scholarly journals Spectral methods for the wave equation in second-order form

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
Nicholas W. Taylor ◽  
Lawrence E. Kidder ◽  
Saul A. Teukolsky
Keyword(s):  
Wave Equation ◽  
Spectral Methods ◽  
Second Order ◽  
Order Form

scholarly journals Upwind schemes for the wave equation in second-order form

2012 ◽  
Vol 231 (17) ◽  
pp. 5854-5889 ◽  
Author(s):  
Jeffrey W. Banks ◽  
William D. Henshaw
Keyword(s):  
Wave Equation ◽  
Second Order ◽  
Upwind Schemes ◽  
Order Form

Stable Boundary Treatment for the Wave Equation on Second-Order Form

2009 ◽  
Vol 41 (3) ◽  
pp. 366-383 ◽  
Author(s):  
Ken Mattsson ◽  
Frank Ham ◽  
Gianluca Iaccarino
Keyword(s):  
Wave Equation ◽  
Second Order ◽  
Stable Boundary ◽  
Order Form ◽  
Boundary Treatment

Discontinuous Galerkin Galerkin Differences for the Wave Equation in Second-Order Form

2021 ◽  
Vol 43 (2) ◽  
pp. A1497-A1526
Author(s):  
J. W. Banks ◽  
B. Brett Buckner ◽  
T. Hagstrom ◽  
K. Juhnke
Keyword(s):  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Second Order ◽  
Order Form

Dynamic rupture and earthquake sequence simulations using the wave equation in second-order form

2019 ◽  
Vol 219 (2) ◽  
pp. 796-815 ◽  
Author(s):  
Kenneth Duru ◽  
Kali L Allison ◽  
Maxime Rivet ◽  
Eric M Dunham
Keyword(s):  
Wave Equation ◽  
Second Order ◽  
Stability And Convergence ◽  
Energy Estimates ◽  
Difference Operators ◽  
Dynamic Rupture ◽  
Discrete Energy ◽  
Order Form ◽  
Event Dynamic ◽  
Earthquake Sequences

SUMMARY We present a numerical method for simulating both single-event dynamic ruptures and earthquake sequences with full inertial effects in antiplane shear with rate-and-state fault friction. We use the second-order form of the wave equation, expressed in terms of displacements, discretized with high-order-accurate finite difference operators in space. Advantages of this method over other methods include reduced computational memory usage and reduced spurious high frequency oscillations. Our method handles complex geometries, such as non-planar fault interfaces and free surface topography. Boundary conditions are imposed weakly using penalties. We prove time stability by constructing discrete energy estimates. We present numerical experiments demonstrating the stability and convergence of the method, and showcasing applications of the method, including the transition in rupture style from crack-like ruptures to slip pulses for strongly rate-weakening friction and the simulation of earthquake sequences in a viscoelastic solid with a fully dynamic coseismic phase.

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