Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3098

Search results for: numerical quadrature

3098 Using Derivative Free Method to Improve the Error Estimation of Numerical Quadrature

Authors: Chin-Yun Chen


Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

Procedia PDF Downloads 370
3097 Numerical Solution of Integral Equations by Using Discrete GHM Multiwavelet

Authors: Archit Yajnik, Rustam Ali


In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

Procedia PDF Downloads 352
3096 Superconvergence of the Iterated Discrete Legendre Galerkin Method for Fredholm-Hammerstein Equations

Authors: Payel Das, Gnaneshwar Nelakanti


In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

Procedia PDF Downloads 365
3095 Improvement of the Numerical Integration's Quality in Meshless Methods

Authors: Ahlem Mougaida, Hedi Bel Hadj Salah


Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

Procedia PDF Downloads 262
3094 Finding the Elastic Field in an Arbitrary Anisotropic Media by Implementing Accurate Generalized Gaussian Quadrature Solution

Authors: Hossein Kabir, Amir Hossein Hassanpour Mati-Kolaie


In the current study, the elastic field in an anisotropic elastic media is determined by implementing a general semi-analytical method. In this specific methodology, the displacement field is computed as a sum of finite functions with unknown coefficients. These aforementioned functions satisfy exactly both the homogeneous and inhomogeneous boundary conditions in the proposed media. It is worth mentioning that the unknown coefficients are determined by implementing the principle of minimum potential energy. The numerical integration is implemented by employing the Generalized Gaussian Quadrature solution. Furthermore, with the aid of the calculated unknown coefficients, the displacement field, as well as the other parameters of the elastic field, are obtainable as well. Finally, the comparison of the previous analytical method with the current semi-analytical method proposes the efficacy of the present methodology.

Keywords: anisotropic elastic media, semi-analytical method, elastic field, generalized gaussian quadrature solution

Procedia PDF Downloads 222
3093 Transverse Vibration of Non-Homogeneous Rectangular Plates of Variable Thickness Using GDQ

Authors: R. Saini, R. Lal


The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: rectangular, non-homogeneous, bilinear thickness, generalized differential quadrature (GDQ)

Procedia PDF Downloads 305
3092 Development of Fem Code for 2-D Elasticity Problems Using Quadrilateral and Triangular Elements

Authors: Muhammad Umar Kiani, Waseem Sakawat


This study presents the development of FEM code using Quadrilateral 4-Node (Q4) and Triangular 3-Node (T3) elements. Code is formulated using MATLAB language. Instead of using both elements in the same code, two separate codes are written. Quadrilateral element is difficult to handle directly, that is why natural coordinates (eta, ksi) are used. Due to this, Q4 code includes numerical integration (Gauss quadrature). In this case, complete numerical integration is performed using 2 points. On the other hand, T3 element can be modeled directly, by using direct stiffness approach. Axially loaded element, cantilever (special constraints) and Patch test cases were analyzed using both codes and the results were verified by using Ansys.

Keywords: FEM code, MATLAB, numerical integration, ANSYS

Procedia PDF Downloads 329
3091 Free Vibration Analysis of Pinned-Pinned and Clamped-Clamped Equal Strength Columns under Self-Weight and Tip Force Using Differential Quadrature Method

Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana


The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

Procedia PDF Downloads 4
3090 Simple Multipath Compensation for Frequency Modulated Signals: A Case of Radio Frequency vs. Quadrature Baseband

Authors: Lusungu Ndovi


Radio propagation from point-to-point is affected by the physical channel in many ways. A signal arriving at a destination travels through a number of different paths which are referred to as multi-paths. Research in this area of wireless communications has progressed well over the years with the research taking different angles of focus. By this is meant that some researchers focus on ways of reducing or eluding Multipath effects whilst others focus on ways of mitigating the effects of Multipath through compensation schemes. Baseband processing is seen as one field of signal processing that is cardinal to the advancement of software-defined radio technology. This has led to wide research into the carrying out certain algorithms at baseband. This paper considers compensating for Multipath for Frequency Modulated signals. The compensation process is carried out at Radio frequency (RF) and at Quadrature baseband (QBB) and the results are compared. Simulations are carried out using MatLab so as to show the benefits of working at lower QBB frequencies than at RF.

