Leading and Second Order Homogenization of an Elastic Scattering Problem for Highly Oscillating Anisotropic Medium
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or...
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| Published in | Journal of elasticity Vol. 137; no. 2; pp. 177 - 217 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Springer Netherlands
01.12.2019
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| Abstract | We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or overall wave field. We further pursue a higher-order homogenization with the help of complimentary boundary correctors and provide a detailed analysis on the rate of higher-order convergence. Finally we provide preliminary numerical examples to demonstrate the higher-order homogenization. |
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| AbstractList | We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or overall wave field. We further pursue a higher-order homogenization with the help of complimentary boundary correctors and provide a detailed analysis on the rate of higher-order convergence. Finally we provide preliminary numerical examples to demonstrate the higher-order homogenization. |
| Author | Lin, Yi-Hsuan Meng, Shixu |
| Author_xml | – sequence: 1 givenname: Yi-Hsuan surname: Lin fullname: Lin, Yi-Hsuan organization: Institute for Advanced Study, The Hong Kong University Science and Technology – sequence: 2 givenname: Shixu surname: Meng fullname: Meng, Shixu email: shixumen@umich.edu organization: Department of Mathematics, University of Michigan |
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| Title | Leading and Second Order Homogenization of an Elastic Scattering Problem for Highly Oscillating Anisotropic Medium |
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