International Science Index
Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions
Numerical computation of wave propagation in a large
domain usually requires significant computational effort. Hence, the
considered domain must be truncated to a smaller domain of interest.
In addition, special boundary conditions, which absorb the outward
travelling waves, need to be implemented in order to describe the
system domains correctly. In this work, the linear one dimensional
wave equation is approximated by utilizing the Fourier Galerkin
approach. Furthermore, the artificial boundaries are realized with
absorbing boundary conditions. Within this work, a systematic work
flow for setting up the wave problem, including the absorbing
boundary conditions, is proposed. As a result, a convenient modal
system description with an effective absorbing boundary formulation
is established. Moreover, the truncated model shows high accuracy
compared to the global domain.
Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation
The generalized wave equation models various
problems in sciences and engineering. In this paper, a new three-time
level implicit approach based on cubic trigonometric B-spline for the
approximate solution of wave equation is developed. The usual finite
difference approach is used to discretize the time derivative while
cubic trigonometric B-spline is applied as an interpolating function in
the space dimension. Von Neumann stability analysis is used to
analyze the proposed method. Two problems are discussed to exhibit
the feasibility and capability of the method. The absolute errors and
maximum error are computed to assess the performance of the
proposed method. The results were found to be in good agreement
with known solutions and with existing schemes in literature.
Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation
In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.
A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations
In this article, we propose a new approximate procedure
based on He’s variational iteration method for solving nonlinear
hyperbolic equations. We introduce two transformations q = ut and
σ = ux and formulate a first-order system of equations. We can
obtain the approximation solution for the scalar unknown u, time
derivative q = ut and space derivative σ = ux, simultaneously.
Finally, some examples are provided to illustrate the effectiveness of
Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method
This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
Alternating Implicit Block FDTD Method For Scalar Wave Equation
In this paper, an alternating implicit block method for
solving two dimensional scalar wave equation is presented. The
new method consist of two stages for each time step implemented
in alternating directions which are very simple in computation. To
increase the speed of computation, a group of adjacent points is
computed simultaneously. It is shown that the presented method
increase the maximum time step size and more accurate than the
conventional finite difference time domain (FDTD) method and other
existing method of natural ordering.
High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation
This paper deals with a high-order accurate Runge
Kutta Discontinuous Galerkin (RKDG) method for the numerical
solution of the wave equation, which is one of the simple case of a
linear hyperbolic partial differential equation. Nodal DG method is
used for a finite element space discretization in 'x' by discontinuous
approximations. This method combines mainly two key ideas which
are based on the finite volume and finite element methods. The
physics of wave propagation being accounted for by means of
Riemann problems and accuracy is obtained by means of high-order
polynomial approximations within the elements. High order accurate
Low Storage Explicit Runge Kutta (LSERK) method is used for
temporal discretization in 't' that allows the method to be nonlinearly
stable regardless of its accuracy. The resulting RKDG
methods are stable and high-order accurate. The L1 ,L2 and L∞ error
norm analysis shows that the scheme is highly accurate and effective.
Hence, the method is well suited to achieve high order accurate
solution for the scalar wave equation and other hyperbolic equations.
Photon Localization inside a Waveguide Modeled by Uncertainty Principle
In the present work, an attempt is made to understand
electromagnetic field confinement in a subwavelength waveguide
structure using concepts of quantum mechanics. Evanescent field in
the waveguide is looked as inability of the photon to get confined in
the waveguide core and uncertainty of position is assigned to it. The
momentum uncertainty is calculated from position uncertainty.
Schrödinger wave equation for the photon is written by incorporating
position-momentum uncertainty. The equation is solved and field
distribution in the waveguide is obtained. The field distribution and
power confinement is compared with conventional waveguide theory.
They were found in good agreement with each other.
A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide
In this paper, a novel wave equation for electromagnetic
waves in a medium having anisotropic permittivity has been derived
with the help of Maxwell-s curl equations. The x and y components
of the Maxwell-s equations are written with the permittivity () being
a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey,
Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z
components of the Maxwell-s curl are then used to arrive to the
generalized Helmholtz equations for Ez and Hz.
Analyzing of Noise inside a Simple Vehicle Cabin using Boundary Element Method
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.
Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole
This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.
Action Functional of the Electomagnetic Field: Effect of Gravitation
The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.
Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method
In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).