Absorbing boundary conditions for the FD-TLM method : the perfectly matched layer and the one-way equation technique

2013 ◽  
Vol 27 (1) ◽  
pp. 62-78 ◽  
Author(s):  
M. Attia ◽  
M. Ney ◽  
T. Aguili
Keyword(s):  
Boundary Conditions ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Tlm Method ◽  
The One

Wave Equation Simulation by Finite-Element Method with Perfectly Matched Layer

2012 ◽  
Vol 524-527 ◽  
pp. 96-100 ◽  
Author(s):  
Hong Wei Guo ◽  
Shang Xu Wang ◽  
Nai Chuan Guo ◽  
Wei Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorption Effect ◽  
Absorbing Boundary ◽  
The One ◽  
First Time ◽  
Element Method

In numerical simulation, the treatment of boundary conditions is of great significance. In this paper, we have deduced the one order governing equations of the acoustic wave finite-element method with perfectly matched layer (PML) for the first time. The one order equations are easier to realize than the two order form and have a good absorption effect. Then, we have analyzed the absorption effect of the absorbing boundary conditions (ABCs) and the PML. Finally, we get some useful conclusions.

Absorbing boundary conditions for the TLM method

1992 ◽  
Vol 40 (11) ◽  
pp. 2095-2099 ◽  
Author(s):  
J.A. Morente ◽  
J.A. Porti ◽  
M. Khalladi
Keyword(s):  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Tlm Method

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.

Modified Unsplitted Perfectly Matched Layer Absorbing Boundary Conditions for Truncating Anisotropic Medium

2014 ◽  
Vol 900 ◽  
pp. 386-389
Author(s):  
Zhi Chao Cai ◽  
Li Xia Yang ◽  
Hao Chuan Deng ◽  
Xiao Wei ◽  
Hong Cheng Yin
Keyword(s):  
Boundary Conditions ◽  
Anisotropic Medium ◽  
Electromagnetic Wave Propagation ◽  
Simulation Analysis ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Derivatives Of ◽  
Difference Time

To simulate Electromagnetic wave propagation in anisotropic media, absorbing boundary conditions are needed to truncate the computation domains. Based on the finite difference time domain method in anisotropic medium, the implementation of the modified nearly perfectly matched layer absorbing boundary conditions for truncating anisotropic medium is presented. By using the partial derivatives of space variables stretched-scheme in the coordinate system, the programming complexity is reduced greatly. According to one dimensional numerical simulation analysis, the modified nearly perfectly matched layer absorbing boundary condition is validated.

scholarly journals Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

2011 ◽  
Vol 10 (5) ◽  
pp. 1280-1304 ◽  
Author(s):  
Pauline Klein ◽  
Xavier Antoine ◽  
Christophe Besse ◽  
Matthias Ehrhardt
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Absorbing Boundary Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Nonlinear Potential ◽  
Linear And Nonlinear ◽  
The One

AbstractWe propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.

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