Search results for: Lax Pair Equation

Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

It has been shown that a load discontinuity at the end of an impulse will result in an extra impulse and hence an extra amplitude distortion if a step-by-step integration method is employed to yield the shock response. In order to overcome this difficulty, three remedies are proposed to reduce the extra amplitude distortion. The first remedy is to solve the momentum equation of motion instead of the force equation of motion in the step-by-step solution of the shock response, where an external momentum is used in the solution of the momentum equation of motion. Since the external momentum is a resultant of the time integration of external force, the problem of load discontinuity will automatically disappear. The second remedy is to perform a single small time step immediately upon termination of the applied impulse while the other time steps can still be conducted by using the time step determined from general considerations. This is because that the extra impulse caused by a load discontinuity at the end of an impulse is almost linearly proportional to the step size. Finally, the third remedy is to use the average value of the two different values at the integration point of the load discontinuity to replace the use of one of them for loading input. The basic motivation of this remedy originates from the concept of no loading input error associated with the integration point of load discontinuity. The feasibility of the three remedies are analytically explained and numerically illustrated.

Keywords: Dynamic analysis, load discontinuity, shock response, step-by-step integration

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: T. Tchawe Moukam, N. Ngongang François, D. Thomas, K. Bienvenu, T. -Toko Dénis

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Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.

Keywords: Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.

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Authors: A. Selmi

Abstract:

Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: Differential transformation method, functionally graded material, mode shape, natural frequency.

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Authors: K. N. C. Njoku, Chinwendu Best Eleje, Christian Chukwuemeka Nwandu

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One of the problems facing most insurance companies is how best the burden of paying claims to its policy holders can be managed whenever need arises. Hence there is need for the insurer to buy a reinsurance contract in order to reduce risk which will enable the insurer to share the financial burden with the reinsurer. In this paper, the insurer’s and reinsurer’s strategy is investigated under the modified constant elasticity of variance (M-CEV) process and proportional administrative charges. The insurer considered investment in one risky asset and one risk free asset where the risky asset is modeled based on the M-CEV process which is an extension of constant elasticity of variance (CEV) process. Next, a nonlinear partial differential equation in the form of Hamilton Jacobi Bellman equation is obtained by dynamic programming approach. Using power transformation technique and variable change, the explicit solutions of the optimal investment strategy and optimal reinsurance strategy are obtained. Finally, some numerical simulations of some sensitive parameters were obtained and discussed in details where we observed that the modification factor only affects the optimal investment strategy and not the reinsurance strategy for an insurer with exponential utility function.

Keywords: Reinsurance strategy, Hamilton Jacobi Bellman equation, power transformation, M-CEV process, exponential utility.

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Authors: Jia-Ru Li, Ching-Wen Lin

Abstract:

The study was designed to develop a measurement of the positive emotion regulation questionnaire (PERQ) that assesses positive emotion regulation strategies through self-report. The 14 items developed for the surveying instrument of the study were based upon literatures regarding elements of positive regulation strategies. 319 elementary students (age ranging from 12 to14) were recruited among three public elementary schools to survey on their use of positive emotion regulation strategies. Of 319 subjects, 20 invalid questionnaire s yielded a response rate of 92%. The data collected wasanalyzed through methods such as item analysis, factor analysis, and structural equation models. In reference to the results from item analysis, the formal survey instrument was reduced to 11 items. A principal axis factor analysis with varimax was performed on responses, resulting in a 2-factor equation (savoring strategy and neutralizing strategy), which accounted for 55.5% of the total variance. Then, the two-factor structure of scale was also identified by structural equation models. Finally, the reliability coefficients of the two factors were Cronbach-s α .92 and .74. Gender difference was only found in savoring strategy. In conclusion, the positive emotion regulation strategies questionnaire offers a brief, internally consistent, and valid self-report measure for understanding the emotional regulation strategies of children that may be useful to researchers and applied professionals.

Keywords: Emotional regulation, emotional regulation strategies, scale, SEM.

