High-accuracy finite-difference schemes for solving elastodynamic problems in curvilinear coordinates within multiblock approach

Dovgilovich, Leonid; Sofronov, Ivan

doi:10.1016/j.apnum.2014.06.005

Cited by 28 publications

(17 citation statements)

References 26 publications

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“…Numerous computations with the proposed algorithm allow us to conclude the necessity of at least three more directions for further development of the method: (i)Use of schemes with higher orders of accuracy, e.g., the schemes that are proposed in (Dovgilovich ; Dovgilovich and Sofronov , , ). They are based on the summation‐by‐parts approach (Mattsson ; Strand ) and allow approximation of boundary conditions and the equations inside the block with fourth‐ and eighth‐order accuracy, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…(i) Use of schemes with higher orders of accuracy, e.g., the schemes that are proposed in (Dovgilovich 2013;Dovgilovich and Sofronov 2013, 2014a, 2014b. They are based on the summation-by-parts approach (Mattsson 2012;Strand 1994) and allow approximation of boundary conditions and the equations inside the block with fourth-and eighth-order accuracy, respectively.…”

Section: C O N C L U S I O N Smentioning

confidence: 99%

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Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Sofronov

Зайцев

Dovgilovich

2015

Geophysical Prospecting

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Prediction of elastic full wavefields is required for reverse time migration, full waveform inversion, borehole seismology, seismic modelling, etc. We propose a novel algorithm to solve the Navier wave equation, which is based on multi‐block methodology for high‐order finite‐difference schemes on curvilinear grids. In the current implementation, the blocks are subhorizontal layers. Smooth anisotropic heterogeneous media in each layer can have strong discontinuities at the interfaces. A curvilinear adaptive hexahedral grid in blocks is generated by mapping the original 3D physical domain onto a parametric cube with horizontal layers and interfaces. These interfaces correspond to the main curvilinear physical contrast interfaces of a subhorizontally layered formation. The top boundary of the parametric cube handles the land surface with smooth topography. Free‐surface and solid–solid transmission boundary conditions at interfaces are approximated with the second‐order accuracy. Smooth media in the layers are approximated up to sixth‐order spatial schemes. All expected properties of the developed algorithm are demonstrated in numerical tests using corresponding parallel message passing interface code.

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Section: Discussionmentioning

confidence: 99%

Section: C O N C L U S I O N Smentioning

confidence: 99%

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Sofronov

Зайцев

Dovgilovich

2015

Geophysical Prospecting

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“…ese operators can be referred to as classical SBP operators. Other types of SBP operators are generalized SBP [25,[33][34][35], multidimensional SBP [36,37], upwind SBP [38,39], and staggered and upwind SBP operators [40]. Generalized SBP operators have one or more characteristics of nonrepeating interior operators, nonuniform nodal distribution, and exclude one or both boundary nodes.…”

Section: Introductionmentioning

confidence: 99%

Multiblock SBP-SAT Methodology of Symmetric Matrix Form of Elastic Wave Equations on Curvilinear Grids

Sun

Yang

Jiang

et al. 2020

Shock and Vibration

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A stable and accurate finite-difference discretization of first-order elastic wave equations is derived in this work. To simplify the origin and proof of the formulas, a symmetric matrix form (SMF) for elastic wave equations is presented. The curve domain is discretized using summation-by-parts (SBP) operators, and the boundary conditions are weakly enforced using the simultaneous-approximation-term (SAT) technique, which gave rise to a provably stable high-order SBP-SAT method via the energy method. In addition, SMF can be extended to wave equations of different types (SH wave and P-SV wave) and dimensions, which can simplify the boundary derivation process and improve its applicability. Application of this approximation can divide the domain into a multiblock context for calculation, and the interface boundary conditions of blocks can also be used to simulate cracks and other structures. Several numerical simulation examples, including actual elevation within the area of Lushan, China, are presented, which verifies the viability of the framework present in this paper. The applicability of simulating elastic wave propagation and the application potential in the seismic numerical simulation of this method are also revealed.

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“…SBP introduced above can be referred to as a classical SBP operator. Recently, the theory of classical SBP operators has been extended to a broader set of operators, for instance, upwind SBP operators [28,29], staggered and upwind SBP operators [30], generalized SBP operators [31][32][33], and multi-dimensional SBP operators [34,35]. Newly proposed SBP operators have new properties not presented in the classical SBP operators.…”

Section: Introductionmentioning

confidence: 99%

Stable Symmetric Matrix Form Framework for the Elastic Wave Equation Combined with Perfectly Matched Layer and Discretized in the Curve Domain

2020

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In this paper, we present a stable and accurate high-order methodology for the symmetric matrix form (SMF) of the elastic wave equation. We use an accurate high-order upwind finite difference method to define spatial discretization. Then, an efficient complex frequency-shifted (CFS) unsplit multi-axis perfectly matched layer (MPML) is implemented using the auxiliary differential equation (ADE) that is used to build higher-order time schemes for elastodynamics in the unbounded curve domain. It is derived to be compatible with SMF. The SMF framework has a general form of a hyperbolic partial differential equation (PDE) that can be expanded to different dimensions (2D, 3D) or different wave modal (SH, P-SV) without requiring significant modifications owing to a simplified process of derivation and programming. Subsequently, an energy analysis on the framework combined with initial boundary value problems is conducted, and the stability analysis can be extended to a semi-discrete approximation similarly. Thus, we propose a semi-discrete approximation based on ADE CFS-MPML in which the curve domain is discretized using the upwind summation-by-parts (SBP) operators, and where the boundary conditions are enforced weakly using the simultaneous approximation terms (SAT). The proposed method’s robustness and adequacy are illustrated by conducting several numerical simulations.

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High-accuracy finite-difference schemes for solving elastodynamic problems in curvilinear coordinates within multiblock approach

Cited by 28 publications

References 26 publications

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Multiblock SBP-SAT Methodology of Symmetric Matrix Form of Elastic Wave Equations on Curvilinear Grids

Stable Symmetric Matrix Form Framework for the Elastic Wave Equation Combined with Perfectly Matched Layer and Discretized in the Curve Domain

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