Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures

We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize disper...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Numerische Mathematik Ročník 140; číslo 2; s. 265 - 326
Hlavní autori:	Allaire, Grégoire, Yamada, T
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Science and Business Media LLC 01.10.2018 Springer Berlin Heidelberg Springer Nature B.V Springer Verlag
Predmet:	49K20 [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Bloch waves dispersion homogenization Lower bounds Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematics Mathematics and Statistics MSC 35B27 MSC 35B27, 49K20 Numerical Analysis Numerical and Computational Physics Optimization Optimization and Control periodic structure Periodic structures Periodic variations shape optimization Simulation Theoretical Wave dispersion Wave equations Wave propagation 35B27 49K20 homogenization periodic structure shape optimization Bloch waves dispersion
ISSN:	0029-599X, 0945-3245
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries.
AbstractList	We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries. We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an 8-fold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries.
Author	Yamada, T Allaire, Grégoire
Author_xml	– sequence: 1 fullname: Allaire, Grégoire – sequence: 2 orcidid: 0000-0002-5349-6690 fullname: Yamada, T
BackLink	https://cir.nii.ac.jp/crid/1874242817443049856$$DView record in CiNii https://hal.science/hal-01341082$$DView record in HAL
BookMark	eNp9kc9rFDEUx4NUsK39A7wN6MXD6HtJZpMcS7G2sNCLQm9hNj-6KbvJNslU9K9vxqkoHnpJwuPzeXxf3gk5iik6Qt4hfEIA8bkAUMQeUPagBO35K3IMig89o3w4am-gqh-Uun1DTkq5B0Cx4nhMws2hhn34NdaQYpd8Z0M5uFzCo-tMct4HE1yspQuxq1vXbdM-3bn4jzBXf4wNdw_TUmxoaxGSDaYrNU-mTtmVt-S1H3fFnT3fp-T75ZdvF1f9-ubr9cX5ujecD7VnjrKNVGZgIx2kstIik55vrEDfRrEb71cgKBiUFtrJV0itbbT1QhoB7JR8XPpux50-5LAf80-dxqCvztd6rgEyjiDpIzb2_cIecnqYXKn6Pk05tniaglJKtE9ljRILZXIqJTuvTai_R615DDuNoOcd6GUHrb_U8w40byb-Z_4J9JJDF6c0Nt65_DfTS9KHRYohtHTziVJwyqlEwTkDruSwYk_X9aWd
CitedBy_id	crossref_primary_10_1080_27660400_2024_2320691 crossref_primary_10_1137_23M1593528 crossref_primary_10_3233_ASY_211707 crossref_primary_10_1016_j_euromechsol_2023_104979 crossref_primary_10_1137_20M1348078 crossref_primary_10_1002_zamm_202100227 crossref_primary_10_1038_s41598_022_08144_w crossref_primary_10_1016_j_jmr_2018_11_006 crossref_primary_10_1016_j_jmps_2021_104773 crossref_primary_10_3233_ASY_241923 crossref_primary_10_1002_nme_6352
Cites_doi	10.1007/s00466-002-0382-3 10.1016/0022-5096(63)90060-7 10.1007/978-3-642-58106-9 10.1051/m2an/1995290606571 10.1080/00036811.2011.625017 10.1364/JOSAB.25.000088 10.1007/BF02484273 10.1006/jcph.2001.6789 10.1137/13094195X 10.1007/s00205-011-0452-9 10.1016/0020-7683(94)90154-6 10.1103/PhysRevE.54.3621 10.1016/j.jcp.2011.03.024 10.1002/nme.424 10.1364/JOSAB.16.000441 10.1515/jiip.2010.015 10.1063/1.2919066 10.1007/978-3-642-84659-5 10.1142/S021820251100557X 10.1137/15M1025633 10.1088/0266-5611/14/1/008 10.1007/978-94-009-2247-1 10.1137/S0036141001382200 10.1137/0151049 10.1299/mej.2014cm0039 10.1137/130935033 10.1017/S0308210500027050 10.1016/S0022-5096(99)00090-3 10.1063/1.2179048 10.1007/978-3-642-87722-3 10.1007/978-1-4684-9286-6 10.1007/s40324-016-0067-z 10.1137/S0036139995294743 10.1051/cocv/2013076 10.1016/0021-9991(88)90002-2 10.1080/17455030701501851 10.1142/S0252959903000189 10.1016/S0045-7825(02)00559-5 10.1016/j.jcp.2003.09.032 10.1142/S0218202509003930 10.1098/rspa.2009.0516 10.1016/j.cma.2003.10.008 10.1016/j.crma.2005.07.005 10.1007/BF02790171 10.1007/BFb0063630 10.1007/978-3-642-05195-1 10.1007/978-1-4612-2032-9_3 10.1090/gsm/133
ContentType	Journal Article
Contributor	Kyoto University École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) Department of Mechanical Engineering and Science Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP) ; Institut National de Recherche en Informatique et en Automatique (Inria)-École polytechnique (X) ; Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS) Post-doctoral fellowship of the Japan Society for the Promotion of Science Department of Mechanical Engineering and Science ; Kyoto University Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) ; École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) Department of Mechanical Engineering and Science ; Kyoto University [Kyoto]
