Search results for: finite segment method.

Authors: Aaron Aboshio, Jianqioa Ye

Abstract:

In this study, static and dynamic responses of a typical reinforced concrete solid slab, designed to British Standard (BS 8110: 1997) and under self and live loadings for dance halls are reported. Linear perturbation analysis using finite element method was employed for modal, impulse loading and frequency response analyses of the slab under the aforementioned loading condition. Results from the static and dynamic analyses, comprising of the slab fundamental frequencies and mode shapes, dynamic amplification factor, maximum deflection, stress distributions among other valuable outcomes are presented and discussed. These were gauged with the limiting provisions in the design code with a view of justifying valid optimization objective function for the structure that can ensure both adequate strength and economical section for large clear span slabs. This is necessary owing to the continued increase in cost of erecting building structures and the squeeze on public finance globally.

Keywords: Economical design, Finite element method, Modal dynamics, Reinforced concrete, Slab.

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Authors: Esmaeil Asadzadeh, Mehtab Alam

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Progressive collapse of the layered hyperbolic tower shells are studied considering the influences of changes in the supporting columns’ types and angles. 3-D time history analyses employing the finite element method are performed for the towers supported with I-type and ᴧ-type column. It is found that the inclination angle of the supporting columns is a very important parameter in optimization and safe design of the cooling towers against the progressive collapse. It is also concluded that use of Demand Capacity Ratio (DCR) criteria of the linear elastic approach recommended by GSA is un-conservative for the hyperbolic tower shells.

Keywords: Progressive collapse, cooling towers, finite element analysis, crack generation, reinforced concrete.

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: Coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method.

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Authors: Guang Zeng, Jin Huang, Zicai Li

Abstract:

In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

Keywords: Finite-difference equation, computational stability, hirt method.

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Authors: S. Lecheb, A. Nour, A. Chellil, A. Basta, D. Belmiloud, H. Kebi

Abstract:

In recent years, a new numerical method has been developed, the extended finite element method (X-FEM). The objective of this work is to exploit the (X-FEM) for the treatment of the fracture mechanics problems on 3D geometries, where we showed the ability of this method to simulate the fatigue crack growth into two cases: edge and central crack. In the results we compared the six first natural frequencies of mode shapes uncracking with the cracking initiation in the structure, and showed the stress intensity factor (SIF) evolution function as crack size propagation into structure, the analytical validation of (SIF) is presented. For to evidence the aspects of this method, all result is compared between FEA and X-FEM.

Keywords: 3D fatigue crack growth, FEA, natural frequencies, stress intensity factor (SIF), X-FEM.

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Authors: P. Zamani, S. Mohajerzadeh, R. Masoudinejad, Kh. Farhangdoost

Abstract:

Riveting process is one of the important ways to keep fastening the lap joints in aircraft structures. Failure of aircraft lap joints directly depends on the stress field in the joint. An important application of riveting process is in the construction of aircraft fuselage structures. In this paper, a 3D finite element method is carried out in order to optimize residual stress field in a riveted lap joint and also to estimate its fatigue life. In continue, a number of experiments are designed and analyzed using design of experiments (DOE). Then, Taguchi method is used to select an optimized case between different levels of each factor. Besides that, the factor which affects the most on residual stress field is investigated. Such optimized case provides the maximum residual stress field. Fatigue life of the optimized joint is estimated by Paris-Erdogan law. Stress intensity factors (SIFs) are calculated using both finite element analysis and experimental formula. In addition, the effect of residual stress field, geometry and secondary bending are considered in SIF calculation. A good agreement is found between results of such methods. Comparison between optimized fatigue life and fatigue life of other joints has shown an improvement in the joint’s life.

Keywords: Fatigue life, Residual stress, Riveting process, Stress intensity factor, Taguchi method.

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Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands.

The DTC of SRM is analyzed by two methods. In one method, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: Direct Toque Control, Simplified Torque Equation, Finite Element Analysis, Torque Ripple.

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Authors: Marcelo Hayashi, João Lima, Bruno Chieregatti, Ernani Volpe

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The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation.

Keywords: Adjoint method, optimisation, non–geometric sensitivities, boundary conditions.

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Authors: Indu Saini, Phool Singh, Vikas Malik

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A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Genetic Algorithm is used to calculate shooting angle. The initial value problems arisen during shooting are computed by Runge-Kutta Fehlberg method. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors.

