Search results for: matrix equation

Authors: Yoichi Hikino, Mutsuto Kawahara

Abstract:

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.

Keywords: Shape Optimization, Optimal Control Theory, Finite Element Method, Weighted Gradient Method, Fluid Force, Orthogonal Basis Bubble Function, Four-step Explicit Scheme, Acoustic Velocity.

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Authors: Dhruba Das

Abstract:

In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: Imprecise number, Imprecise vector, Membership surface, Imprecise matrix.

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Authors: Alexander Breitholz, Wolfgang Arlt, Ki-Pung Yoo

Abstract:

Group contribution based models are widely used in industrial applications for its convenience and flexibility. Although a number of group contribution models have been proposed, there were certain limitations inherent to those models. Models based on group contribution excess Gibbs free energy are limited to low pressures and models based on equation of state (EOS) cannot properly describe highly nonideal mixtures including acids without introducing additional modification such as chemical theory. In the present study new a new approach derived from quantum chemistry have been used to calculate necessary EOS group interaction parameters. The COSMO-RS method, based on quantum mechanics, provides a reliable tool for fluid phase thermodynamics. Benefits of the group contribution EOS are the consistent extension to hydrogen-bonded mixtures and the capability to predict polymer-solvent equilibria up to high pressures. The authors are confident that with a sufficient parameter matrix the performance of the lattice EOS can be improved significantly.

Keywords: COSMO-RS, Equation of State, Group contribution, Lattice Fluid, Phase equilibria.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong

Abstract:

The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.

Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

Abstract:

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: Somayeh Arbabi Mohammad-Abadi, Maliheh Najafi

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In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.

Keywords: Three-wave method, (3+1)-dimensional Soliton equation, Hirota's bilinear form.

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Authors: Alibek Issakhov

Abstract:

In this paper developed and realized absolutely new algorithm for solving three-dimensional Poisson equation. This equation used in research of turbulent mixing, computational fluid dynamics, atmospheric front, and ocean flows and so on. Moreover in the view of rising productivity of difficult calculation there was applied the most up-to-date and the most effective parallel programming technology - MPI in combination with OpenMP direction, that allows to realize problems with very large data content. Resulted products can be used in solving of important applications and fundamental problems in mathematics and physics.

Keywords: MPI, OpenMP, three dimensional Poisson equation

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Authors: Z. El Felsoufi, L. Azrar

Abstract:

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.

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Authors: R.Rahimi, F.Moharrami

Abstract:

Titanium gels doped with water-soluble cationic porphyrin were synthesized by the sol–gel polymerization of Ti (OC4H9)4. In this work we investigate the spectroscopic properties along with SEM images of tetra carboxyl phenyl porphyrin when incorporated into porous matrix produced by the sol–gel technique.

Keywords: TCPP, Titanium matrix, UV/Vis spectroscopy, SEM.

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

Existence of plastic equation of state has been investigated by performing a series of load relaxation tests at various temperatures using an Al-Li alloy. A plastic equation of state is first developed from a simple kinetics consideration for a mechanical activation process of a leading dislocation piled up against grain boundaries. A series of load relaxation test has been conducted at temperatures ranging from 200 to 530^oC to obtain the stress-strain rate curves. A plastic equation of state has been derived from a simple consideration of dislocation kinetics and confirmed by experimental results.

Keywords: Plastic equation of state, Dislocation kinetics, Load relaxation test, Al-Li alloy, Microstructure.

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

Abstract:

Cubic equations of state like Redlich–Kwong (RK)  EOS have been proved to be very reliable tools in the prediction of  phase behavior. Despite their good performance in compositional  calculations, they usually suffer from weaknesses in the predictions  of saturated liquid density. In this research, RK equation was  modified. The result of this study show that modified equation has  good agreement with experimental data.

 

Keywords: Equation of state, modification, ammonia, genetic algorithm.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: Anirut Luadsong, Nitima Aschariyaphotha

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting upwind schemes for avoiding stability problems and prove that it is consistent to the upwind scheme with same accuracy. The splitting upwind schemes was adopted to split the wave spectral action balance equation into four onedimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-processor computer.

Keywords: upwind scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Xian Ming Gu, Ting Zhu Huang, Hou Biao Li

Abstract:

In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.

Keywords: Parallel algorithm, Pentadiagonal matrix, Polynomial approximate inverse, Preconditioners, Stair matrix.

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.

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Authors: Ch. Surawut, D. Sukawat

Abstract:

In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. This equation provides downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: Dynamic Equation, Downscaling, Inverse distance weight interpolation.

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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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: Z. Feng, V. Viswanathan, D. Navarro, I. O'Connor

Abstract:

This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.

Keywords: CMOS image sensor, high speed simulation, image sensor matrix simulation.

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Authors: Ling Zhang, Ting-Zhu Huang

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A P0-matrix is a real square matrix all of whose principle minors are nonnegative. In this paper, we consider the class of P0-matrix. Our main aim is to determine which sign pattern matrices are admissible for this class of real matrices.

Keywords: Sign pattern matrices, P0 matrices, graph, digraph.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Rectangular and circular membranes, propagation matrix, reflection matrix, vibration analysis.

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: R.Marsalek

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (ν ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ν <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: ferro-precipitate, adsorption, SDS, zeta potential

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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Authors: Roozbeh Mansouri, Hassan Hadidi

Abstract:

Truss spars are used for oil exploitation in deep and ultra-deep water if storage crude oil is not needed. The linear hydrodynamic analysis of truss spar in random sea wave load is necessary for determining the behaviour of truss spar. This understanding is not only important for design of the mooring lines, but also for optimising the truss spar design. In this paper linear hydrodynamic analysis of truss spar is carried out in frequency domain. The hydrodynamic forces are calculated using the modified Morison equation and diffraction theory. Added mass and drag coefficients of truss section computed by transmission matrix and normal acceleration and velocity component acting on each element and for hull section computed by strip theory. The stiffness properties of the truss spar can be separated into two components; hydrostatic stiffness and mooring line stiffness. Then, platform response amplitudes obtained by solved the equation of motion. This equation is non-linear due to viscous damping term therefore linearised by iteration method [1]. Finally computed RAOs and significant response amplitude and results are compared with experimental data.

Keywords: Truss Spar, Hydrodynamic analysis, Wave spectrum, Frequency Domain

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Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: Channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow.

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