Contributor_xml	– sequence: 1 fullname: Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP) ; Institut National de Recherche en Informatique et en Automatique (Inria)-École polytechnique (X) ; Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS) – sequence: 2 fullname: Department of Mechanical Engineering and Science ; Kyoto University – sequence: 3 fullname: Post-doctoral fellowship of the Japan Society for the Promotion of Science – sequence: 4 fullname: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) ; École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) – sequence: 5 fullname: Department of Mechanical Engineering and Science ; Kyoto University [Kyoto] – sequence: 6 fullname: Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) – sequence: 7 fullname: École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) – sequence: 8 fullname: Department of Mechanical Engineering and Science – sequence: 9 fullname: Kyoto University
Copyright	Springer-Verlag GmbH Germany, part of Springer Nature 2018 Copyright Springer Science & Business Media 2018 licence_http://creativecommons.org/publicdomain/zero
Copyright_xml	– notice: Springer-Verlag GmbH Germany, part of Springer Nature 2018 – notice: Copyright Springer Science & Business Media 2018 – notice: licence_http://creativecommons.org/publicdomain/zero
DBID	RYH AAYXX CITATION 1XC VOOES
DOI	10.1007/s00211-018-0972-4
DatabaseName	CiNii Complete CrossRef Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access)
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science Mathematics
EISSN	0945-3245
EndPage	326
ExternalDocumentID	oai:HAL:hal-01341082v1 10_1007_s00211_018_0972_4
GroupedDBID	--Z -~C -~X .86 .DC .VR 06D 0R~ 0VY 123 199 1N0 203 29N 2J2 2JN 2JY 2KG 2KM 2LR 2WC 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 6TJ 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN ABAKF ABBBX ABBRH ABBXA ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABUFD ABWNU ABXPI ACAOD ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACSTC ACZOJ ADHHG ADHIR ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFLOW AFOHR AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAS LLZTM M4Y MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P9R PF0 PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV RYH S16 S27 S3B SAP SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 YLTOR YNT YQT Z45 ZMTXR ~EX -52 -5D -5G -BR -EM -Y2 1SB 2P1 2VQ 41~ 5QI 692 AARHV AAYTO AAYZH ABQSL ABULA ACBXY ADINQ AEBTG AEFIE AFDYV AFEXP AFFNX AFGCZ AGGDS AJBLW BBWZM CAG COF GQ6 H~9 KOW KQ8 LO0 N2Q NDZJH O9- OK1 PKN R4E REI RIG RNI RYB RZK RZZ S1Z S26 S28 SCLPG T16 XJT Z5O Z7R Z7X Z83 Z86 Z88 Z8M Z8R Z8W Z92 ZWQNP AAYXX ADHKG AGQPQ CITATION 1XC VOOES
ID	FETCH-LOGICAL-c445t-3e23b89c53a2589d8d138f4bd71f245dbff60720c18d00c14612dd53adf78c703
IEDL.DBID	RSV
ISICitedReferencesCount	17
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000443885800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0029-599X
IngestDate	Wed Nov 26 06:50:45 EST 2025 Mon Oct 06 16:35:41 EDT 2025 Sat Nov 29 01:36:00 EST 2025 Tue Nov 18 22:43:04 EST 2025 Fri Feb 21 02:34:05 EST 2025 Thu Oct 30 04:34:22 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	2
Keywords	35B27 49K20 homogenization periodic structure shape optimization Bloch waves dispersion
Language	English
License	licence_http://creativecommons.org/publicdomain/zero/: http://creativecommons.org/publicdomain/zero
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c445t-3e23b89c53a2589d8d138f4bd71f245dbff60720c18d00c14612dd53adf78c703
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-5349-6690 0000-0002-8213-1092
OpenAccessLink	https://hal.science/hal-01341082
PQID	2099970213
PQPubID	2043616
PageCount	62
