scholarly journals Optimal damping profile ratios for stabilization of perfectly matched layers in general anisotropic media

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. T15-T30 ◽  
Author(s):  
Kai Gao ◽  
Lianjie Huang
Keyword(s):  
Anisotropic Media ◽  
Complex Frequency ◽  
System Matrix ◽  
Perfectly Matched Layers ◽  
Numerical Examples ◽  
Damping Coefficients ◽  
Optimal Damping ◽  
The Stability ◽  
2D And 3D ◽  
Matched Layers

Conventional perfectly matched layers (PMLs) can be unstable for certain kinds of anisotropic media. The multiaxial PML removes such instability using nonzero damping coefficients in the directions tangential with the PML interface. Although using nonzero damping profile ratios can stabilize PMLs, it is important to obtain the smallest possible damping profile ratios to minimize artificial reflections caused by these nonzero ratios, particularly for 3D general anisotropic media. Using the eigenvectors of the PML system matrix, we have developed a straightforward and efficient numerical algorithm to determine the optimal damping profile ratios to stabilize PMLs in 2D and 3D general anisotropic media. Numerical examples indicate that our algorithm provides optimal damping profile ratios to ensure the stability of PMLs and complex-frequency-shifted PMLs for elastic-wave modeling in 2D and 3D general anisotropic media.

Modelling Seismic Oceanography Experiments by Using First- and Second-Order Complex Frequency Shifted Perfectly Matched Layers

2009 ◽  
Vol 95 (6) ◽  
pp. 1104-1111 ◽  
Author(s):  
Jean Kormann ◽  
Pedro Cobo ◽  
Manuel Recuero ◽  
Berta Biescas ◽  
Valentí Sallarés
Keyword(s):  
Second Order ◽  
Complex Frequency ◽  
Order Complex ◽  
Perfectly Matched Layers ◽  
Seismic Oceanography ◽  
Matched Layers

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

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