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Outer Radiation Boundary Conditions
Published in Karl S. Kunz, Raymond J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, 2018
Karl S. Kunz, Raymond J. Luebbers
Alternate formulations using expansions other than the Taylor series expansion of Mur have been investigated5 in 2-D problem spaces. The one-way wave equation is expressed as () L-≡∂x−∂tc1−S2 () L−1W|x=0=0
The Principles of Migration
Published in E.A. Kozlov, Migration in Seismic Prospecting, 1990
The one-way wave equation (1.24) can also be transferred to the new co-ordinate system (1.67). For υ = const, θ = ±z/υ, one gets ∂P′∂z′=±i(ω′2v2+∂2∂x′2−ω′v)P′
Optical Waveguiding
Published in Joachim Piprek, Handbook of Optoelectronic Device Modeling and Simulation, 2017
If only one of the product components is considered, the so-called one-way wave equation is obtained ∂F∂z=−jL+ω2μεF.
Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer
Published in Waves in Random and Complex Media, 2018
Amin Rahimi Dalkhani, Abdolrahim Javaherian, Hadi Mahdavi Basir
All numerical methods of wave propagation modeling suffer from the problem of artificial reflections from boundaries introduced by a truncated computational domain. A variety of methods has been proposed to truncate a model while emulating it as being infinite. All the methods can be categorized in three main groups of the absorbing boundary, absorbing layer and hybrid. The absorbing boundary methods are trying to suppress spurious reflections in truncation point and are based on approximations of the one-way wave equation. The methods proposed by Clayton and Engquist [16], Reynolds [17] and Higdon [18,19] are the main absorbing boundary methods. Collino used auxiliary variables to avoid computation of high derivatives in Higdon method and is known as high order absorbing boundary condition (ABC) [20]. This method then discussed and implemented by several researchers such as [21–23]. The absorbing layer methods are introducing an extra boundary layer to the modeling domain and are trying to gradually suppress wave amplitude in this layer. The sponge boundary layer [24–26] and perfectly matched layer (PML) [27–30] are the main methods of absorbing layers. The hybrid methods are trying to combine absorbing boundary methods and absorbing layer methods by introducing a transition zone to create a smooth transition between the one-way and two-way wave equations [31–33]. Recently, a new method proposed by [34] as the double ABC used in seismic modeling by [35]. It uses Collino method on two parallel artificial boundaries. The auxiliary variables are defined on the two boundaries and inside the layer bounded by them [34], so it is an absorbing layer that uses high order ABCs.