ParticipantIDs	hal_primary_oai_HAL_hal_01341082v1 proquest_journals_2099970213 crossref_citationtrail_10_1007_s00211_018_0972_4 crossref_primary_10_1007_s00211_018_0972_4 springer_journals_10_1007_s00211_018_0972_4 nii_cinii_1874242817443049856
PublicationCentury	2000
PublicationDate	2018-10-01
PublicationDateYYYYMMDD	2018-10-01
PublicationDate_xml	– month: 10 year: 2018 text: 2018-10-01 day: 01
PublicationDecade	2010
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationTitle	Numerische Mathematik
PublicationTitleAbbrev	Numer. Math
PublicationYear	2018
Publisher	Springer Science and Business Media LLC Springer Berlin Heidelberg Springer Nature B.V Springer Verlag
Publisher_xml	– name: Springer Science and Business Media LLC – name: Springer Berlin Heidelberg – name: Springer Nature B.V – name: Springer Verlag
References	Conca, Orive, Vanninathan (CR19) 2006; 47 Abdulle, Pouchon (CR2) 2016; 54 Conca, Vanninathan (CR17) 1997; 57 Allaire (CR3) 2002 Bensoussan, Lions, Papanicolaou (CR12) 2011 Allaire, Dapogny, Delgado, Michailidis (CR5) 2014; 20 CR39 CR38 Osher, Sethian (CR41) 1988; 79 Lombardo, Askes (CR33) 2010; 466 Abdulle, Grote, Stohrer (CR1) 2014; 12 Allaire, Briane, Vanninathan (CR4) 2016; 73 Lamacz (CR32) 2011; 21 Christov, Maugin, Velarde (CR16) 1996; 54 Hettlich, Rundell (CR28) 1998; 14 Pantz (CR42) 2005; 341 Reed, Simon (CR45) 1978 Osher, Santosa (CR40) 2001; 171 Isakari, Kuriyama, Harada, Yamada, Takahashi, Matsumoto (CR29) 2014; 1 Conca, San Martín, Smaranda, Vanninathan (CR22) 2012; 91 Allaire, Dapogny, Frey (CR6) 2014; 282 CR47 CR44 Conca, San Martín, Smaranda, Vanninathan (CR21) 2009; 19 Karchevsky (CR31) 2010; 18 Sigmund (CR49) 1994; 31 Smyshlyaev, Cherednichenko (CR50) 2000; 48 Hashin, Shtrikman (CR25) 1963; 11 Mei, Wang (CR35) 2004; 20 Allaire, Jouve, Goethem (CR7) 2011; 230 Pironneau (CR43) 1984 McKinnon, Smyth, Worthy (CR34) 1999; 16 Bakhvalov, Panasenko (CR10) 1989 Wang, Wang (CR55) 2004; 193 Stainko, Sigmund (CR52) 2007; 17 CR15 CR14 Moskow, Vogelius (CR37) 1997; 127 Sokolowski, Zolesio (CR51) 1992 CR53 Jikov, Kozlov, Oleinik (CR30) 1994 Allaire, Jouve, Toader (CR8) 2004; 194 Santosa, Symes (CR48) 1991; 51 Wang, Wang, Guo (CR54) 2003; 192 Haslinger, Dvorak (CR26) 1995; 29 Riishede, Sigmund (CR46) 2008; 25 Barbarosie (CR11) 2003; 30 Fish, Chen, Nagai (CR24) 2002; 54 Hecht (CR27) 2012; 20 Conca, San Martín, Smaranda, Vanninathan (CR20) 2008; 49 Wilcox (CR56) 1978; 33 Mohammadi, Pironneau (CR36) 2001 Conca, Orive, Vanninathan (CR18) 2002; 33 Allaire, Palombaro, Rauch (CR9) 2011; 202 Bernardi, Pironneau (CR13) 2003; 24 Dohnal, Lamacz, Schweizer (CR23) 2014; 12 G Allaire (972_CR8) 2004; 194 M Reed (972_CR45) 1978 C Conca (972_CR22) 2012; 91 S Osher (972_CR40) 2001; 171 R Stainko (972_CR52) 2007; 17 G Allaire (972_CR4) 2016; 73 T Dohnal (972_CR23) 2014; 12 G Allaire (972_CR7) 2011; 230 G Allaire (972_CR9) 2011; 202 V Jikov (972_CR30) 1994 M Lombardo (972_CR33) 2010; 466 Y Mei (972_CR35) 2004; 20 972_CR15 F Santosa (972_CR48) 1991; 51 972_CR14 C Conca (972_CR20) 2008; 49 972_CR53 C Conca (972_CR19) 2006; 47 J Riishede (972_CR46) 2008; 25 G Allaire (972_CR5) 2014; 20 C Conca (972_CR17) 1997; 57 C Barbarosie (972_CR11) 2003; 30 VP Smyshlyaev (972_CR50) 2000; 48 C Wilcox (972_CR56) 1978; 33 A Lamacz (972_CR32) 2011; 21 CI Christov (972_CR16) 1996; 54 K McKinnon (972_CR34) 1999; 16 S Osher (972_CR41) 1988; 79 A Abdulle (972_CR1) 2014; 12 C Conca (972_CR18) 2002; 33 Z Hashin (972_CR25) 1963; 11 C Bernardi (972_CR13) 2003; 24 S Moskow (972_CR37) 1997; 127 F Hecht (972_CR27) 2012; 20 N Bakhvalov (972_CR10) 1989 M Wang (972_CR55) 2004; 193 972_CR38 O Sigmund (972_CR49) 1994; 31 B Mohammadi (972_CR36) 2001 G Allaire (972_CR6) 2014; 282 O Pironneau (972_CR43) 1984 AL Karchevsky (972_CR31) 2010; 18 H Isakari (972_CR29) 2014; 1 972_CR39 C Conca (972_CR21) 2009; 19 F Hettlich (972_CR28) 1998; 14 J Haslinger (972_CR26) 1995; 29 G Allaire (972_CR3) 2002 J Sokolowski (972_CR51) 1992 O Pantz (972_CR42) 2005; 341 A Bensoussan (972_CR12) 2011 J Fish (972_CR24) 2002; 54 A Abdulle (972_CR2) 2016; 54 972_CR47 972_CR44 MY Wang (972_CR54) 2003; 192