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Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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Authors: Soumiya Bhattacharjee, P. K. Champati Ray, Shovan L. Chattoraj, Mrinmoy Dhara

Abstract:

The entire Himalayan range is globally renowned for rainfall-induced landslides. The prime focus of the study is to determine rainfall based threshold for initiation of landslides that can be used as an important component of an early warning system for alerting stake holders. This research deals with temporal dimension of slope failures due to extreme rainfall events along the National Highway-58 from Karanprayag to Badrinath in the Garhwal Himalaya, India. Post processed 3-hourly rainfall intensity data and its corresponding duration from daily rainfall data available from Tropical Rainfall Measuring Mission (TRMM) were used as the prime source of rainfall data. Landslide event records from Border Road Organization (BRO) and some ancillary landslide inventory data for 2013 and 2014 have been used to determine Intensity Duration (ID) based rainfall threshold. The derived governing threshold equation, I= 4.738D^-0.025, has been considered for prediction of landslides of the study region. This equation was validated with an accuracy of 70% landslides during August and September 2014. The derived equation was considered for further prediction of landslides of the study region. From the obtained results and validation, it can be inferred that this equation can be used for initiation of landslides in the study area to work as a part of an early warning system. Results can significantly improve with ground based rainfall estimates and better database on landslide records. Thus, the study has demonstrated a very low cost method to get first-hand information on possibility of impending landslide in any region, thereby providing alert and better preparedness for landslide disaster mitigation.

Keywords: Landslide, intensity-duration, rainfall threshold, Tropical Rainfall Measuring Mission, slope, inventory, early warning system.

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Authors: Wei Jun-xia, Yuan Guang-wei, Yang Shu-lin, Shen Wei-dong

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In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.

Keywords: Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

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This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.

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Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail

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Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: R. Alipour, F.Najarian

Abstract:

Explosive welding is a process which uses explosive detonation to move the flyer plate material into the base material to produce a solid state joint. Experimental tests have been carried out by other researchers; have been considered to explosively welded aluminium 7039 and steel 4340 tubes in one step. The tests have been done using various stand-off distances and explosive ratios. Various interface geometries have been obtained from these experiments. In this paper, all the experiments carried out were simulated using the finite element method. The flyer plate and collision velocities obtained from the analysis were validated by the pin-measurement experiments. The numerical results showed that very high localized plastic deformation produced at the bond interface. The Ls_dyna_971 FEM has been used for all simulation process.

Keywords: Explosive Welding, Johnson-Cook Equation, Finite Element, JWL Equation.

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Authors: E.G. Bautista, F. Méndez, O. Bautista, J.C. Arcos

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In this work we study analytically and numerically the performance of the mean heave motion of an OWC coupled with the governing equation of the spreading ocean waves due to the wide variation in an open parabolic channel with constant depth. This paper considers that the ocean wave propagation is under the assumption of a shallow flow condition. In order to verify the effect of the waves in the OWC firstly we establish the analytical model in a non-dimensional form based on the energy equation. The proposed wave-power system has to aims: one is to perturb the ocean waves as a consequence of the channel shape in order to concentrate the maximum ocean wave amplitude in the neighborhood of the OWC and the second is to determine the pressure and volume oscillation of air inside the compression chamber.

Keywords: Oscillating water column, Shallow flow, Waveenergy.

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Authors: B. Tomczyk, R. Mania

Abstract:

Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Navid Javidtash, Abdolmohamad Davodi, Mojtaba Hakimzadeh, Abdolreza Roozbeh

Abstract:

Economic dispatch (ED) is considered to be one of the key functions in electric power system operation. This paper presents a new hybrid approach based genetic algorithm (GA) to economic dispatch problems. GA is most commonly used optimizing algorithm predicated on principal of natural evolution. Utilization of chaotic queue with GA generates several neighborhoods of near optimal solutions to keep solution variation. It could avoid the search process from becoming pre-mature. For the objective of chaotic queue generation, utilization of tent equation as opposed to logistic equation results in improvement of iterative speed. The results of the proposed approach were compared in terms of fuel cost, with existing differential evolution and other methods in literature.

Keywords: Economic Dispatch(ED), Optimization, Fuel Cost, Genetic Algorithm (GA).

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

Abstract:

The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Abdurrahim Dal, Tuncay Karaçay

Abstract:

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: Mohammad M. Toufigh, Ahad Ouria

Abstract:

This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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