Numerical reflecting boundary conditions and treatment of edge singularities for electromagnetic diffraction in the time domain

1992 ◽  
Author(s):  
M.D. White ◽  
J.J. Chattot
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Edge Singularities ◽  
The Time Domain ◽  
Electromagnetic Diffraction

Statement of absorbing Mur boundary conditions of the first order of accuracy for solving problems of electrodynamics by the method of finite differences in the time domain

2021 ◽  
Vol 8 ◽  
pp. 57-68
Author(s):  
R.Yu. Borodulin ◽  
N.O. Lukyanov
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Correct Choice ◽  
Absorbing Boundary Conditions ◽  
Practical Significance ◽  
Stable Operation ◽  
Absorbing Boundary ◽  
Spherical Waves ◽  
The One ◽  
The Time Domain

Problem statement. The accuracy and convergence of calculations for solving problems of electrodynamics by the finite difference method in the time domain significantly depends on the correct choice of parameters and the correct setting of the absorbing boundary conditions (ABC). Two main types of absorbing boundary conditions are known: Mur ABC; Beranger ABC. It is believed that the Mur ABC is less effective at absorbing spherical waves than the Beranger ABC, but they do not require the introduction of additional parameters (the so-called "Beranger fields"), which simplifies the implementation of program code and saves computer RAM. Calculations have shown that the efficiency of the Mur ABC will depend on their thickness. On the one hand, an increase in the thickness of the ABC layers will lead to an increase in the accuracy of calculations, on the other hand, to an increase in the size of the calculation area and, as a result, an increase in RAM. The problem arises of determining the criterion for evaluating the efficiency of ABC to determine their optimal thickness. Goal. Identification of new factors that make it possible to use the Mur ABC as efficiently as the Beranger ABC, while significantly saving computer resources. Result. The expressions for the ABC are presented, taking into account the interaction of all components of the electromagnetic field within a single cell of the FDTD. Calculations of the reflection coefficient – a criterion for evaluating the efficiency of the ABC, are presented. Practical significance. Calculations are presented that allow automating the selection of ABC parameters for their stable operation in solving electrodynamic problems.

Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model

2020 ◽  
pp. 239779142093170
Author(s):  
M Faraji Oskouie ◽  
R Ansari ◽  
H Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Time Domain ◽  
Beam Model ◽  
Viscoelastic Foundation ◽  
Timoshenko Beam Model ◽  
Governing Equations ◽  
The Time Domain

On the basis of fractional viscoelasticity, the size-dependent free-vibration response of viscoelastic carbon nanotubes conveying fluid and resting on viscoelastic foundation is studied in this article. To this end, a nonlocal Timoshenko beam model is developed in the context of fractional calculus. Hamilton’s principle is applied in order to obtain the fractional governing equations including nanoscale effects. The Kelvin–Voigt viscoelastic model is also used for the constitutive equations. The free-vibration problem is solved using two methods. In the first method, which is limited to the simply supported boundary conditions, the Galerkin technique is employed for discretizing the spatial variables and reducing the governing equations to a set of ordinary differential equations on the time domain. Then, the Duffing-type time-dependent equations including fractional derivatives are solved via fractional integrator transfer functions. In the second method, which can be utilized for carbon nanotubes with different types of boundary conditions, the generalized differential quadrature technique is used for discretizing the governing equations on spatial grids, whereas the finite difference technique is used on the time domain. In the results, the influences of nonlocality, geometrical parameters, fractional derivative orders, viscoelastic foundation, and fluid flow velocity on the time responses of carbon nanotubes are analyzed.

INVERSE RECONSTRUCTION OF THERMAL AND MECHANICAL BOUNDARY CONDITIONS IN COUPLED NONLINEAR THERMO-ELASTIC PROBLEMS

2014 ◽  
Vol 06 (02) ◽  
pp. 1450014 ◽  
Author(s):  
S. KHAJEHPOUR ◽  
M. R. HEMATIYAN
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Inverse Analysis ◽  
Optimization Method ◽  
Elastic Problem ◽  
Unknown Boundary ◽  
The Finite Element Method ◽  
Inverse Reconstruction ◽  
The Time Domain ◽  
Unknown Boundary Conditions

A stable technique based on the finite element method for inverse analysis of coupled nonlinear thermo-elastic problems is presented. Not only the time-domain is divided into small intervals, but also the space-domain is divided into several sub-domains. The inverse problem is solved in each sub-domain subsequently. For the inverse analysis in each sub-domain, the unknown boundary conditions are found by using an optimization method and also by employing the information obtained in the previous sub-domain. The method is sufficiently stable to be used for inverse analysis of a thermo-elastic problem under a thermal shock. Three numerical examples are provided to demonstrate the efficiency of the proposed method. The effects of the number of sub-domains are investigated in the examples.

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