References_xml	– year: 2001 ident: CR36 publication-title: Applied Shape Optimization for Fluids – volume: 30 start-page: 235 year: 2003 end-page: 246 ident: CR11 article-title: Shape optimization of periodic structures publication-title: Comput. Mech. doi: 10.1007/s00466-002-0382-3 – volume: 11 start-page: 127 year: 1963 end-page: 140 ident: CR25 article-title: A variational approach to the theory of the elastic behaviour of multiphase materials publication-title: J. Mech. Phys. Solids doi: 10.1016/0022-5096(63)90060-7 – year: 1992 ident: CR51 publication-title: Introduction to Shape Optimization: Shape Sensitivity Analysis doi: 10.1007/978-3-642-58106-9 – volume: 29 start-page: 657 year: 1995 end-page: 686 ident: CR26 article-title: Optimum composite material design publication-title: RAIRO M2AN doi: 10.1051/m2an/1995290606571 – year: 1978 ident: CR45 publication-title: Methods of Modern Mathematical Physics – ident: CR39 – volume: 91 start-page: 1155 issue: 6 year: 2012 end-page: 1176 ident: CR22 article-title: Burnett coefficients and laminates publication-title: Appl. Anal. doi: 10.1080/00036811.2011.625017 – volume: 25 start-page: 88 issue: 1 year: 2008 end-page: 97 ident: CR46 article-title: Inverse design of dispersion compensating optical fiber using topology optimization publication-title: J. Opt. Soc. Am. B Opt. Phys. doi: 10.1364/JOSAB.25.000088 – volume: 20 start-page: 507 issue: 5 year: 2004 end-page: 518 ident: CR35 article-title: A level set method for structural topology optimization with multi-constraints and multi-materials publication-title: Acta Mechanica Sinica doi: 10.1007/BF02484273 – volume: 171 start-page: 272 year: 2001 end-page: 288 ident: CR40 article-title: Level set methods for optimization problems involving geometry and constraints: frequencies of a two-density inhomogeneous drum publication-title: J. Comput. Phys. doi: 10.1006/jcph.2001.6789 – volume: 12 start-page: 1230 year: 2014 end-page: 1257 ident: CR1 article-title: Finite element heterogeneous multiscale method for the wave equation: long-time effects publication-title: Multiscale Model. Simul. doi: 10.1137/13094195X – volume: 202 start-page: 373 year: 2011 end-page: 426 ident: CR9 article-title: Diffractive geometric optics for Bloch wave packets publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-011-0452-9 – volume: 31 start-page: 2313 year: 1994 end-page: 2329 ident: CR49 article-title: Materials with prescribed constitutive parameters: an inverse homogenization problem publication-title: Int. J. Solids Struct. doi: 10.1016/0020-7683(94)90154-6 – volume: 54 start-page: 3621 year: 1996 end-page: 3638 ident: CR16 article-title: Well-posed Boussinesq paradigm with purely spatial higher-order derivatives publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.54.3621 – volume: 230 start-page: 5010 year: 2011 end-page: 5044 ident: CR7 article-title: Damage and fracture evolution in brittle materials by shape optimization methods publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.03.024 – ident: CR15 – volume: 54 start-page: 347 issue: 3 year: 2002 end-page: 363 ident: CR24 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 – volume: 16 start-page: 441 issue: 3 year: 1999 end-page: 447 ident: CR34 article-title: Optimization of soliton amplitude in dispersion-decreasing nonlinear optical fibers publication-title: J. Opt. Soc. Am. B Opt. Phys. doi: 10.1364/JOSAB.16.000441 – volume: 18 start-page: 371 issue: 4 year: 2010 end-page: 388 ident: CR31 article-title: Reconstruction of pressure velocities and boundaries of thin layers in thinly-stratified layers publication-title: J. Inverse Ill-Posed Probl. doi: 10.1515/jiip.2010.015 – volume: 49 start-page: 23 issue: 5 year: 2008 ident: CR20 article-title: On Burnett coefficients in periodic media in low contrast regime publication-title: J. Math. Phys. doi: 10.1063/1.2919066 – year: 1994 ident: CR30 publication-title: Homogenization of Differential Operators and Integral Functionals doi: 10.1007/978-3-642-84659-5 – volume: 21 start-page: 1871 issue: 9 year: 2011 end-page: 1899 ident: