**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5052

# Search results for: Fourier Galerkin approach

##### 5052 Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions

**Authors:**
Alexandra Leukauf,
Alexander Schirrer,
Emir Talic

**Abstract:**

**Keywords:**
Absorbing boundary conditions,
boundary control,
Fourier Galerkin approach,
modal approach,
wave equation.

##### 5051 Coupled Galerkin-DQ Approach for the Transient Analysis of Dam-Reservoir Interaction

**Authors:**
S. A. Eftekhari

**Abstract:**

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

**Keywords:**
Dam-reservoir system,
Differential quadrature method,
Fluid-structure interaction,
Galerkin method,
Integral quadrature method.

##### 5050 Bernstein-Galerkin Approach for Perturbed Constant-Coefficient Differential Equations, One-Dimensional Analysis

**Authors:**
Diego Garijo

**Abstract:**

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

**Keywords:**
Bernstein polynomials,
Galerkin,
differential equation,
boundary layer.

##### 5049 Adaptive Fourier Decomposition Based Signal Instantaneous Frequency Computation Approach

**Authors:**
Liming Zhang

**Abstract:**

**Keywords:**
Adaptive Fourier decomposition,
Fourier series,
signal processing,
instantaneous frequency

##### 5048 Numerical Studies of Galerkin-type Time-discretizations Applied to Transient Convection-diffusion-reaction Equations

**Authors:**
Naveed Ahmed,
Gunar Matthies

**Abstract:**

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

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

##### 5047 On Fourier Type Integral Transform for a Class of Generalized Quotients

**Authors:**
A. S. Issa,
S. K. Q. AL-Omari

**Abstract:**

**Keywords:**
Fourier type integral,
Fourier integral,
generalized
quotient,
Boehmian,
distribution.

##### 5046 Recursive Wiener-Khintchine Theorem

**Authors:**
Khalid M. Aamir,
Mohammad A. Maud

**Abstract:**

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

**Keywords:**
Power Spectral Density (PSD),
Wiener-KhintchineTheorem,
Periodogram,
Short Time Fourier Transform (STFT),
TheSliding DFT.

##### 5045 A New Time-Frequency Speech Analysis Approach Based On Adaptive Fourier Decomposition

**Authors:**
Liming Zhang

**Abstract:**

In this paper, a new adaptive Fourier decomposition (AFD) based time-frequency speech analysis approach is proposed. Given the fact that the fundamental frequency of speech signals often undergo fluctuation, the classical short-time Fourier transform (STFT) based spectrogram analysis suffers from the difficulty of window size selection. AFD is a newly developed signal decomposition theory. It is designed to deal with time-varying non-stationary signals. Its outstanding characteristic is to provide instantaneous frequency for each decomposed component, so the time-frequency analysis becomes easier. Experiments are conducted based on the sample sentence in TIMIT Acoustic-Phonetic Continuous Speech Corpus. The results show that the AFD based time-frequency distribution outperforms the STFT based one.

**Keywords:**
Adaptive fourier decomposition,
instantaneous
frequency,
speech analysis,
time-frequency distribution.

##### 5044 Numerical Investigation of Multiphase Flow in Pipelines

**Authors:**
Gozel Judakova,
Markus Bause

**Abstract:**

**Keywords:**
Discontinuous Galerkin method,
Euler system,
inviscid two-fluid model,
streamline upwind Petrov-Galerkin
method,
two-phase flow.

##### 5043 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 5042 An H1-Galerkin Mixed Method for the Coupled Burgers Equation

**Authors:**
Xianbiao Jia,
Hong Li,
Yang Liu,
Zhichao Fang

**Abstract:**

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

**Keywords:**
The coupled Burgers equation,
H1-Galerkin mixed
finite element method,
Backward Euler's method,
Optimal error
estimates.

##### 5041 Discontinuous Galerkin Method for Total Variation Minimization on Inpainting Problem

**Authors:**
Xijian Wang

**Abstract:**

**Keywords:**
finite element method,
discontinuous Galerkin method,
total variation minimization,
inpainting

##### 5040 Quality Factor Variation with Transform Order in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
K. Pardha Saradhi,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Quality Factor,
Fractional Fourier span,
transient signals.

