Optimal Fourth-order Staggered-grid Finite-difference Scheme for 3D Frequency-domain Viscoelastic Wave Modeling

Li, Y.; Han, Bo; Chen, Y.; He, Qun

doi:10.3997/2214-4609.201413341

Cited by 2 publications

(12 citation statements)

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“…That is not the case with nodal discretizations. Finally, it is worthy to note that we use this second order scheme, as in [59,41], to demonstrate our solver, but expect that it will also be effective for the high-order staggered discretizations [28,29]. That is similarly to [20] and [55] which show that the shifted Laplacian methods works with similar efficiency for both second order and high-order nodal schemes for the acoustic Helmholtz case.…”

Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 68%

“…µ = µ( x) and λ = λ( x) are the Lame parameters, and ρ is the density of the medium as in (1.1). These parameters determine the pressure and shear wave velocities by V p = λ+2µ ρ , and V s = µ ρ , respectively [29]. The term…”

Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 99%

“…On the other hand, compact high-order finite difference discretizations are currently not available. For example, the fourth order schemes of [28,29] create stencils that are wider than the 27-point stencil block, because the gradient itself is approximated by a fourth order operator. This leads to relatively high memory access time in matrix-vector products, and relatively high fill-in using direct methods.…”

Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 99%

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A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations

Treister¹,

Yovel²

2018

Preprint

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The shifted Laplacian multigrid method is a well known approach for preconditioning the indefinite linear system arising from the discretization of the acoustic Helmholtz equation. This equation is used to model wave propagation in the frequency domain. However, in some cases the acoustic equation is not sufficient for modeling the physics of the wave propagation, and one has to consider the elastic Helmholtz equation. Such a case arises in geophysical seismic imaging applications, where the earth's subsurface is the elastic medium. The elastic Helmholtz equation is much harder to solve than its acoustic counterpart, partially because it is three times larger, and partially because it models more complicated physics. Despite this, there are very few solvers available for the elastic equation compared to the array of solvers that are available for the acoustic one. In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation, by combining the complex shift idea with approaches for linear elasticity. We demonstrate the efficiency and properties of our solver using numerical experiments for problems with heterogeneous media in two and three dimensions.

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Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 68%

Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 99%

Section: Introduction the Helmholtz Equation Is Used To Model The Pro...mentioning

confidence: 99%

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A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations

Treister¹,

Yovel²

2018

Preprint

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show abstract

“…CARP‐CG is the parallel equivalent of the Björck and Elfving's CGMN algorithm 29 . It was also used in several previous works on elasticity; see References 14,15,30. The following is a brief outline of CARP‐CG.…”

Section: Implementation Detailsmentioning

confidence: 99%

“…The ability to handle variable wave speeds is essential for many applications in which the domain is heterogeneous. For the solver of the elastic equation, we use the CARP‐CG algorithm, 22 which was very useful for solving the Helmholtz equation at high frequencies 18,23,24 and for the elastic wave equation 14,15 . For the elastic equation, we do not use any absorbing boundary conditions, as our purpose is to test the accuracy of the compact fourth‐order scheme.…”

Section: Introductionmentioning

confidence: 99%

A compact three‐dimensional fourth‐order scheme for elasticity using the first‐order formulation

Gordon

Turkel

Gordon

2021

Numerical Meth Engineering

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We develop a compact fourth-order scheme for the three-dimensional elastic wave equation in frequency space, using the first-order velocity-stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one-directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second-order scheme.

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Optimal Fourth-order Staggered-grid Finite-difference Scheme for 3D Frequency-domain Viscoelastic Wave Modeling

Cited by 2 publications

References 0 publications

A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations

A hybrid shifted Laplacian multigrid and domain decomposition preconditioner for the elastic Helmholtz equations

A compact three‐dimensional fourth‐order scheme for elasticity using the first‐order formulation

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