CR32 article-title: Dispersive effective models for waves in heterogeneous media publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S021820251100557X – volume: 54 start-page: 1507 issue: 3 year: 2016 end-page: 1534 ident: CR2 article-title: A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M1025633 – volume: 14 start-page: 67 year: 1998 ident: CR28 article-title: The determination of a discontinuity in a conductivity from a single boundary measurement publication-title: Inverse Probl. doi: 10.1088/0266-5611/14/1/008 – year: 1989 ident: CR10 publication-title: Homogenization: Averaging Processes in Periodic Media doi: 10.1007/978-94-009-2247-1 – volume: 33 start-page: 1166 issue: 5 year: 2002 end-page: 1198 ident: CR18 article-title: Bloch approximation in homogenization and applications publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141001382200 – volume: 51 start-page: 984 year: 1991 end-page: 1005 ident: CR48 article-title: A dispersive effective medium for wave propagation in periodic composites publication-title: SIAM J. Appl. Math. doi: 10.1137/0151049 – volume: 1 start-page: CM0039 year: 2014 ident: CR29 article-title: A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method publication-title: Mech. Eng. J. doi: 10.1299/mej.2014cm0039 – volume: 12 start-page: 488 issue: 2 year: 2014 end-page: 513 ident: CR23 article-title: Bloch-wave homogenization on large time scales and dispersive effective wave equations publication-title: Multiscale Model. Simul. doi: 10.1137/130935033 – ident: CR47 – volume: 127 start-page: 1263 year: 1997 end-page: 1295 ident: CR37 article-title: First order corrections to the homogenized eigenvalues of a periodic composite medium. A convergence proof publication-title: Proc. R. Soc. Edinb. doi: 10.1017/S0308210500027050 – volume: 48 start-page: 1325 issue: 6–7 year: 2000 end-page: 1357 ident: CR50 article-title: On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media, The J. R. Willis 60th anniversary volume publication-title: J. Mech. Phys. Solids doi: 10.1016/S0022-5096(99)00090-3 – ident: CR14 – ident: CR53 – volume: 47 start-page: 11 issue: 3 year: 2006 ident: CR19 article-title: On Burnett coefficients in periodic media publication-title: J. Math. Phys. doi: 10.1063/1.2179048 – year: 1984 ident: CR43 publication-title: Optimal Shape Design for Elliptic Systems doi: 10.1007/978-3-642-87722-3 – start-page: 456 year: 2002 ident: CR3 publication-title: Shape Optimization by the Homogenization Method, Applied Mathematical Sciences doi: 10.1007/978-1-4684-9286-6 – volume: 73 start-page: 237 issue: 3 year: 2016 end-page: 259 ident: CR4 article-title: A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures publication-title: SEMA J. doi: 10.1007/s40324-016-0067-z – volume: 282 start-page: 22 year: 2014 end-page: 53 ident: CR6 article-title: Shape optimization with a level set based mesh evolution method publication-title: CMAME – volume: 57 start-page: 1639 year: 1997 end-page: 1659 ident: CR17 article-title: Homogenization of periodic structures via Bloch decomposition publication-title: SIAM J. Appl. Math. doi: 10.1137/S0036139995294743 – volume: 20 start-page: 576 year: 2014 end-page: 611 ident: CR5 article-title: Multi-phase structural optimization via a level set method, publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2013076 – ident: CR44 – volume: 79 start-page: 12 issue: 1 year: 1988 end-page: 49 ident: CR41 article-title: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(88)90002-2 – ident: CR38 – volume: 17 start-page: 477 issue: 4 year: 2007 end-page: 489 ident: CR52 article-title: Tailoring dispersion properties of photonic crystal waveguides by topology optimization publication-title: Waves Random Complex Media doi: 10.1080/17455030701501851 – volume: 24 start-page: 205 year: 2003 end-page: 214 ident: CR13 article-title: Sensitivity of Darcy’s law to discontinuities publication-title: Chin. Ann. Math. doi: 10.1142/S0252959903000189 – volume: 192 start-page: 227 year: 2003 end-page: 246 ident: CR54 article-title: A level set method for