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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Format | Journal Article |
Language | English |
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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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Cites_doi | 10.1016/S0165-2125(02)00091-4 10.1007/s007910050004 10.1115/1.1357165 10.1002/nme.424 10.1137/15M1018009 10.1103/PhysRevLett.115.094301 10.1016/j.jmps.2015.03.001 10.1007/978-1-4614-8827-9 10.1111/j.1365-246X.2007.03462.x 10.1038/nphys1804 10.1088/1367-2630/8/10/248 10.1002/cpa.3160420203 10.1002/nme.423 10.1002/cpa.3160400607 10.1038/nature12608 10.1137/0151049 10.1007/s00205-017-1103-6 10.1007/s00205-011-0469-0 10.1002/cpa.21482 10.1016/j.matpur.2018.01.007 |
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References | Capdeville, Marigo (CR8) 2007; 170 Kenig, Lin, Shen (CR16) 2012; 203 Schöberl (CR25) 1997; 1 Chen, Fish (CR9) 2001; 68 CR15 Fish, Chen, Nagai (CR12) 2002; 54 McLean (CR20) 2000 Santosa, Symes (CR24) 1991; 51 Gächter, Grote (CR13) 2003; 37 Cakoni, Guzina, Moskow (CR7) 2016; 48 Geng, Shen, Song (CR14) 2017; 224 Maldovan (CR19) 2013; 503 Bensoussan, Lions, Papanicolaou (CR5) 2011 Kenig, Lin, Shen (CR17) 2014; 67 Allaire, Briane, Vanninathan (CR1) 2016; 73 Cakoni, Colton (CR6) 2014 Milton, Briane, Willis (CR22) 2006; 8 Pavliotis, Stuart (CR23) 2008 Zhu, Christensen, Jung, Martin-Moreno, Yin, Fok, Zhang, Garcia-Vidal (CR28) 2011; 7 Fish, Chen, Nagai (CR11) 2002; 54 CR26 Wautier, Guzina (CR27) 2015; 78 Cioranescu, Donato (CR10) 2000 CR21 Lambert, Näsholm, Nordsletten, Michler, Juge, Serfaty, Bilston, Guzina, Holm, Sinkus (CR18) 2015; 115 Avellaneda, Lin (CR2) 1987; 40 Bao, Hu, Sun, Yin (CR4) 2018; 117 Avellaneda, Lin (CR3) 1989; 42 M. Avellaneda (9725_CR2) 1987; 40 C. Kenig (9725_CR16) 2012; 203 M. Avellaneda (9725_CR3) 1989; 42 A. Wautier (9725_CR27) 2015; 78 9725_CR15 G.A. Pavliotis (9725_CR23) 2008 J. Schöberl (9725_CR25) 1997; 1 A. Bensoussan (9725_CR5) 2011 G.W. Milton (9725_CR22) 2006; 8 F. Cakoni (9725_CR6) 2014 C. Kenig (9725_CR17) 2014; 67 J. Zhu (9725_CR28) 2011; 7 Y. Capdeville (9725_CR8) 2007; 170 M. Maldovan (9725_CR19) 2013; 503 G.K. Gächter (9725_CR13) 2003; 37 G. Allaire (9725_CR1) 2016; 73 9725_CR21 W. Chen (9725_CR9) 2001; 68 S.A. Lambert (9725_CR18) 2015; 115 J. Fish (9725_CR12) 2002; 54 F. Cakoni (9725_CR7) 2016; 48 9725_CR26 J. Fish (9725_CR11) 2002; 54 W.C.H. McLean (9725_CR20) 2000 J. Geng (9725_CR14) 2017; 224 G. Bao (9725_CR4) 2018; 117 F. Santosa (9725_CR24) 1991; 51 D. Cioranescu (9725_CR10) 2000 |
References_xml | – year: 2011 ident: CR5 publication-title: Asymptotic Analysis for Periodic Structures contributor: fullname: Papanicolaou – volume: 37 start-page: 293 issue: 3 year: 2003 end-page: 311 ident: CR13 article-title: Dirichlet-to-Neumann map for three-dimensional elastic waves publication-title: Wave Motion doi: 10.1016/S0165-2125(02)00091-4 contributor: fullname: Grote – volume: 1 start-page: 41 issue: 1 year: 1997 end-page: 52 ident: CR25 article-title: NETGEN an advancing front 2D/3D-mesh generator based on abstract rules publication-title: Comput. Vis. Sci. doi: 10.1007/s007910050004 contributor: fullname: Schöberl – volume: 68 start-page: 153 issue: 2 year: 2001 end-page: 161 ident: CR9 article-title: A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales publication-title: J. Appl. Mech. doi: 10.1115/1.1357165 contributor: fullname: Fish – volume: 54 start-page: 347 issue: 3 year: 2002 end-page: 363 ident: CR11 article-title: Non-local dispersive model for wave propagation in heterogeneous media: multi-dimensional case publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.424 contributor: fullname: Nagai – volume: 48 start-page: 2532 issue: 4 year: 2016 end-page: 2560 ident: CR7 article-title: On the homogenization of a scalar scattering problem for highly oscillating anisotropic media publication-title: SIAM J. Math. Anal. doi: 10.1137/15M1018009 contributor: fullname: Moskow – volume: 115 issue: 9 year: 2015 ident: CR18 article-title: Bridging three orders of magnitude: multiple scattered waves sense fractal microscopic structures via dispersion publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.115.094301 contributor: fullname: Sinkus – volume: 78 start-page: 382 year: 2015 end-page: 414 ident: CR27 article-title: On the second-order homogenization of wave motion in periodic media and the sound of a chessboard publication-title: J. Mech. Phys. Solids doi: 10.1016/j.jmps.2015.03.001 contributor: fullname: Guzina – year: 2014 ident: CR6 publication-title: A Qualitative Approach to Inverse Scattering Theory doi: 10.1007/978-1-4614-8827-9 contributor: fullname: Colton – volume: 170 start-page: 823 issue: 2 year: 2007 end-page: 838 ident: CR8 article-title: Second order homogenization of the elastic wave equation for non-periodic layered media publication-title: Geophys. J. Int. doi: 10.1111/j.1365-246X.2007.03462.x contributor: fullname: Marigo – volume: 7 start-page: 52 issue: 1 year: 2011 end-page: 55 ident: CR28 article-title: A holey-structured