Stable and High-Order Accurate Boundary Treatments for the Elastic Wave Equation on Second-Order Form

2014 ◽  
Vol 36 (6) ◽  
pp. A2787-A2818 ◽  
Author(s):  
Kenneth Duru ◽  
Gunilla Kreiss ◽  
Ken Mattsson
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Second Order ◽  
High Order ◽  
Elastic Wave Equation ◽  
Order Form ◽  
Boundary Treatments

scholarly journals High-order cut finite elements for the elastic wave equation

2020 ◽  
Vol 46 (3) ◽  
Author(s):  
Simon Sticko ◽  
Gustav Ludvigsson ◽  
Gunilla Kreiss
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Elastic Wave ◽  
High Order ◽  
Elastic Wave Equation

Stable Difference Approximations for the Elastic Wave Equation in Second Order Formulation

2007 ◽  
Vol 45 (5) ◽  
pp. 1902-1936 ◽  
Author(s):  
Stefan Nilsson ◽  
N. Anders Petersson ◽  
Björn Sjögreen ◽  
Heinz-Otto Kreiss
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Second Order ◽  
Elastic Wave Equation ◽  
Difference Approximations

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

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 202
Author(s):  
Cheng Sun ◽  
Zailin Yang ◽  
Guanxixi Jiang
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Symmetric Matrix ◽  
Perfectly Matched Layer ◽  
High Order ◽  
Matrix Form ◽  
Discrete Approximation ◽  
Complex Frequency ◽  
Elastic Wave Equation

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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