A fast solver for elastic scattering from axisymmetric objects by boundary integral equations

Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a novel boundary integral formulation for the three-dimensional...

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Bibliographic Details
Published in:Advances in computational mathematics Vol. 48; no. 3
Main Authors: Lai, J., Dong, H.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Advances in Computational Integral Equations
Algorithms
Axisymmetric bodies
Boundary integral method
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Elastic scattering
Geometric accuracy
Green's functions
Integral equations
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Maxwell's equations
Operators (mathematics)
Regularization
Rigid structures
Solvers
Visualization
Nyström method
Elastic wave scattering
65R20
45L05
Helmholtz decomposition
75B05
35J05
Navier equations
45E05
Boundary integral equations
ISSN:1019-7168, 1572-9044
Online Access:Get full text
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Summary:Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a novel boundary integral formulation for the three-dimensional elastic scattering based on the Helmholtz decomposition of elastic fields, which converts the Navier equation to a coupled system consisted of Helmholtz and Maxwell equations. An FFT-accelerated separation of variables solver is proposed to efficiently invert boundary integral formulations of the coupled system for elastic scattering from axisymmetric rigid bodies. In particular, by combining the regularization properties of the singular boundary integral operators and the FFT-based fast evaluation of modal Green’s functions, our numerical solver can rapidly solve the resulting integral equations with a high-order accuracy. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed algorithm, including geometries with corners at different wavenumbers.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-022-09935-5