structural topology optimization publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(02)00559-5 – volume: 194 start-page: 363 issue: 1 year: 2004 end-page: 393 ident: CR8 article-title: Structural optimization using sensitivity analysis and a level set method publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2003.09.032 – start-page: 398 year: 2011 ident: CR12 publication-title: Asymptotic Analysis for Periodic Structures, Corrected Reprint of the 1978 Original – volume: 20 start-page: 251 issue: 3–4 year: 2012 end-page: 265 ident: CR27 article-title: New development in FreeFem++ publication-title: J. Numer. Math. – volume: 19 start-page: 1743 issue: 9 year: 2009 end-page: 1764 ident: CR21 article-title: Optimal bounds on dispersion coefficient in one-dimensional periodic media publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202509003930 – volume: 466 start-page: 1789 year: 2010 end-page: 1807 ident: CR33 article-title: Elastic wave dispersion in microstructured membranes publication-title: Proc. R. Soc. A doi: 10.1098/rspa.2009.0516 – volume: 193 start-page: 469 year: 2004 end-page: 496 ident: CR55 article-title: Color level sets: a multi-phase method for structural topology optimization with multiple materials publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2003.10.008 – volume: 341 start-page: 333 year: 2005 end-page: 337 ident: CR42 article-title: Sensibilité de l’équation de la chaleur aux sauts de conductivité publication-title: C.R. Acad. Dci. Paris Ser. 1 doi: 10.1016/j.crma.2005.07.005 – volume: 33 start-page: 146 year: 1978 end-page: 167 ident: CR56 article-title: Theory of Bloch waves publication-title: J. Anal. Math. doi: 10.1007/BF02790171 – volume: 202 start-page: 373 year: 2011 ident: 972_CR9 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-011-0452-9 – ident: 972_CR14 doi: 10.1007/BFb0063630 – volume: 19 start-page: 1743 issue: 9 year: 2009 ident: 972_CR21 publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202509003930 – volume: 20 start-page: 251 issue: 3–4 year: 2012 ident: 972_CR27 publication-title: J. Numer. Math. – volume: 20 start-page: 507 issue: 5 year: 2004 ident: 972_CR35 publication-title: Acta Mechanica Sinica doi: 10.1007/BF02484273 – volume: 54 start-page: 347 issue: 3 year: 2002 ident: 972_CR24 publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.424 – volume: 282 start-page: 22 year: 2014 ident: 972_CR6 publication-title: CMAME – volume: 48 start-page: 1325 issue: 6–7 year: 2000 ident: 972_CR50 publication-title: J. Mech. Phys. Solids doi: 10.1016/S0022-5096(99)00090-3 – volume: 18 start-page: 371 issue: 4 year: 2010 ident: 972_CR31 publication-title: J. Inverse Ill-Posed Probl. doi: 10.1515/jiip.2010.015 – ident: 972_CR39 – volume: 73 start-page: 237 issue: 3 year: 2016 ident: 972_CR4 publication-title: SEMA J. doi: 10.1007/s40324-016-0067-z – volume: 54 start-page: 1507 issue: 3 year: 2016 ident: 972_CR2 publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M1025633 – volume-title: Homogenization of Differential Operators and Integral Functionals year: 1994 ident: 972_CR30 doi: 10.1007/978-3-642-84659-5 – volume: 466 start-page: 1789 year: 2010 ident: 972_CR33 publication-title: Proc. R. Soc. A doi: 10.1098/rspa.2009.0516 – volume: 20 start-page: 576 year: 2014 ident: 972_CR5 publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2013076 – volume: 194 start-page: 363 issue: 1 year: 2004 ident: 972_CR8 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2003.09.032 – volume: 29 start-page: 657 year: 1995 ident: 972_CR26 publication-title: RAIRO M2AN doi: 10.1051/m2an/1995290606571 – volume: 193 start-page: 469 year: 2004 ident: 972_CR55 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2003.10.008 – volume: 127 start-page: 1263 year: 1997 ident: 972_CR37 publication-title: Proc. R. Soc. Edinb. doi: 10.1017/S0308210500027050 – volume: 12 start-page: 1230 year: 2014 ident: 972_CR1 publication-title: Multiscale Model. Simul. doi: 10.1137/13094195X – volume: 30 start-page: 235 year: 2003 ident: 972_CR11 publication-title: Comput. Mech. doi: 