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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Vydáno v:	Advances in computational mathematics Ročník 48; číslo 3
Hlavní autoři:	Lai, J., Dong, H.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.06.2022 Springer Nature B.V
Témata:	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
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Abstract	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.
AbstractList	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.
ArticleNumber	20
Author	Dong, H. Lai, J.
Author_xml	– sequence: 1 givenname: J. surname: Lai fullname: Lai, J. organization: School of Mathematical Sciences, Zhejiang University – sequence: 2 givenname: H. orcidid: 0000-0002-7241-4064 surname: Dong fullname: Dong, H. email: dhp@jlu.edu.cn organization: School of Mathematics, Jilin University
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Snippet	Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic...
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SubjectTerms	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
Title	A fast solver for elastic scattering from axisymmetric objects by boundary integral equations
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