Keywords: quadrature baseband, qadio frequency, qultipath compensation, frequency qodulation, signal processing

Procedia PDF Downloads 412
3089 Quadrature Mirror Filter Bank Design Using Population Based Stochastic Optimization

Authors: Ju-Hong Lee, Ding-Chen Chung


The paper deals with the optimal design of two-channel linear-phase (LP) quadrature mirror filter (QMF) banks using a metaheuristic based optimization technique. Based on the theory of two-channel QMF banks using two recursive digital all-pass filters (DAFs), the design problem is appropriately formulated to result in an objective function which is a weighted sum of the group delay error of the designed QMF bank and the magnitude response error of the designed low-pass analysis filter. Through a frequency sampling and a weighted least squares approach, the optimization problem of the objective function can be solved by utilizing a particle swarm optimization algorithm. The resulting two-channel QMF banks can possess approximately LP response without magnitude distortion. Simulation results are presented for illustration and comparison.

Keywords: quadrature mirror filter bank, digital all-pass filter, weighted least squares algorithm, particle swarm optimization

Procedia PDF Downloads 446
3088 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators

Authors: Fethi Soltani, Adel Almarashi, Idir Mechai


Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

Procedia PDF Downloads 234
3087 Molecular Dynamics Simulation for Buckling Analysis at Nanocomposite Beams

Authors: Babak Safaei, A. M. Fattahi


In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ)

Procedia PDF Downloads 260
3086 Stress Analysis of Tubular Bonded Joints under Torsion and Hygrothermal Effects Using DQM

Authors: Mansour Mohieddin Ghomshei, Reza Shahi


Laminated composite tubes with adhesively bonded joints are widely used in aerospace and automotive industries as well as oil and gas industries. In this research, adhesively tubular single lap joints subjected to torsional and hygrothermal loadings are studied using the differential quadrature method (DQM). The analysis is based on the classical shell theory. At first, an approximate closed form solution is developed by omitting the lateral deflections in the connecting tubes. Using the analytical model, the circumferential displacements in tubes and the shear stresses in the interfacing adhesive layer are determined. Then, a numerical formulation is presented using DQM in which the lateral deflections are taken into account. By using the DQM formulation, the circumferential and radial displacements in tubes as well as shear and peel stresses in the adhesive layer are calculated. Results obtained from the proposed DQM solutions are compared well with those of the approximate analytical model and those of some published references. Finally using the DQM model, parametric studies are carried out to investigate the influence of various parameters such as adhesive layer thickness, torsional loading, overlap length, tubes radii, relative humidity, and temperature.

Keywords: adhesively bonded joint, differential quadrature method (DQM), hygrothermal, laminated composite tube

Procedia PDF Downloads 217
3085 An Application of Sinc Function to Approximate Quadrature Integrals in Generalized Linear Mixed Models

Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif


This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

Procedia PDF Downloads 320
3084 Nonlinear Static Analysis of Laminated Composite Hollow Beams with Super-Elliptic Cross-Sections

Authors: G. Akgun, I. Algul, H. Kurtaran


In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

Procedia PDF Downloads 177
3083 Optimization of the Numerical Fracture Mechanics

Authors: H. Hentati, R. Abdelmoula, Li Jia, A. Maalej


In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time.

Keywords: fracture mechanics, optimization, variation approach, mechanic

Procedia PDF Downloads 439
3082 Biaxial Buckling of Single Layer Graphene Sheet Based on Nonlocal Plate Model and Molecular Dynamics Simulation

Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin


The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory

Procedia PDF Downloads 210
3081 Molecular Dynamics Simulation for Vibration Analysis at Nanocomposite Plates

Authors: Babak Safaei, A. M. Fattahi


Polymer/carbon nanotube nanocomposites have a wide range of promising applications Due to their enhanced properties. In this work, free vibration analysis of single-walled carbon nanotube-reinforced composite plates is conducted in which carbon nanotubes are embedded in an amorphous polyethylene. The rule of mixture based on various types of plate model namely classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT) was employed to obtain fundamental frequencies of the nanocomposite plates. Generalized differential quadrature (GDQ) method was used to discretize the governing differential equations along with the simply supported and clamped boundary conditions. The material properties of the nanocomposite plates were evaluated using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites. Then the results obtained directly from MD simulations were fitted with those calculated by the rule of mixture to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results are presented to address the influences of nanotube volume fraction and edge supports on the value of fundamental frequency of carbon nanotube-reinforced composite plates corresponding to both long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, free vibration, generalized, differential quadrature (GDQ) method

Procedia PDF Downloads 258
3080 Some Results on the Generalized Higher Rank Numerical Ranges

Authors: Mohsen Zahraei


‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

Procedia PDF Downloads 339
3079 Bit Error Rate Monitoring for Automatic Bias Control of Quadrature Amplitude Modulators

