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Purpose — The purpose of this paper is to seek improved solution techniques for combined boundary‐initial value problems (IVPs) associated with the time‐dependent creep deformation and rupture of engineering structures at high temperatures and hence to reconfigure a parallel iterative preconditioned conjugate gradient (PCG) solver and the DAMAGE XXX software, for 3‐D finite element creep continuum damage mechanics (CDM) analysis.Design/methodology/approach — The potential to speed up the computer numerical solution of the combined BV‐IVPs is addressed using parallel computers. Since the computational bottleneck is associated with the matrix solver, the parallelisation of a direct and an iterative solver has been studied. The creep deformation and rupture of a tension bar has been computed for a range of the number of degrees of freedom (ndf), and the performance of the two solvers is compared and assessed.Findings — The results show the superior scalability of the iterative solver compared to the direct solver, with larger speed‐ups gained by the PCG solver for higher degrees of freedom. Also, a new algorithm for the first trial solution of the PCG solver provides additional speed‐ups.Research limitations/implications — The results show that the ideal parallel speed‐up of the iterative solver of 16, relative to two processors, is achieved when using 32 processors for a mesh of ndf = 153,238. Originality/value — Techniques have been established in this paper for the parallelisation of CDM creep analysis software using an iterative equation solver. The significant computational speed‐ups achieved will enable the analysis of failures in weldments of industrial significance.

Presents a direct solution method for the determination of the capacitance, conductance or inductance of static linear problems with the dual finite element method. The direct solution method provides an entirely energy‐based method for the calculation of these global parameters and differs from the conventional solution techniques in that no recourse is required to the intermediate determination of the potential distribution. The direct solution method can be seen as the reduction of a dual circuit parameter network for the finite element representation. Compares the dual‐circuit parameter description with another, well‐known variational method called “Tubes and Slices”. Shows that by aligning the finite element mesh with the approximate positions of the equipotentials and flux lines in the system, the dual finite element model can be simplified to the equivalent of Tubes and Slices model and that both methods can produce exactly the same results.

Presents a direct solution method for the determination of quantities such as capacitance, conductance and inductance from the finite element representation of electrostatic and magnetostatic problems. The method can be used to complement existing finite element software which utilizes a field approach, or can be used for determining such quantities without the requirement for intermediate determination of a potential distribution within the system. Expresses the quantities in terms of parameters which depend only on the materials used in the system and their geometric distribution. In multi‐electrode systems, the direct method allows for the determination of the entire capacitance, inductance or conductance matrix in a single factorization process, without the need for the repeated numerical determination and evaluation of the potential distribution for each electrode in turn. The direct solutions for capacitance and inductance can be used to derive expressions for the forces and torques within the system, using the principle of virtual work.

The purpose of this study is to target the solution of nonlinear porous fin problem. In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

This study uses a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

Explicit closed-form formulae for the fin tip temperature as well as for the heat transfer rate, hence for the fin efficiency, which are functions of the porosity parameter and Biot number, are provided. The thresholds and the convergence regions regarding the physical parameters of the resulting approximations are easy to determine from the residual formula.

The novelty of the method is that the accuracy of the solution is controllable and can be gained up to any significant digit of desire by increasing the number of terms in the series solution.

A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear analysis of 3D reinforced concrete structures. Examples highlight the dramatic savings in computer storage and more modest savings in solution times obtained using PCG especially for large problems.

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its solution procedure. This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue. Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE.

This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent. The proposed approach is validated and assessed by a comparative study.

This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation).

The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems.

The general problem of sizing, material and loading parameter sensitivity of non‐linear systems is presented. Both kinematic and path‐dependent material non‐linearities are considered; non‐linear sensitivity path is traced by an incremental solution strategy. The variational approach employed is quite general and can be employed for studying sensitivity of various path‐dependent highly non‐linear phenomena. Both the direct differentiation method (DDM) and adjoint system method (ASM) are discussed in the context of continuum and finite element mechanics. The merits of using the consistent tangent matrix and the necessity of accumulation of design derivatives of stresses and internal parameters are indicated. Aspects of sensitivity problems in metal forming are also discussed. A number of examples illustrate the paper.

To present a new direct solution method for the Boltzmann‐Poisson system for simulating one‐dimensional semiconductor devices.

A combination of finite difference and finite element methods is applied to deal with the differential operators in the Boltzmann transport equation. By taking advantage of a piecewise polynomial approximation of the electron distribution function, the collision operator can be treated without further simplifications. The finite difference method is formulated as a third order WENO approach for non‐uniform grids.

Comparisons with other methods for a well‐investigated test case reveal that the new method allows faster simulations of devices without losing physical information. It is shown that the presented model provides a better convergence behaviour with respect to the applied grid size than the Minmod scheme of the same order.

The presented direct solution methods provide an easily extensible base for other simulations in 1D or 2D. By modifying the boundary conditions, the simulation of metal‐semiconductor junctions becomes possible. By applying a dimension by dimension approximation models for two‐dimensional devices can be obtained.

The new model is an efficient tool to acquire transport coefficients or current‐voltage characteristics of 1D semiconductor devices due to short computation times.

New grounds have been broken by directly solving the Boltzmann equation based on a combination of finite difference and finite elements methods. This approach allows us to equip the model with the advantages of both methods. The finite element method assures macroscopic balance equations, while the WENO approximation is well‐suited to deal with steep gradients due to the doping profiles. Consequently, the presented model is a good choice for the fast and accurate simulation of one‐dimensional semiconductor devices.

The purpose of this paper is to describe an inverse approach to estimate the pressure distribution, temperature distribution, and pressure‐viscosity index (z) in a thermal elastohydrodynamic lubrication (TEHL) line contact.

Once the film thickness is given, the pressure distribution can be calculated using the inverse approach. Subsequently, thermal expansivity and temperature‐viscosity coefficient of lubricant are given, and then the z is guessed initially. The Gauss‐Seidel iteration is employed to calculate the temperature distribution from the rheology, energy, and surface temperature equations. In order to increase the algorithm stability, the least‐squares method must be employed to calculate the optimum value of the z in the computational domain. Furthermore, the pressure‐viscosity index must be updated by the iteration method to calculate accurate temperature distribution and apparent viscosity until convergence.

This approach presents a smooth curve of the pressure and temperature distributions with the measurement error from the resolution in the film thickness measurement and z value. Furthermore, this approach still provides a superior solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.

The paper describes an inverse approach to estimate the pressure distribution, temperature distribution, and pressure‐viscosity index in a TEHL line contact. This approach overcomes the problems of pressure and temperature rise fluctuations and generates accurate results of pressure and temperature distribution from a small number of measured points of film thickness, which also saves computing time. Furthermore, this approach still provides a superior solution in apparent viscosity.