##### 5039 An Efficient Hamiltonian for Discrete Fractional Fourier Transform

**Authors:**
Sukrit Shankar,
Pardha Saradhi K.,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Hamiltonian,
Eigen
Vectors,
Discrete Hermite Gaussians.

##### 5038 A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations

**Authors:**
Yang Liu,
Jinfeng Wang,
Hong Li,
Wei Gao,
Siriguleng He

**Abstract:**

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

**Keywords:**
Pseudo-hyperbolic equations,
splitting system,
H1-Galerkin mixed method,
error estimates.

##### 5037 Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

**Keywords:**
Fractional Fourier Transform,
uncertainty principle,
Fractional Fourier Span,
amplitude,
phase.

##### 5036 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function

**Authors:**
Sukrit Shankar,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Perturbation,
Fractional Fourier span,
amplitude,
phase,
transform order,
filterbanks.

##### 5035 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

**Authors:**
Watcharakorn Thongchuay,
Puntip Toghaw,
Montri Maleewong

**Abstract:**

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

##### 5034 Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method

**Authors:**
Saeed Sarabadan,
Kamal Rashedi

**Abstract:**

**Keywords:**
Inverse problem,
parabolic equations,
heat equation,
Ritz-Galerkin method,
Landweber iterations.

##### 5033 Applying Element Free Galerkin Method on Beam and Plate

**Authors:**
Mahdad M’hamed,
Belaidi Idir

**Abstract:**

**Keywords:**
Numerical computation,
element-free Galerkin,
moving least squares,
meshless methods.

##### 5032 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
N. Aliniya

**Abstract:**

**Keywords:**
Calculus of variation; Sinc functions; Galerkin; Numerical method

##### 5031 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators

**Authors:**
Fethi Soltani,
Adel Almarashi,
Idir Mechai

**Abstract:**

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

##### 5030 MRI Reconstruction Using Discrete Fourier Transform: A tutorial

**Authors:**
Abiodun M. Aibinu,
Momoh J. E. Salami,
Amir A. Shafie,
Athaur Rahman Najeeb

**Abstract:**

The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.

**Keywords:**
Discrete Fourier Transform (DFT),
K-space Data,
Magnetic Resonance (MR),
Spin,
Windows.

##### 5029 Implementation of Meshless FEM for Engineering Applications

**Authors:**
A. Seidl,
Th. Schmidt

**Abstract:**

**Keywords:**
Finite Elements,
meshless,
element-free Galerkin,
point-interpolation.

##### 5028 New Approach to Spectral Analysis of High Bit Rate PCM Signals

**Authors:**
J. P. Dubois

**Abstract:**

**Keywords:**
Coding,
discrete Fourier,
power spectral density,
pulse code modulation,
Riemann-Stieltjes integrals.

##### 5027 New Recursive Representations for the Favard Constants with Application to the Summation of Series

**Authors:**
Snezhana G. Gocheva-Ilieva,
Ivan H. Feschiev

**Abstract:**

**Keywords:**
Effective summation of series,
Favard constants,
finite recursive representations,
Fourier series

##### 5026 Nonlinear Structural Behavior of Micro- and Nano-Actuators Using the Galerkin Discretization Technique

**Authors:**
Hassen M. Ouakad

**Abstract:**

In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

**Keywords:**
MEMS,
NEMS,
fringing-fields,
mid-plane stretching,
Galerkin method.

##### 5025 Fourier Spectral Method for Analytic Continuation

**Authors:**
Zhenyu Zhao,
Lei You

**Abstract:**

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

**Keywords:**
Analytic continuation,
ill-posed problem,
regularization method Fourier spectral method,
the discrepancy principle.

##### 5024 Cubic Splines and Fourier Series Approach to Study Temperature Variation in Dermal Layers of Elliptical Shaped Human Limbs

**Authors:**
Mamta Agrawal,
Neeru Adlakha,
K.R. Pardasani

**Abstract:**

**Keywords:**
Blood Mass Flow Rate,
Metabolic Heat Generation,
Fourier Series,
Cubic splines and Thermal Conductivity.

##### 5023 High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation

**Authors:**
Faheem Ahmed,
Fareed Ahmed,
Yongheng Guo,
Yong Yang

**Abstract:**

**Keywords:**
Nodal Discontinuous Galerkin Method,
RKDG,
Scalar Wave Equation,
LSERK