scholarly journals CONVERGENCE OF THE GALERKIN METHOD IN THE ELECTROMAGNETIC WAVES DIFFRACTION PROBLEM ON A SYSTEM OF ARBITRARY LOCATED BODIES AND SCREENS

2016 ◽  
Author(s):  
Y.G. Smirnov ◽  
◽  
M.A. Moskaleva ◽  
Keyword(s):  
Galerkin Method ◽  
Electromagnetic Waves ◽  
Diffraction Problem ◽  
The Galerkin Method

scholarly journals Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides

2018 ◽  
Vol 186 ◽  
pp. 01010
Author(s):  
Dmitriy Divakov ◽  
Anastasiia Tiutiunnik ◽  
Anton Sevastianov
Keyword(s):  
Galerkin Method ◽  
Numerical Solution ◽  
Dimensional Space ◽  
Diffraction Problem ◽  
Liouville Problem ◽  
Planar Waveguides ◽  
Problem Solution ◽  
Scalar Diffraction ◽  
Open Waveguide ◽  
The Galerkin Method

This paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equation with a variable coefficient in two-dimensional space. The eigenmode problem for an open three-layer waveguide is the Sturm-Liouville problem for a second-order operator with piecewise constant potential on the axis, where the potential is proportional to the refractive index. The described problem is singular and has a mixed spectrum and therefore the Galerkin method can not be used in this definition. One way to adapt the Galerkin method for the problem solution is to artificially limit the area, which is equivalent to placing the open waveguide in question in a hollow closed waveguide whose boundaries are remote from the real boundaries of the waveguide layer of the open waveguide. Thus, we obtain a diffraction problem on a finite interval and with a discrete spectrum, which can be solved by the projection method, as done in this paper.

scholarly journals Modeling the Diffraction of Electromagnetic Waves over Underwater Objects; the Wiener-Hopf Integral Equation

2020 ◽  
pp. 135-144
Author(s):  
Yajni Warnapala ◽  
Cole Foster
Keyword(s):  
Integral Equation ◽  
Electromagnetic Wave ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Electromagnetic Waves ◽  
Good Convergence ◽  
Convergence Results ◽  
Lossy Media ◽  
The Galerkin Method ◽  
Airline Flight

This research, inspired by the loss of Malaysian Airline Flight 370, investigates the feasibility of obtaining good convergence results for a model of the interaction of electromagnetic waves over the surface of the Spherical Biconcave Disc. The Galerkin Method is used to numerically solve the Dirichlet and Neumann exterior boundary value problems for the Wiener-Hopf Integral Equation over the half-plane of the Spherical Biconcave Disc. This modeling accounts for the attenuation losses of the propagating electromagnetic wave as a result of absorption and scattering in lossy media with comparison to lossless propagation. The numerical results of this research nds good convergence for this model as well as limitations in the transmission of electromagnetic waves underwater.

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

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