Keywords: Boundary Layer Flow, Falkner–Skan equation, Genetic Algorithm, Shooting method.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: S. M. Abdur Razzak, M. A. Rashid, Y. Namihira, A. Sayeem

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A simple microstructure optical fiber design based on an octagonal cladding structure is presented for simultaneously controlling dispersion and leakage properties. The finite difference method with anisotropic perfectly matched boundary layer is used to investigate the guiding properties. It is demonstrated that octagonal photonic crystal fibers with four rings can assume negative ultra-flattened dispersion of -19 + 0.23 ps/nm/km in the wavelength range of 1.275 μm to 1.68 μm, nearly zero ultra-flattened dispersion of 0 ± 0.40 ps/nm/km in a 1.38 to 1.64 μm, and low confinement losses less than 10-3 dB/km in the entire band of interest.

Keywords: Finite difference modeling, group velocity dispersion, optical fiber design, photonic crystal fiber.

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Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.

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Authors: Brajesh Kumar Jha, Neeru Adlakha, M. N. Mehta

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Calcium [Ca2+] is an important second messenger which plays an important role in signal transduction. There are several parameters that affect its concentration profile like buffer source etc. The effect of stationary immobile buffer on Ca2+ concentration has been incorporated which is a very important parameter needed to be taken into account in order to make the model more realistic. Interdependence of all the important parameters like diffusion coefficient and influx over [Ca2+] profile has been studied. Model is developed in the form of advection diffusion equation together with buffer concentration. A program has been developed using finite volume method for the entire problem and simulated on an AMD-Turion 32-bit machine to compute the numerical results.

Keywords: Ca2+ profile, buffer, Astrocytes, Advection diffusion, FVM

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Authors: Majid Mirzaei, Saeid Samiezadeh , Abbas Khodadadi, Mohammad R. Ghazavi

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This paper presents a novel method for prediction of the mechanical behavior of proximal femur using the general framework of the quantitative computed tomography (QCT)-based finite element Analysis (FEA). A systematic imaging and modeling procedure was developed for reliable correspondence between the QCT-based FEA and the in-vitro mechanical testing. A speciallydesigned holding frame was used to define and maintain a unique geometrical reference system during the analysis and testing. The QCT images were directly converted into voxel-based 3D finite element models for linear and nonlinear analyses. The equivalent plastic strain and the strain energy density measures were used to identify the critical elements and predict the failure patterns. The samples were destructively tested using a specially-designed gripping fixture (with five degrees of freedom) mounted within a universal mechanical testing machine. Very good agreements were found between the experimental and the predicted failure patterns and the associated load levels.

Keywords: Bone, Osteoporosis, Noninvasive methods, Failure Analysis

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Kimia Khoshdel Vajari, Saber Saffar

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Reducing the residual stresses caused by welding is desirable for the industry. The effect of welding sequence, as well as the effect of yield stress on the number of residual stresses generated in Inconel X750 superalloy sheets and beams, have been investigated. The finite element model used in this research is a three-dimensional thermal and mechanical model, and the type of analysis is indirect coupling. This analysis is done in two stages. First, thermal analysis is performed, and then the thermal changes of the first analysis are used as the applied load in the second analysis. ABAQUS has been used for modeling, and the Dflux subroutine has been used in the Fortran programming environment to move the arc and the molten pool. The results of this study show that the amount of tensile residual stress in symmetric, discontinuous, and symmetric-discontinuous welds is reduced to a maximum of 27%, 54%, and 37% compared to direct welding, respectively. The results also show that the amount of residual stresses created by welding increases linearly with increasing yield stress with a slope of 40%.

Keywords: Residual stress, X750 superalloy, finite element, welding, thermal analysis.

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Authors: Liu Ying-jie, Lu Wen-bo, Peng Cheng-jian

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With the development of the automotive technology and electric vehicle, the contribution of the wind noise on the interior noise becomes the main source of noise. The main transfer path which the exterior excitation is transmitted through is the greenhouse panels and side windows. Simulating the wind noise transmitted into the vehicle accurately in the early development stage can be very challenging. The basic methodologies of this study were based on the Lighthill analogy; the exterior flow field around a passenger car was computed using unsteady Computational Fluid Dynamics (CFD) firstly and then a Finite Element Method (FEM) was used to compute the interior acoustic response. The major findings of this study include: 1) The Sound Pressure Level (SPL) response at driver’s ear locations is mainly induced by the turbulence pressure fluctuation; 2) Peaks were found over the full frequency range. It is found that the methodology used in this study could predict the interior wind noise induced by the exterior aerodynamic excitation in industry.

Keywords: Wind noise, computational fluid dynamics, finite element method, passenger car.

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Authors: Zhengyi Kong, Seung-Eock Kim

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Single angle connections, which are bolted to the beam web and the column flange, are studied to investigate their moment-rotation behavior. Elastic–perfectly plastic material behavior is assumed. ABAQUS software is used to analyze the nonlinear behavior of a single angle connection. The identical geometric and material conditions with Lipson’s test are used for verifying finite element models. Since Kishi and Chen’s Power model and Lee and Moon’s Log model are accurate only for a limited range of mechanism, simpler and more accurate hyperbolic function models are proposed.