Authors: Naji Ali Albakay, Abdulrahman Alothaim, Isa Barshushi


The most common quadrature amplitude modulator (QAM) applies two Mach-Zehnder Modulators (MZM) and one phase shifter to generate high order modulation format. The bias of MZM changes over time due to temperature, vibration, and aging factors. The change in the biasing causes distortion to the generated QAM signal which leads to deterioration of bit error rate (BER) performance. Therefore, it is critical to be able to lock MZM’s Q point to the required operating point for good performance. We propose a technique for automatic bias control (ABC) of QAM transmitter using BER measurements and gradient descent optimization algorithm. The proposed technique is attractive because it uses the pertinent metric, BER, which compensates for bias drifting independently from other system variations such as laser source output power. The proposed scheme performance and its operating principles are simulated using OptiSystem simulation software for 4-QAM and 16-QAM transmitters.

Keywords: automatic bias control, optical fiber communication, optical modulation, optical devices

Procedia PDF Downloads 114
3078 Dynamic Analysis of Composite Doubly Curved Panels with Variable Thickness

Authors: I. Algul, G. Akgun, H. Kurtaran


Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: differential quadrature method, doubly curved panels, laminated composite materials, small displacement

Procedia PDF Downloads 139
3077 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir


This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

Procedia PDF Downloads 217
3076 Analysis of Thermal Effect on Functionally Graded Micro-Beam via Mixed Finite Element Method

Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent


Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

Procedia PDF Downloads 58
3075 Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis

Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon


The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

Procedia PDF Downloads 318
3074 Numerical Methods versus Bjerksund and Stensland Approximations for American Options Pricing

Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea


Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

Procedia PDF Downloads 359
3073 Numerical Simulations for Nitrogen Flow in Piezoelectric Valve

Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski


Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

Procedia PDF Downloads 405
3072 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

Authors: Fuziyah Ishak, Siti Norazura Ahmad


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

Procedia PDF Downloads 263
3071 Design of Two-Channel Quincunx Quadrature Mirror Filter Banks Using Digital All-Pass Lattice Filters

Authors: Ju-Hong Lee, Chong-Jia Ciou


This paper deals with the problem of two-dimensional (2-D) recursive two-channel quincunx quadrature mirror filter (QQMF) banks design. The analysis and synthesis filters of the 2-D recursive QQMF bank are composed of 2-D recursive digital allpass lattice filters (DALFs) with symmetric half-plane (SHP) support regions. Using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters, we facilitate the design of the proposed QQMF bank. For finding the coefficients of the 2-D recursive SHP DALFs, we present a structure of 2-D recursive digital allpass filters by using 2-D SHP recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive QQMF bank is that the resulting 2-D recursive QQMF bank provides better performance than the existing 2-D recursive QQMF banks. Simulation results are also presented for illustration and comparison.

Keywords: all-pass digital filter, lattice structure, quincunx QMF bank, symmetric half-plane digital filter

Procedia PDF Downloads 273
3070 Time and Wavelength Division Multiplexing Passive Optical Network Comparative Analysis: Modulation Formats and Channel Spacings

Authors: A. Fayad, Q. Alqhazaly, T. Cinkler


In light of the substantial increase in end-user requirements and the incessant need of network operators to upgrade the capabilities of access networks, in this paper, the performance of the different modulation formats on eight-channels Time and Wavelength Division Multiplexing Passive Optical Network (TWDM-PON) transmission system has been examined and compared. Limitations and features of modulation formats have been determined to outline the most suitable design to enhance the data rate and transmission reach to obtain the best performance of the network. The considered modulation formats are On-Off Keying Non-Return-to-Zero (NRZ-OOK), Carrier Suppressed Return to Zero (CSRZ), Duo Binary (DB), Modified Duo Binary (MODB), Quadrature Phase Shift Keying (QPSK), and Differential Quadrature Phase Shift Keying (DQPSK). The performance has been analyzed by varying transmission distances and bit rates under different channel spacing. Furthermore, the system is evaluated in terms of minimum Bit Error Rate (BER) and Quality factor (Qf) without applying any dispersion compensation technique, or any optical amplifier. Optisystem software was used for simulation purposes.

Keywords: BER, DuoBinary, NRZ-OOK, TWDM-PON

Procedia PDF Downloads 66
3069 3-D Numerical Model for Wave-Induced Seabed Response around an Offshore Pipeline

Authors: Zuodong Liang, Dong-Sheng Jeng


Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

Procedia PDF Downloads 169