metamaterial for acoustic deep-subwavelength imaging publication-title: Nat. Phys. doi: 10.1038/nphys1804 contributor: fullname: Garcia-Vidal – volume: 8 start-page: 248 issue: 10 year: 2006 ident: CR22 article-title: On cloaking for elasticity and physical equations with a transformation invariant form publication-title: New J. Phys. doi: 10.1088/1367-2630/8/10/248 contributor: fullname: Willis – volume: 42 start-page: 139 issue: 2 year: 1989 end-page: 172 ident: CR3 article-title: Compactness methods in the theory of homogenization II: equations in non-divergence form publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160420203 contributor: fullname: Lin – volume: 54 start-page: 331 issue: 3 year: 2002 end-page: 346 ident: CR12 article-title: Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.423 contributor: fullname: Nagai – volume: 40 start-page: 803 issue: 6 year: 1987 end-page: 847 ident: CR2 article-title: Compactness methods in the theory of homogenization publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160400607 contributor: fullname: Lin – volume: 503 start-page: 209 issue: 7475 year: 2013 end-page: 217 ident: CR19 article-title: Sound and heat revolutions in phononics publication-title: Nature doi: 10.1038/nature12608 contributor: fullname: Maldovan – ident: CR21 – volume: 51 start-page: 984 issue: 4 year: 1991 end-page: 1005 ident: CR24 article-title: A dispersive effective medium for wave propagation in periodic composites publication-title: SIAM J. Appl. Math. doi: 10.1137/0151049 contributor: fullname: Symes – volume: 73 start-page: 237 issue: 3 year: 2016 end-page: 259 ident: CR1 article-title: A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures publication-title: Bol. Soc. Esp. Mat. Apl. contributor: fullname: Vanninathan – year: 2000 ident: CR20 publication-title: Strongly Elliptic Systems and Boundary Integral Equations contributor: fullname: McLean – volume: 224 start-page: 1205 issue: 3 year: 2017 end-page: 1236 ident: CR14 article-title: Boundary Korn inequality and Neumann problems in homogenization of systems of elasticity publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-017-1103-6 contributor: fullname: Song – ident: CR15 – year: 2008 ident: CR23 publication-title: Multiscale Methods: Averaging and Homogenization contributor: fullname: Stuart – volume: 203 start-page: 1009 issue: 3 year: 2012 end-page: 1036 ident: CR16 article-title: Convergence rates in for elliptic homogenization problems publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-011-0469-0 contributor: fullname: Shen – year: 2000 ident: CR10 publication-title: Introduction to Homogenization contributor: fullname: Donato – volume: 67 start-page: 1219 issue: 8 year: 2014 end-page: 1262 ident: CR17 article-title: Periodic homogenization of Green and Neumann functions publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21482 contributor: fullname: Shen – ident: CR26 – volume: 117 start-page: 263 year: 2018 end-page: 301 ident: CR4 article-title: Direct and inverse elastic scattering from anisotropic media publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2018.01.007 contributor: fullname: Yin – volume-title: Asymptotic Analysis for Periodic Structures year: 2011 ident: 9725_CR5 contributor: fullname: A. Bensoussan – volume: 7 start-page: 52 issue: 1 year: 2011 ident: 9725_CR28 publication-title: Nat. Phys. doi: 10.1038/nphys1804 contributor: fullname: J. Zhu – volume: 78 start-page: 382 year: 2015 ident: 9725_CR27 publication-title: J. Mech. Phys. Solids doi: 10.1016/j.jmps.2015.03.001 contributor: fullname: A. Wautier – volume: 170 start-page: 823 issue: 2 year: 2007 ident: 9725_CR8 publication-title: Geophys. J. Int. doi: 10.1111/j.1365-246X.2007.03462.x contributor: fullname: Y. Capdeville – volume: 51 start-page: 984 issue: 4 year: 1991 ident: 9725_CR24 publication-title: SIAM J. Appl. Math. doi: 10.1137/0151049 contributor: fullname: F. Santosa – volume: 54 start-page: 347 issue: 3 year: 2002 ident: 9725_CR11 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.424 contributor: fullname: J. Fish – volume: 67 start-page: 1219 issue: 8 year: 2014 ident: 9725_CR17 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.21482 contributor: fullname: C. Kenig – volume: 40 start-page: 803 issue: 6 year: 1987 ident: 9725_CR2 publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160400607 contributor: fullname: M. Avellaneda – volume: 117 start-page: 263 year: 2018 ident: 9725_CR4 publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2018.01.007 contributor: fullname: G. Bao – volume-title: Multiscale Methods: Averaging and Homogenization year: 2008 ident: 9725_CR23 contributor: fullname: G.A. Pavliotis – ident: 9725_CR26 – volume: 224 start-page: 1205 issue: 3 year: 2017 ident: 9725_CR14 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-017-1103-6 contributor: fullname: J. 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Title | Leading and Second Order Homogenization of an Elastic Scattering Problem for Highly Oscillating Anisotropic Medium |
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