A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 98; no. 3; p. 65
Main Authors: Yao, Jianan, Xie, Baoling, Lai, Jun
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2024
Springer Nature B.V
Subjects:
Algorithms
Asymptotic properties
Boundary integral method
Boundary value problems
Computational Mathematics and Numerical Analysis
Decomposition
Domains
Eigenvalues
Elastic scattering
Elastic waves
Integral equations
Integrals
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Nondestructive testing
Numerical analysis
Operators (mathematics)
Preconditioning
Radiation
Robustness (mathematics)
Smooth boundaries
Theoretical
Wave scattering
Nyström method
Elastic wave scattering
RCIP method
65R20
45L05
75B05
Kernel-splitting method
35J05
Navier equations
45E05
Boundary integral equations
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic elastic wave scattering problems from cornered domains via the boundary integral equations in two dimensions. The approach is based on the combination of Nyström discretization, analytical singular integrals and kernel-splitting method, which results in a high-order solver for smooth boundaries. It is then combined with the recursively compressed inverse preconditioning (RCIP) method to solve elastic scattering problems from cornered domains. Numerical experiments demonstrate that the proposed approach achieves high accuracy, with stabilized errors close to machine precision in various geometric configurations. The algorithm is further applied to investigate the asymptotic behavior of density functions associated with boundary integral operators near corners, and the numerical results are highly consistent with the theoretical formulas.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02453-0