Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation

2010 ◽  
Author(s):  
M. J. Grote ◽  
T. Mitkova ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Time Stepping ◽  
Local Time Stepping

Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation

2010 ◽  
Author(s):  
M. J. Grote ◽  
T. Mitkova ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Time Stepping ◽  
Local Time Stepping

scholarly journals Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. T67-T77 ◽  
Author(s):  
Sara Minisini ◽  
Elena Zhebel ◽  
Alexey Kononov ◽  
Wim A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Heterogeneous Media ◽  
Small Scale ◽  
Time Step ◽  
Element Discretization ◽  
Time Stepping ◽  
Local Time Stepping

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than finite-difference methods, but this is compensated by their superior accuracy if the finite-element mesh follows the sharp impedance contrasts and by their improved efficiency if the element size scales with wavelength, hence with the local wave velocity. However, 3D complex geologic settings often contain details on a very small scale compared to the dominant wavelength, requiring the mesh to contain elements that are smaller than dictated by the wavelength. Also, limitations of the mesh generation software may produce regions where the elements are much smaller than desired. In both cases, this leads to a reduction of the time step required to solve the wave propagation and significantly increases the computational cost. Local time stepping (LTS) can improve the computational efficiency and speed up the simulation. We evaluated a local formulation of an LTS scheme with second-order accuracy for the discontinuous Galerkin finite-element discretization of the wave equation. We tested the benefits of the scheme by considering a geologic model for a North-Sea-type example.

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