Keywords: Single-web angle connections, finite element method, moment and rotation, hyperbolic function models.

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Authors: R. Haoui

Abstract:

The aim of this work is to determine the supersonic nozzle profiles used in propulsion, for the launchers or embarked with the satellites. This design has as a role firstly, to give a important propulsion, i.e. with uniform and parallel flow at exit, secondly to find a short length profiles without modification of the flow in the nozzle. The first elaborate program is used to determine the profile of divergent by using the characteristics method for an axisymmetric flow. The second program is conceived by using the finite volume method to determine and test the profile found connected to a convergent.

Keywords: Characteristic method, nozzles, supersonic flow, propellers.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

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In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves and circles.

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Authors: Bhaskar Thakker, Anoop Lal Vyas

Abstract:

Wrist pulse analysis for identification of health status is found in Ancient Indian as well as Chinese literature. The preprocessing of wrist pulse is necessary to remove outlier pulses and fluctuations prior to the analysis of pulse pressure signal. This paper discusses the identification of irregular pulses present in the pulse series and intricacies associated with the extraction of time domain pulse features. An approach of Dynamic Time Warping (DTW) has been utilized for the identification of outlier pulses in the wrist pulse series. The ambiguity present in the identification of pulse features is resolved with the help of first derivative of Ensemble Average of wrist pulse series. An algorithm for detecting tidal and dicrotic notch in individual wrist pulse segment is proposed.

Keywords: Wrist Pulse Segment, Ensemble Average, Dynamic Time Warping (DTW), Pulse Similarity Vector.

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Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

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This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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Authors: Monika Neda, Elena Nikonova

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We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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Authors: Bijit Kalita, K. V. N. Surendra

Abstract:

Rotating disk is one of the most indispensable parts of a rotating machine. Rotating disk has found many applications in the diverging field of science and technology. In this paper, we have taken into consideration the problem of a heavy spinning disk mounted on a rotor system acted upon by boundary traction. Finite element modelling is used at various loading condition to determine the mixed mode stress intensity factors. The effect of combined shear and normal traction on the boundary is incorporated in the analysis under the action of gravity. The variation near the crack tip is characterized in terms of the stress intensity factor (SIF) with an aim to find the SIF for a wide range of parameters. The results of the finite element analyses carried out on the compressed disk of a belt pulley arrangement using fracture mechanics concepts are shown. A total of hundred cases of the problem are solved for each of the variations in loading arc parameter and crack orientation using finite element models of the disc under compression. All models were prepared and analyzed for the uncracked disk, disk with a single crack at different orientation emanating from shaft hole as well as for a disc with pair of cracks emerging from the same center hole. Curves are plotted for various loading conditions. Finally, crack propagation paths are determined using kink angle concepts.

Keywords: Crack-tip deformations, static loading, stress concentration, stress intensity factor.

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: W. Lai, A. A. Khan

Abstract:

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Keywords: Discontinuous finite element, TVD Runge-Kuttascheme, slope limiters, Riemann solvers, shallow water flow.

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Authors: Masamitsu Chikaraishi, Mutsuto Kawahara

Abstract:

This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.

Keywords: Parameter identification, finite element method, average acceleration method, first order adjoint equation method, weighted gradient method, geological boundary, navier equation, optimal control theory.

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Authors: Thomas Rowan, Mohammed Seaid

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A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: Erosion, finite volume method, sediment transport, shallow water equations.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: N. Santatriniaina, J. Deseure, T.Q. Nguyen, H. Fontaine, C. Beitia, L. Rakotomanana

Abstract:

Nowadays, with the increasing of the wafer's size and the decreasing of critical size of integrated circuit manufacturing in modern high-tech, microelectronics industry needs a maximum attention to challenge the contamination control. The move to 300 [mm] is accompanied by the use of Front Opening Unified Pods for wafer and his storage. In these pods an airborne cross contamination may occur between wafers and the pods. A predictive approach using modeling and computational methods is very powerful method to understand and qualify the AMCs cross contamination processes. This work investigates the required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs. Numerical optimization and finite element formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. The least square distance between the model (analytical 1D solution) and the experimental data are minimized. The behavior of the AMCs intransient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. The methodology is applied, first using the optimization methods with analytical solution to define physical constants, and second using finite element method including adsorption kinetic and the switch of Dirichlet to Neumann condition.

Keywords: AMCs, FOUP, cross-contamination, adsorption, diffusion, numerical analysis, wafers, Dirichlet to Neumann, finite elements methods, Fick’s law, optimization.

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