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Explicit finite-difference method with time-step n-tupling and extended CFL stability limit for acoustic wave

Yingjie Gao1,2, Meng-Hua Zhu1,2, Huai Zhang3,4

  • 1State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China.

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This study introduces time step n-tupling for seismic wave simulations, enhancing computational efficiency by reducing iterations. This method maintains accuracy while overcoming Courant-Friedrichs-Lewy (CFL) stability limits.

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Area of Science:

  • Computational Seismology
  • Numerical Methods
  • Wave Propagation

Background:

  • Explicit finite-difference schemes are standard for seismic wave simulation.
  • Large time steps improve efficiency but reduce accuracy (temporal dispersion) and face Courant-Friedrichs-Lewy (CFL) stability limits.

Purpose of the Study:

  • Develop an explicit finite-difference method for acoustic wave simulation that increases computational efficiency.
  • Extend the CFL stability limit and maintain numerical accuracy with larger time steps.

Main Methods:

  • Developed an explicit finite-difference method with time step n-tupling based on the wavefield iteration equation in matrix form.
  • Constructed two n-tupling algorithms by combining n successive iteration operators.
  • Applied complementary strategies to suppress time dispersion.

Main Results:

  • The n-tupling method expands the CFL stability limit by a factor of n, allowing larger time steps.
  • Simulations achieved accuracy comparable to single-step methods with approximately 1/n computation time.
  • Time dispersion was effectively suppressed, ensuring high numerical accuracy.

Conclusions:

  • Time step n-tupling significantly enhances computational efficiency for seismic wave simulations.
  • The method overcomes traditional CFL limitations and maintains high accuracy.
  • This approach offers a viable solution for faster and more accurate seismic wave modeling.