10.1007/s00466-002-0382-3 – volume: 79 start-page: 12 issue: 1 year: 1988 ident: 972_CR41 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(88)90002-2 – volume-title: Homogenization: Averaging Processes in Periodic Media year: 1989 ident: 972_CR10 doi: 10.1007/978-94-009-2247-1 – volume: 47 start-page: 11 issue: 3 year: 2006 ident: 972_CR19 publication-title: J. Math. Phys. doi: 10.1063/1.2179048 – volume: 54 start-page: 3621 year: 1996 ident: 972_CR16 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.54.3621 – volume: 25 start-page: 88 issue: 1 year: 2008 ident: 972_CR46 publication-title: J. Opt. Soc. Am. B Opt. Phys. doi: 10.1364/JOSAB.25.000088 – volume: 11 start-page: 127 year: 1963 ident: 972_CR25 publication-title: J. Mech. Phys. Solids doi: 10.1016/0022-5096(63)90060-7 – volume: 33 start-page: 146 year: 1978 ident: 972_CR56 publication-title: J. Anal. Math. doi: 10.1007/BF02790171 – ident: 972_CR47 – volume: 33 start-page: 1166 issue: 5 year: 2002 ident: 972_CR18 publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141001382200 – volume: 24 start-page: 205 year: 2003 ident: 972_CR13 publication-title: Chin. Ann. Math. doi: 10.1142/S0252959903000189 – volume: 17 start-page: 477 issue: 4 year: 2007 ident: 972_CR52 publication-title: Waves Random Complex Media doi: 10.1080/17455030701501851 – volume: 192 start-page: 227 year: 2003 ident: 972_CR54 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(02)00559-5 – volume: 1 start-page: CM0039 year: 2014 ident: 972_CR29 publication-title: Mech. Eng. J. doi: 10.1299/mej.2014cm0039 – volume: 341 start-page: 333 year: 2005 ident: 972_CR42 publication-title: C.R. Acad. Dci. Paris Ser. 1 doi: 10.1016/j.crma.2005.07.005 – volume-title: Introduction to Shape Optimization: Shape Sensitivity Analysis year: 1992 ident: 972_CR51 doi: 10.1007/978-3-642-58106-9 – volume: 171 start-page: 272 year: 2001 ident: 972_CR40 publication-title: J. Comput. Phys. doi: 10.1006/jcph.2001.6789 – volume: 57 start-page: 1639 year: 1997 ident: 972_CR17 publication-title: SIAM J. Appl. Math. doi: 10.1137/S0036139995294743 – volume: 51 start-page: 984 year: 1991 ident: 972_CR48 publication-title: SIAM J. Appl. Math. doi: 10.1137/0151049 – volume: 16 start-page: 441 issue: 3 year: 1999 ident: 972_CR34 publication-title: J. Opt. Soc. Am. B Opt. Phys. doi: 10.1364/JOSAB.16.000441 – volume: 49 start-page: 23 issue: 5 year: 2008 ident: 972_CR20 publication-title: J. Math. Phys. doi: 10.1063/1.2919066 – start-page: 456 volume-title: Shape Optimization by the Homogenization Method, Applied Mathematical Sciences year: 2002 ident: 972_CR3 doi: 10.1007/978-1-4684-9286-6 – volume: 12 start-page: 488 issue: 2 year: 2014 ident: 972_CR23 publication-title: Multiscale Model. Simul. doi: 10.1137/130935033 – start-page: 398 volume-title: Asymptotic Analysis for Periodic Structures, Corrected Reprint of the 1978 Original year: 2011 ident: 972_CR12 – volume-title: Optimal Shape Design for Elliptic Systems year: 1984 ident: 972_CR43 doi: 10.1007/978-3-642-87722-3 – volume: 91 start-page: 1155 issue: 6 year: 2012 ident: 972_CR22 publication-title: Appl. Anal. doi: 10.1080/00036811.2011.625017 – volume-title: Methods of Modern Mathematical Physics year: 1978 ident: 972_CR45 – ident: 972_CR53 doi: 10.1007/978-3-642-05195-1 – volume: 21 start-page: 1871 issue: 9 year: 2011 ident: 972_CR32 publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S021820251100557X – ident: 972_CR15 – volume-title: Applied Shape Optimization for Fluids year: 2001 ident: 972_CR36 – volume: 230 start-page: 5010 year: 2011 ident: 972_CR7 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.03.024 – ident: 972_CR38 doi: 10.1007/978-1-4612-2032-9_3 – ident: 972_CR44 doi: 10.1090/gsm/133 – volume: 31 start-page: 2313 year: 1994 ident: 972_CR49 publication-title: Int. J. Solids Struct. doi: 10.1016/0020-7683(94)90154-6 – volume: 14 start-page: 67 year: 1998 ident: 972_CR28 publication-title: Inverse Probl. doi: 10.1088/0266-5611/14/1/008
SSID	ssj0017641
Score	2.3144875
Snippet	We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The...
