N.R. ALURU, K.H. LAW, P.M. PINSKY and R.W. DUTTON
A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device…
Abstract
A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.
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…
Abstract
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.
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Luca Ballestra and Fausto Saleri
In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we…
Abstract
In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we consider the simulation of a one‐dimensional n+‐n ‐n+ diode, whose solution exhibits at low temperatures strong discontinuities, and investigate the effect of the momentum viscosity on the shock waves. Numerical experiments, performed also on a two‐dimensional test case, demonstrate that the numerical scheme, working on non‐uniform grids, is suitable to describe solutions with strong variations in time and space. Well‐posedness for the boundary conditions is discussed, and a linear stability estimate is established for the one‐dimensional n+‐n ‐n+ diode benchmark problem.
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Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower…
Abstract
Purpose
Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters.
Design/methodology/approach
The Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated.
Findings
To evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving.
Originality/value
This paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.
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Dongliang Qi, Dongdong Wang, Like Deng, Xiaolan Xu and Cheng-Tang Wu
Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack…
Abstract
Purpose
Although high-order smooth reproducing kernel mesh-free approximation enables the analysis of structural vibrations in an efficient collocation formulation, there is still a lack of systematic theoretical accuracy assessment for such approach. The purpose of this paper is to present a detailed accuracy analysis for the reproducing kernel mesh-free collocation method regarding structural vibrations.
Design/methodology/approach
Both second-order problems such as one-dimensional (1D) rod and two-dimensional (2D) membrane and fourth-order problems such as Euler–Bernoulli beam and Kirchhoff plate are considered. Staring from a generic equation of motion deduced from the reproducing kernel mesh-free collocation method, a frequency error measure is rationally attained through properly introducing the consistency conditions of reproducing kernel mesh-free shape functions.
Findings
This paper reveals that for the second-order structural vibration problems, the frequency accuracy orders are p and (p − 1) for even and odd degree basis functions; for the fourth-order structural vibration problems, the frequency accuracy orders are (p − 2) and (p − 3) for even and odd degree basis functions, respectively, where p denotes the degree of the basis function used in mesh-free approximation.
Originality/value
A frequency accuracy estimation is achieved for the reproducing kernel mesh-free collocation analysis of structural vibrations, which can effectively underpin the practical applications of this method.
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C. De Maria, L. Grassi, F. Vozzi, A. Ahluwalia and G. Vozzi
This paper aims to develop a novel micro-ablation system to realise micrometric and well-defined hydrogel structures. To engineer a tissue it is necessary to evaluate several…
Abstract
Purpose
This paper aims to develop a novel micro-ablation system to realise micrometric and well-defined hydrogel structures. To engineer a tissue it is necessary to evaluate several aspects, such as cell-cell and cell-substrate interactions, its micro-architecture and mechanical stimuli that act on it. For this reason, it is important to fabricate a substrate which presents a microtopology similar to natural tissue and has chemical and mechanical properties able to promote cell functions. In this paper, well-defined hydrogel structures embedding cells were microfabricated using a purposely developed technique, micro-laser ablation, based on a thulium laser. Its working parameters (laser power emission, stepper motor velocity) were optimised to produce shaded “serpentine” pattern on a hydrogel film.
Design/methodology/approach
In this study, initially, swelling/contraction tests on agarose and alginate hydrogel in different solutions of main components of cell culture medium were performed and were compared with the MECpH model. This comparison matched with good approximation experimental measurements. Once known how hydrogel changed its topology, microstructures with a well-defined topology were realised using a purposely developed micro-laser ablation system design. S5Y5 neuroblastoma cell lines were embedded in hydrogel matrix and the whole structure was ablated with a laser microfabrication system. The cells did not show damages due to mechanical stress present in the hydrogel matrix and to thermal increase induced by the laser beam.
