Unsplit perfectly matched layer absorbing boundary conditions for second-order poroelastic wave equations

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 116-130 ◽  
Author(s):  
Yanbin He ◽  
Tianning Chen ◽  
Jinghuai Gao
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Second Order ◽  
Absorbing Boundary

Nonsplit complex-frequency shifted perfectly matched layer combined with symplectic methods for solving second-order seismic wave equations — Part 1: Method

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. T301-T311 ◽  
Author(s):  
Xiao Ma ◽  
Dinghui Yang ◽  
Xueyuan Huang ◽  
Yanjie Zhou
Keyword(s):  
Boundary Condition ◽  
Seismic Wave ◽  
Wave Equations ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Second Order ◽  
Complex Frequency ◽  
Absorbing Boundary ◽  
Time Layer ◽  
The Time Domain

The absorbing boundary condition plays an important role in seismic wave modeling. The perfectly matched layer (PML) boundary condition has been established as one of the most effective and prevalent absorbing boundary conditions. Among the existing PML-type conditions, the complex frequency shift (CFS) PML attracts considerable attention because it can handle the evanescent and grazing waves better. For solving the resultant CFS-PML equation in the time domain, one effective technique is to apply convolution operations, which forms the so-called convolutional PML (CPML). We have developed the corresponding CPML conditions with nonconstant grid compression parameter, and used its combination algorithms specifically with the symplectic partitioned Runge-Kutta and the nearly analytic SPRK methods for solving second-order seismic wave equations. This involves evaluating second-order spatial derivatives with respect to the complex stretching coordinates at the noninteger time layer. Meanwhile, two kinds of simplification algorithms are proposed to compute the composite convolutions terms contained therein.

scholarly journals ABSORBING BOUNDARY CONDITIONS FOR A WAVE EQUATION WITH A TEMPERATURE-DEPENDENT SPEED OF SOUND

2013 ◽  
Vol 21 (02) ◽  
pp. 1250028 ◽  
Author(s):  
IGOR SHEVCHENKO ◽  
MANFRED KALTENBACHER ◽  
BARBARA WOHLMUTH
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Speed Of Sound ◽  
Wave Equations ◽  
Focused Ultrasound ◽  
Absorbing Boundary Conditions ◽  
Second Order ◽  
High Intensity Focused Ultrasound ◽  
Temperature Dependent ◽  
Absorbing Boundary

In this work, new absorbing boundary conditions (ABCs) for a wave equation with a temperature-dependent speed of sound are proposed. Based on the theory of pseudo-differential calculus, first- and second-order ABCs for the one- and two-dimensional wave equations are derived. Both boundary conditions are local in space and time. The well-posedness of the wave equation with the developed ABCs is shown through the reduction of the original problem to an equivalent one for which the uniqueness and existence of the solution has already been established. Although the second-order ABC is more accurate, the numerical realization is more challenging. Here we use a Lagrange multiplier approach which fits into the abstract framework of saddle point formulations and yields stable results. Numerical examples illustrating stability, accuracy and flexibility of the ABCs are given. As a test setting, we perform computations for a high-intensity focused ultrasound (HIFU) application, which is a typical thermo-acoustic multi-physics problem.

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 acoustic and elastic wave equations

1977 ◽  
Vol 67 (6) ◽  
pp. 1529-1540 ◽  
Author(s):  
Robert Clayton ◽  
Björn Engquist
Keyword(s):  
Boundary Conditions ◽  
Elastic Wave ◽  
Wave Equations ◽  
Absorbing Boundary Conditions ◽  
Limited Area ◽  
Absorbing Boundary ◽  
Physical Behavior ◽  
Wide Range ◽  
Elastic Wave Equations ◽  
Numerical Wave

abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

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