SourceID	hal proquest crossref springer nii
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	265
SubjectTerms	49K20 [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Bloch waves dispersion homogenization Lower bounds Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematics Mathematics and Statistics MSC 35B27 MSC 35B27, 49K20 Numerical Analysis Numerical and Computational Physics Optimization Optimization and Control periodic structure Periodic structures Periodic variations shape optimization Simulation Theoretical Wave dispersion Wave equations Wave propagation
Title	Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures
URI	https://cir.nii.ac.jp/crid/1874242817443049856 https://link.springer.com/article/10.1007/s00211-018-0972-4 https://www.proquest.com/docview/2099970213 https://hal.science/hal-01341082
Volume	140
WOSCitedRecordID	wos000443885800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAVX databaseName: Springer LINK customDbUrl: eissn: 0945-3245 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017641 issn: 0029-599X databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwEB6xCwc4lFcrlgKyUE-gSHFir53jqgLtgZegRXuLNn6ISJAUdln-PjPZJGWrFqlcfEhmEssee2Y0M98AfHNG8kwqHqA6SALhvArGRtqgQv9GCXK-gmO4PVMXF3o0Sq7qOu5Jk-3ehCSrm7otdiN1RK4vhetVFIgOLKO2U9Sv4frmtg0dqL7gTV6HTJJRE8r82ycWlFHnjlIhO0WeL1ibfwRIK71zuv6hGW_Ap9rMZIO5XGzCkiu2YL1p4cDqE70Fa-ctbOtkG_JLvEAe6spMVnpmcwISpwx3ZkpXoU1Q4gXLC4Zs7K58KFEA3zDQ05cxkrvHOYY4kRKYcmlzw-Zgtc_o4X-Gn6cnP74Pg7oXQ2CEkNMgdlGc6cTIeBxJnVhteay9yKziPhLSZt73QxWFhmsb4ijQcrIWqa1X2uC18gW6RVm4HWDSZyrmJvNJbNG7Izx74S2PvFBZgmMPwmZTUlMDlVO_jPu0hViuFjbFhU1pYVNkOWpZfs1ROt4jPsSdbukIX3s4OEvpWUjwdmgUzXgP9lEQ8P80Ut9CNGU0em-CwpJa9nuw14hIWp_6SUplyCiQEY97cNyIxO_X_5zR7n9Rf4XViGSqyijcgy5unduHFTOb5pOng-owvAIXMv9q
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9QwDLe4gcR42GAwcfuACPEEqtS0ySV5nKZNh7gdSIzp3qJrPrRKrN24ffz72L22sIlNgpc8pHYTJU5sy_YvAO-Dk7yQiieoDkwiQlTJ3EmfNOjfKEEhNnAMJxM1nerZzHxt67gXXbZ7F5Jsbuq-2I3UEbm-FK5XWSIG8FgQ4Be56N9O-tCBGgne5XVIY2ZdKPNvv7iljAanlAo5qMrylrV5J0Da6J3D9f-a8XNYa81MtreUixfwKFQbsN494cDaE70Bz4562NbFSyi_4AVy1lZmsjoyXxKQOGW4M1eHBm2CEi9YWTFkY6f1WY0C-AcD9d7MkTxcLDHEiZTAlGtfOrYEq71CD_8VfD88ON4fJ-1bDIkTQl4mecjyQhsn83kmtfHa81xHUXjFYyakL2IcpSpLHdc-xVag5eQ9UvuotMNrZRNWqroKr4HJWKicuyKa3KN3R3j2InqeRaEKg-0Q0m5TrGuByum9jB-2h1huFtbiwlpaWIssH3qW8yVKx0PE73CnezrC1x7vTSz1pQRvh0bRNR_CLgoCjk8tvVuIpoxG701QWFLL0RB2OhGx7alfWCpDNgqHy4fwsROJ35_vndHWP1G_hafj46OJnXyaft6G1Yzkq8ku3IEV3MawC0_c9WW5-PmmORi_ABZpAl0
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LbxQxDLbYghAcWigglrYQIU6gUSczySY5VoVVEctS8aj2Fu3koY5EZwq7lL-PPa9SBEiISw4ZexIlTmLL9meAZ8FJXkjFE3wOTCJCVMnSSZ806N8oQSE2cAwnMzWf68XCHHd1Tld9tHvvkmxzGgilqVrvn_u4PyS-0dNEZjC57lWWiBFcF2jIUEzf-w8ngxtBTQTvYzykMYverfm7X1x5mEanFBY5qsryiub5i7O0eYOmW_89-zuw2amf7KCVl7twLVTbsNWXdmDdSd-G228HONfVPSjf4cVy1mVssjoyXxLAOEW-M1eHBoWCAjJYWTFkY6f1WY2C-RMD9X5fInn40mKLEymBLNe-dKwFsf2Glv99-DR99fHwKOlqNCROCLlO8pDlhTZO5stMauO157mOovCKx0xIX8Q4SVWWOq59iq1Ajcp7pPZRaYfXzQPYqOoqPAQmY6Fy7opoco9WH-Hci-h5FoUqDLZjSPsNsq4DMKc6Gp_tAL3cLKzFhbW0sBZZng8s5y16x9-In-KuD3SEu310MLPUlxLsHSpLF3wMeygUOD61VM8QVRyNVp0gd6WWkzHs9uJiu9tgZSk92SgcLh_Di148Lj__cUaP_on6Cdw8fjm1s9fzNztwKyPxaoIOd2EDdzHswQ13sS5XXx83Z-QHWK8LQQ
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Optimization+of+dispersive+coefficients+in+the+homogenization+of+the+wave+equation+in+periodic+structures&rft.jtitle=Numerische+Mathematik&rft.au=Allaire%2C+G.&rft.au=Yamada%2C+T.&rft.date=2018-10-01&rft.issn=0029-599X&rft.eissn=0945-3245&rft.volume=140&rft.issue=2&rft.spage=265&rft.epage=326&rft_id=info:doi/10.1007%2Fs00211-018-0972-4&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00211_018_0972_4
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-599X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-599X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-599X&client=summon