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Volume 12, Issue 4
Stability of High-Order Finite-Difference Schemes for Poroelastic Wave Simulation

Wensheng Zhang & Atish Kumar Joardar

East Asian J. Appl. Math., 12 (2022), pp. 891-911.

Published online: 2022-08

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  • Abstract

The stability of high-order finite-difference schemes on a staggered-grid for two-dimensional poroelastic wave equations with spatially varying material parameters is studied. Using the energy method, we obtain sufficient stability conditions. This allows to find suitable time and spatial steps according to material parameters and the difference scheme coefficients. Two numerical examples verify the theoretical analysis and show that the corresponding range for the time step is close to that in the necessary condition. The perfectly matched layer is adopted in order to eliminate boundary reflections.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-891, author = {Zhang , Wensheng and Joardar , Atish Kumar}, title = {Stability of High-Order Finite-Difference Schemes for Poroelastic Wave Simulation}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {4}, pages = {891--911}, abstract = {

The stability of high-order finite-difference schemes on a staggered-grid for two-dimensional poroelastic wave equations with spatially varying material parameters is studied. Using the energy method, we obtain sufficient stability conditions. This allows to find suitable time and spatial steps according to material parameters and the difference scheme coefficients. Two numerical examples verify the theoretical analysis and show that the corresponding range for the time step is close to that in the necessary condition. The perfectly matched layer is adopted in order to eliminate boundary reflections.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260122.280422}, url = {http://global-sci.org/intro/article_detail/eajam/20889.html} }
TY - JOUR T1 - Stability of High-Order Finite-Difference Schemes for Poroelastic Wave Simulation AU - Zhang , Wensheng AU - Joardar , Atish Kumar JO - East Asian Journal on Applied Mathematics VL - 4 SP - 891 EP - 911 PY - 2022 DA - 2022/08 SN - 12 DO - http://doi.org/10.4208/eajam.260122.280422 UR - https://global-sci.org/intro/article_detail/eajam/20889.html KW - Stability, poroelastic wave equation, energy method, high-order scheme, wave simulation. AB -

The stability of high-order finite-difference schemes on a staggered-grid for two-dimensional poroelastic wave equations with spatially varying material parameters is studied. Using the energy method, we obtain sufficient stability conditions. This allows to find suitable time and spatial steps according to material parameters and the difference scheme coefficients. Two numerical examples verify the theoretical analysis and show that the corresponding range for the time step is close to that in the necessary condition. The perfectly matched layer is adopted in order to eliminate boundary reflections.

Wensheng Zhang & Atish Kumar Joardar. (2022). Stability of High-Order Finite-Difference Schemes for Poroelastic Wave Simulation. East Asian Journal on Applied Mathematics. 12 (4). 891-911. doi:10.4208/eajam.260122.280422
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