scholarly journals High Order Space-Time Discretization for Elastic Wave Propagation Problems

2013 ◽  
pp. 87-97 ◽  
Author(s):  
Paola F. Antonietti ◽  
Ilario Mazzieri ◽  
Alfio Quarteroni ◽  
Francesca Rapetti
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Time Discretization ◽  
Space Time ◽  
High Order ◽  
Elastic Wave Propagation

Temporal high-order staggered-grid finite-difference schemes for elastic wave propagation

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. T207-T224 ◽  
Author(s):  
Zhiming Ren ◽  
Zhen Chun Li
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
High Order ◽  
Elastic Wave Propagation ◽  
Staggered Grid ◽  
S Wave ◽  
Order Accuracy ◽  
Spatial Derivatives

The traditional high-order finite-difference (FD) methods approximate the spatial derivatives to arbitrary even-order accuracy, whereas the time discretization is still of second-order accuracy. Temporal high-order FD methods can improve the accuracy in time greatly. However, the present methods are designed mainly based on the acoustic wave equation instead of elastic approximation. We have developed two temporal high-order staggered-grid FD (SFD) schemes for modeling elastic wave propagation. A new stencil containing the points on the axis and a few off-axial points is introduced to approximate the spatial derivatives. We derive the dispersion relations of the elastic wave equation based on the new stencil, and we estimate FD coefficients by the Taylor series expansion (TE). The TE-based scheme can achieve ([Formula: see text])th-order spatial and ([Formula: see text])th-order temporal accuracy ([Formula: see text]). We further optimize the coefficients of FD operators using a combination of TE and least squares (LS). The FD coefficients at the off-axial and axial points are computed by TE and LS, respectively. To obtain accurate P-, S-, and converted waves, we extend the wavefield decomposition into the temporal high-order SFD schemes. In our modeling, P- and S-wave separation is implemented and P- and S-wavefields are propagated by P- and S-wave dispersion-relation-based FD operators, respectively. We compare our schemes with the conventional SFD method. Numerical examples demonstrate that our TE-based and TE + LS-based schemes have greater accuracy in time and better stability than the conventional method. Moreover, the TE + LS-based scheme is superior to the TE-based scheme in suppressing the spatial dispersion. Owing to the high accuracy in the time and space domains, our new SFD schemes allow for larger time steps and shorter operator lengths, which can improve the computational efficiency.

scholarly journals A simplified high order doubly asymptotic open boundary for modeling elastic wave propagation in layered foundation

2016 ◽  
Vol 46 (5) ◽  
pp. 527-534
Author(s):  
YiChao GAO ◽  
ChongMin SONG ◽  
Feng JIN ◽  
YanJie XU
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
High Order ◽  
Elastic Wave Propagation ◽  
Open Boundary

scholarly journals FICTITIOUS DOMAINS, MIXED FINITE ELEMENTS AND PERFECTLY MATCHED LAYERS FOR 2-D ELASTIC WAVE PROPAGATION

2001 ◽  
Vol 09 (03) ◽  
pp. 1175-1201 ◽  
Author(s):  
E. BÉCACHE ◽  
P. JOLY ◽  
C. TSOGKA
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Elements ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Mixed Finite Elements ◽  
Time Discretization ◽  
Elastic Wave Propagation ◽  
Perfectly Matched Layers ◽  
Simple Geometry

We design a new and efficient numerical method for the modelization of elastic wave propagation in domains with complex topographies. The main characteristic is the use of the fictitious domain method for taking into account the boundary condition on the topography: the elastodynamic problem is extended in a domain with simple geometry, which permits us to use a regular mesh. The free boundary condition is enforced introducing a Lagrange multiplier, defined on the boundary and discretized with a nonuniform boundary mesh. This leads us to consider the first-order velocity-stress formulation of the equations and particular mixed finite elements. These elements have three main nonstandard properties: they take into account the symmetry of the stress tensor, they are compatible with mass lumping techniques and lead to explicit time discretization schemes, and they can be coupled with the Perfectly Matched Layer technique for the modeling of unbounded domains. Our method permits us to model wave propagation in complex media such as anisotropic, heterogeneous media with complex topographies, as it will be illustrated by several numerical experiments.

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