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A Novel absorbing boundary condition for the Frequency-Dependent Finite-Difference Time-Domain Method

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Journal of Shanghai University(English Edition) 2001年第2期5卷 111-115页

作者： WANG Tong, ZHANG Wen jun, GE Ren wei, LIU Wei liang School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China School of Communication and Information Engineering Shanghai University Shanghai China

A new absorbing boundary condition (ABC) for frequency dependent finite difference time domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD) 2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two dimensions and three dimensions are calculated and the validity of the ABC is verified.

关键词： dispersive media FDTD(finite different time domain) absorbing boundary condition digital filter

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

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Applied Geophysics 2013年第3期10卷 323-336,359页

作者：赵建国史瑞其中国石油大学(北京)地球物理与信息工程学院油气资源与探测国家重点实验室 CNPC物探重点实验室北京102249 中国海洋石油研究总院北京100027

The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

关键词： absorbing boundary condition elastic wave equation perfectly matched layer,finite-element modeling

The implementation of an improved NPML absorbing boundary condition in elastic wave modeling

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Applied Geophysics 2009年第2期6卷 113-121页

作者： Qin Zhen Lu Minghui Zheng Xiaodong Yao Yao Zhang Cai Song Jianyong Research Institute of Petroleum Exploration ＆ Development Beijing 100083 China Institute of Geophysics ＆ Geomatics China University of Geosciences Wuhan 430074 China Faculty of Resource ＆ Information China University of Petroleum Beijing 102249 China

In elastic wave forward modeling, absorbing boundary conditions （ABC） are used to mitigate undesired reflections from the model truncation boundaries. The perfectly matched layer （PML） has proved to be the best available ABC. However, the traditional splitting PML （SPML） ABC has some serious disadvantages： for example, global SPML ABCs require much more computing memory, although the implementation is easy. The implementation of local SPML ABCs also has some difficulties, since edges and corners must be considered. The traditional non-splitting perfectly matched layer （NPML） ABC has complex computation because of the convolution. In this paper, based on non-splitting perfectly matched layer （NPML） ABCs combined with the complex frequency-shifted stretching function （CFS）, we introduce a novel numerical implementation method for PML absorbing boundary conditions with simple calculation equations, small memory requirement, and easy programming.

关键词： PML absorbing boundary condition non-splitting forward modeling

Practical absorbing boundary conditions forWave Propagation on Arbitrary Domain

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Advances in Applied Mathematics and Mechanics 2020年第6期12卷 1384-1415页

作者： Fengru Wang Jerry Zhijian Yang Cheng Yuan School of Mathematics and Statistics Wuhan UniversityWuhanHubei 430072China Computational Science Hubei Key Laboratory Wuhan UniversityWuhanHubei 430072China

This paper presents an absorbing boundary conditions(ABCs)for wave propagations on arbitrary computational *** purpose of ABCs is to eliminate the unwanted spurious reflection at the artificial boundaries and minimize the finite size *** methods are usually complicate in theoretical derivation and implementation and work only for very limited types of boundary *** contrast to other existing methods,our emphasis is placed on the ease of *** particular,we propose a method for which the implementation can be done by fitting or learning from the simulation data in a larger domain,and it is insensitive to the geometry and space dimension of the computational ***,a stability criterion is imposed to ensure the stability of the proposed *** results are presented to demonstrate the effectiveness of our method.

关键词： absorbing boundary condition wave equations stability conditions

absorbing boundary conditions for Simulating Water Waves Near Solid Bodies

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Journal of Applied Mathematics and Physics 2024年第10期12卷 3502-3520页

作者： José Marie Orellana Mathematical and Numerical Modelling Laboratory (M2N) National Conservatory of Arts and Crafts Paris France

The objective of this paper is to present a new method for designing absorbing or non-reflective boundary conditions (ABC) or (NRBC), illustrated by the case study of the modelling of a solid body in water, specifically the capillary gravity waves generated by its motion at the surface. The study analyses the flow of an inviscid, barotropic, and compressible fluid around the stationary solid body. The dynamic behaviour of the fluid is analysed using a two-dimensional coupled Neumann-Kelvin model extended with capillarity and inertia terms. For computational purposes, it is necessary to truncate the unbounded spatial domain with artificial boundaries and then introduce appropriate absorbing boundary conditions. The propagation of short wavelength waves in a convective fluid medium with significant differences in properties between the interior and the surface of the fluid presents a number of difficulties in the design of these conditions. The results are illustrated numerically and commented upon.

关键词： absorbing boundary condition Fluid-Structure Interaction Capillary-Gravity Waves Numerical Simulations

Solution of the time-dependent Schrdinger equation with absorbing boundary conditions

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Journal of Semiconductors 2009年第1期30卷 1-6页

作者：陈志东张进宇余志平 Institute of Microelectronics Tsinghua University

The performances of absorbing boundary conditions （ABCs） in four widely used finite difference time domain （FDTD） methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schrodinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave packet is chosen to demonstrate the performances of the four methods combined with ABCs. It is found that ABCs perfectly eliminate reflection in implicit and explicit staggered-time methods. However, small reflection still exists in explicit and Chebyshev methods even though ABCs are applied.

关键词： finite difference time domain method absorbing boundary condition time-dependent Schrodinger equation

Well-Posedness of Initial boundary Value ProblemsAssociated with absorbing boundary conditions

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Systems Science and Systems Engineering 1999年第1期9卷 96-100页

作者： WEI Suhua(Department of APPlied Geophysics, China Univelsity of Geoscience, Beijing, 100083, China)Zhang Gang(Department of Mathematics, Shijiazhuang Colleage of Education, Shijiazhuang, China)

In this paper we get one-way wave equations by using pseudo-differential operator theory,and present a set of absorbing boundary conditions based on the higher order aPProximations of oneway wave equations. An integral identity is the key point of the approximation. Also, we have provedthe well-posedness of the initial boundary value Problems related to our absorbing boundary conditionsconstructed in this artical.

关键词： one-way wave equation well-posedness absorbing boundary condition initial boundaryvalue problem

Analysis of high-frequency local coupling instability induced by multi- transmitting formula - P-SV wave simulation in a 2D waveguide

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Earthquake Engineering and Engineering Vibration 2017年第1期16卷 1-10页

作者： Xie Zhinan Zhang Xubin Institute of Engineering Mechanics China Earthquake Administration Key Laboratory of Earthquake Engineering and Engineering vibration of China Earthquake Administration Harbin 150080 China

Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.

关键词： absorbing boundary condition local coupling instability dispersion analysis group velocity multi-transmitting formula

LAYER STRIPPING METHOD FOR POTENTIAL INVERSION

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Journal of Computational Mathematics 1999年第1期17卷 25-32页

作者： Dou, XL Zhang, GQ Chinese Acad Sci ICMSEC State Key Lab Sci & Engn Comp Beijing 100080 Peoples R China Beijing Res Inst Remote Sensing Informat Beijing 100011 Peoples R China

To solve the potential inversion problem of the coupled system for one-way wave equations, the absorbing boundary conditions in the lateral direction are derived. The difference schemes are constructed and a layer str... 详细信息

关键词： 2-D potential inversion layer stripping method absorbing boundary condition