. Numerical examples together with FORTRAN 77 routine are given to illustrate the algorithm. Both scalar and vector CPU times are given for comparison.

Based on a lumped mass model and an incremental iteration method, an efficient simultaneous iteration procedure is developed for the finite element solution of the enthalpy model. This procedure uses Gauss elimination to solve the resulting algebraic equation system. A one‐point quadrature program based on the isoparametric quadrilateral element is incorporated for the calculation of the heat conductance matrix, leading to a significant reduction of the computation time.

During the revolution in the field of engineering which is based on the use of computers and numerical methods of calculation, an evolution has emerged. This concerns the development of desktop computers and finite element software suited for the small and cheap machines. By that it became possible to utilize this highly effective tool with only low investments necessary. Described are the way to and the characteristics of such a software package, consisting of a preprocessor, a temperature field analysis part, a linear‐elastic rigidity calculation part, a non‐linear elastic—plastic structural analysis part and a postprocessor.

To provide an analysis of transient heat conduction, which is solved using different iterative solvers for graduate and postgraduate students (researchers) which can help them develop their own research.

Three‐dimensional transient heat conduction in homogeneous materials using different time‐stepping methods such as finite difference (Θ explicit, implicit and Crank‐Nicolson) and finite element (weighted residual and least squared) methods. Iterative solvers used in the paper are conjugate gradient (CG), preconditioned gradient, least square CG, conjugate gradient squared (CGS), preconditioned CGS, bi‐conjugate gradient (BCG), preconditioned BCG, bi‐conjugate gradient stabilized (BCGSTAB), reconditioned BCGSTAB and Gaussian elimination with incomplete Cholesky factorization.

Provides information on which time‐stepping method is the most accurate, which solver is the fastest to solve a symmetric and positive system of linear matrix equations of all those considered.

Fortran 90 code given as an abstract can be very useful for graduate and postgraduate students to develop their own code.

This paper offers practical help to an individual starting his/her research in the finite element technique and numerical methods.

With the availability of powerful personal computers (PCs), workstations and networking devices, the recent trend in parallel computing is to connect a number of individual workstations (PC and PC symmetric multiprocessor systems (SMP)) to solve computation‐intensive tasks in parallel way on such clusters (networks of workstations (NOW), SMP and Grid). In this sense, it is not more true to consider traditionally evolved parallel computing and distributed computing as two separate research disciplines. Current trends in high performance computing are to use NOW (and SMP) as a cheaper alternative to traditionally used massively parallel multiprocessors or supercomputers and to profit from unifying of both mentioned disciplines. The purpose of this paper is to consider the individual workstations could be so single PC as parallel computers based on modern SMP implemented within workstation.

Such parallel systems (NOW and SMP), are connected through widely used communication standard networks and co‐operate to solve one large problem. Each workstation is threatened similarly to a processing element as in a conventional multiprocessor system. But, personal processors or multiprocessors as workstations are far more powerful and flexible than the processing elements in conventional multiprocessors. To make the whole system appear to the applications as a single parallel computing engine (a virtual parallel system), run‐time environments such as OpenMP, Java (SMP), message passing interface, Java (NOW) are used to provide an extra layer of abstraction.

To exploit the parallel processing capability of such cluster, the application program must be paralleled. The effective way how to do it for (parallelisation strategy) belongs to a most important step in developing effective parallel algorithm (optimisation). To behaviour analysis, all overheads that have the influence to performance of parallel algorithms (architecture, computation, communication, etc.) have to be taken into account. In this paper, such complex performance evaluation of iterative parallel algorithms (IPA) and their practical implementations are discussed (Jacobi and Gauss‐Seidel iteration). On real application example, the various influences in process of modelling and performance evaluation and the consequences of their distributed parallel implementations are demonstrated.

The paper usefully shows that better load balancing can be achieved among used network nodes (performance optimisation of parallel algorithm). Generally, it claims that the parallel algorithms or their parts (processes) with more communication (similar to analyzed Gauss‐Seidel parallel algorithm) will have better speed‐up values using modern SMP parallel system as its parallel implementation in NOW. For the algorithms or processes with small communication overheads (similar to analysed Jacobi parallel algorithm) the other network nodes can be used based on single processors.

The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling.

Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage.

When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced.

Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem.

A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core.

More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method.

Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.