Reducing numerical dispersion and reflections in finite element and finite difference simulation of acoustic wave propagation and scattering

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

Download Full-text

Brillouin spectroscopy and finite element method study of surface acoustic wave propagation in clean and Fe3O4(111) covered Pt(111) and Ru(0001) single crystals

Surface and Coatings Technology ◽

10.1016/j.surfcoat.2015.01.055 ◽

2015 ◽

Vol 271 ◽

pp. 13-17 ◽

Cited By ~ 3

Author(s):

A. Trzaskowska ◽

S. Mielcarek ◽

M. Lewandowski ◽

Z. Miłosz ◽

N. Michalak ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Wave Propagation ◽

Acoustic Wave ◽

Single Crystals ◽

Surface Acoustic Wave ◽

Acoustic Wave Propagation ◽

Brillouin Spectroscopy ◽

Element Method

Download Full-text

Residual-driven online multiscale methods for acoustic-wave propagation in 2D heterogeneous media

Geophysics ◽

10.1190/geo2015-0659.1 ◽

2017 ◽

Vol 82 (2) ◽

pp. T69-T77

Author(s):

Eric T. Chung ◽

Yalchin Efendiev ◽

Richard L. Gibson ◽

Wing Tat Leung

Keyword(s):

Finite Element ◽

Wave Propagation ◽

Acoustic Wave ◽

Heterogeneous Media ◽

Computational Cost ◽

Multiscale Methods ◽

Basis Functions ◽

Acoustic Wave Propagation ◽

Fine Grid ◽

Multiscale Finite Element

Common applications, such as geophysical exploration, reservoir characterization, and earthquake quantification, in modeling and inversion aim to apply numerical simulations of elastic- or acoustic-wave propagation to increasingly large and complex models, which can provide more realistic and useful results. However, the computational cost of these simulations increases rapidly, which makes them inapplicable to certain problems. We apply a newly developed multiscale finite-element algorithm, the generalized multiscale finite-element method (GMsFEM), to address this challenge in simulating acoustic-wave propagation in heterogeneous media. The wave equation is solved on a coarse grid using multiscale basis functions that are chosen from the most dominant modes among those computed by solving relevant local problems on a fine-grid representation of the model. These multiscale basis functions are computed once in an off-line stage prior to the simulation of wave propagation. Because these calculations are localized to individual coarse cells, one can improve the accuracy of multiscale methods by revising and updating these basis functions during the simulation. These updated bases are referred to as online basis functions. This is a significant extension of previous applications of similar online basis functions to time-independent problems. We tested our new algorithm and numerical results for acoustic-wave propagation using the acoustic Marmousi model. Long-term developments have a strong potential to enhance inversion algorithms because the basis functions need not be regenerated everywhere. In particular, recomputation of basis functions is required only at regions in which the model is updated. Thus, our method allows faster simulations for repeated calculations, which are needed for inversion purpose.

Download Full-text