Findings
The hydrogel structure is able to reproduce extracellular matrix. Initially, the hydrogel swelling/contraction in different solutions, containing the main components of the most common cell culture media, was analysed. This analysis is important to evaluate if cell culture environment could alter microtopology of realised structures. Then, the same topology was realised on hydrogel film embedding neuronal cells and the cells did not show damages due to mechanical stress present in the hydrogel matrix and to thermal increase induced by the laser beam. The interesting obtained results could be useful to realise well-defined microfabricated hydrogel structures embedding cells to guide tissue formation
Originality/value
The originality of this paper is the design and realisation of a 3D microfabrication system able to microfabricate hydrogel matrix embedding cells without inducing cell damage. The ease of use of this system and its potential modularity render this system a novel potential device for application in tissue engineering and regenerative medicine area.
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Pietro Marco Congedo, Gianluca Geraci, Rémi Abgrall, Valentino Pediroda and Lucia Parussini
– This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.
Abstract
Purpose
This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.
Design/methodology/approach
ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows.
Findings
First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1−T¯ TSI)×100, where T¯ TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy.
Originality/value
Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.
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Arman Shojaei, Bijan Boroomand and Farshid Mossaiby
The purpose of this paper is to present a simple meshless solution method for challenging engineering problems such as those with high wave numbers or convection-diffusion ones…
Abstract
Purpose
The purpose of this paper is to present a simple meshless solution method for challenging engineering problems such as those with high wave numbers or convection-diffusion ones with high Peclet number. The method uses a set of residual-free bases in a local form.
Design/methodology/approach
The residual-free bases, called here as exponential basis functions, are found so that they satisfy the governing equations within each subdomain. The compatibility between the subdomains is weakly satisfied by enforcing the local approximation of the main state variables pass through the data at nodes surrounding the central node of the subdomain. The central state variable is first recovered from the approximation and then re-assigned to the central node to construct the associated equation. This leads to the least compatibility required in the solution, e.g. C0 continuity in Laplace problems.
Findings
The authors shall show that one can solve a variety of problems with regular and irregular point distribution with high convergence rate. The authors demonstrate that this is impossible to achieve using finite element method. Problems with Laplace and Helmholtz operators as well as elasto-static problems are solved to demonstrate the effectiveness of the method. A convection-diffusion problem with high Peclet number and problems with high wave numbers are among the examples. In all cases, results with high rate of convergence are obtained with moderate number of nodes per cloud.
Originality/value
The paper presents a simple meshless method which not only is capable of solving a variety of challenging engineering problems but also yields results with high convergence rate.
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Qingdong Zhang, Boyang Zhang and Xingfu Lu
The purpose of this paper is to propose a hybridization numerical method to solve the plastic deformation of metal working based on the flow function method and meshless method…
Abstract
Purpose
The purpose of this paper is to propose a hybridization numerical method to solve the plastic deformation of metal working based on the flow function method and meshless method.
Design/methodology/approach
The proposed method is named as flow function-element free Galerkin (F-EFG) method. It uses the flow function as the basic unknown quantity to get the basic control equation, the compactly supported approximate function to establish a local approximate flow function by means of moving least square approximation, and the element free Galerkin (EFG) method to solve variational equation. The F-EFG method takes the upper limit method essence of flow function method, and the convergence, stability, and error characteristics of EFG method.
Findings
The steady extrusion process of the axisymmetric extrusion problems as well as the extrusion deformation law and main field variables are subjects in the modeling and simulation analysis using F-EFG method. The results show that the F-EFG method has good computational efficiency and accuracy.
Originality/value
The F-EFG method proposed in this paper has the advantages of high-solution precision of flow function method and large deformation solution of element free method. It overcomes the difficulties in global flow function establishment in flow function method and low-solution efficiency in element free method. The method is beneficial to the development of flow function method and element free method.
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The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.
Abstract
Purpose
The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.
Design/methodology/approach
The numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.
Findings
This model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.
Research limitations/implications
Bearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).
Practical implications
A sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.
Originality/value
The formulation being presented is competitive and could be considered as a potential alternative to other approaches.