An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions

This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using...

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Vydané v:	Structural and multidisciplinary optimization Ročník 58; číslo 2; s. 831 - 849
Hlavní autori:	Wei, Peng, Li, Zuyu, Li, Xueping, Wang, Michael Yu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018 Springer Nature B.V
Predmet:	Basis functions Computational Mathematics and Numerical Analysis Dependence Educational Article Engineering Engineering Design Matlab Modulus of elasticity Neural networks Nucleation Parameterization Radial basis function Theoretical and Applied Mechanics Topology optimization Topology optimization Radial basis functions MATLAB code Level set method
ISSN:	1615-147X, 1615-1488
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes.
AbstractList	This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes. This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes.
Author	Wang, Michael Yu Wei, Peng Li, Zuyu Li, Xueping
Author_xml	– sequence: 1 givenname: Peng orcidid: 0000-0001-5826-1527 surname: Wei fullname: Wei, Peng email: ctpwei@scut.edu.cn organization: State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology – sequence: 2 givenname: Zuyu surname: Li fullname: Li, Zuyu organization: Architecture and Civil Engineering Institute, Guangdong University of Petrochemical Technology – sequence: 3 givenname: Xueping surname: Li fullname: Li, Xueping organization: State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology – sequence: 4 givenname: Michael Yu surname: Wang fullname: Wang, Michael Yu organization: Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology
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Cites_doi	10.1016/j.ijheatmasstransfer.2012.08.028 10.1016/j.jcp.2003.09.033 10.1006/jcph.2001.6789 10.1017/S0956792505006182 10.1007/s00158-015-1372-3 10.1002/nme.1536 10.1016/S0045-7825(02)00559-5 10.1007/s00158-014-1107-x 10.1007/s00158-014-1190-z 10.1006/jcph.1996.0167 10.1137/S0363012997323230 10.1007/s00158-013-0999-1 10.1007/BF02123482 10.1007/s00158-015-1284-2 10.1007/s00158-013-0956-z 10.1007/s00158-013-0912-y 10.1016/j.imavis.2010.08.011 10.1002/nme.2478 10.1016/j.jcp.2003.09.032 10.1007/s00158-003-0322-7 10.1016/j.cma.2010.05.013 10.1016/0021-9991(88)90002-2 10.1007/s00791-012-0180-1 10.1007/s00158-011-0696-x 10.1016/j.advengsoft.2004.06.004 10.1007/s00158-010-0534-6 10.1006/jcph.2000.6581 10.1115/DETC2006-99294 10.1007/s00158-013-0978-6 10.1016/j.enganabound.2004.01.004 10.1109/83.902291 10.1007/s00158-013-0935-4 10.1007/s00158-010-0594-7 10.1007/BF00934777 10.1016/j.advengsoft.2015.02.006 10.1007/s00158-009-0430-0 10.1002/9780470689486 10.1371/journal.pone.0145041 10.1002/nme.1468 10.1006/jcph.1999.6345 10.1016/j.jcp.2006.06.029 10.1109/SMA.2001.923379 10.1007/s00158-015-1294-0 10.1016/j.jcp.2003.11.010 10.1007/s001580050176
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Keywords	Topology optimization Radial basis functions MATLAB code Level set method
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PublicationDate	2018-08-01
PublicationDateYYYYMMDD	2018-08-01
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PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationTitle	Structural and multidisciplinary optimization
PublicationTitleAbbrev	Struct Multidisc Optim
PublicationYear	2018
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	SethianJALevel set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science1999CambridgeCambridge University Press0973.76003 Van DijkNPMauteKLangelaarMVan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y TavakoliRMohseniSMAlternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementationStruct Multidiscip Optim2014494621642318339710.1007/s00158-013-0999-1 OtomoriMYamadaTIzuiKNishiwakiSMATLAB code for a level set-based topology optimization method using a reaction diffusion equationStruct Multidiscip Optim201451511591172335386810.1007/s00158-014-1190-z Wei P, Wang MY (2006) The augmented Lagrangian method in structural shape and topology optimization with RBF based level set method, The 4th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kunming, China OsherSFedkiwRLevel set methods and dynamic implicit surfaces2002New YorkSpringer1026.76001 DeatonJDGrandhiRVA survey of structural and multidisciplinary continuum topology optimization: post 2000Struct Multidiscip Optim2014491138318245010.1007/s00158-013-0956-z OlesenLHOkkelsFBruusHA high-level programming-language implementation of topology optimization applied to steady-state navier-stokes flowInt J Numer Methods Eng20066579751001220169110.1002/nme.14681111.76017 GainALPaulinoGHA critical comparative assessment of differential equation-driven methods for structural topology optimizationStruct Multidiscip Optim2013484685710310759710.1007/s00158-013-0935-4 SigmundOA 99 line topology optimization code written in MATLABStruct Multidiscip Optim2001212112012710.1007/s001580050176 XieXMirmehdiMRadial basis function based level set interpolation and evolution for deformable modellingImage Vis Comput2011292–316717710.1016/j.imavis.2010.08.011 MeiYWangXA level set method for structural topology optimization and its applicationsAdv Eng Softw200435741544110.1016/j.advengsoft.2004.06.0041067.90153 EmreBToACProportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLABPLoS One20151012e014504110.1371/journal.pone.0145041 ZuoZHXieYMA simple and compact python code for complex 3D topology optimizationAdv Eng Softw20158511110.1016/j.advengsoft.2015.02.006 SokołowskiJZolésioJPIntroduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis1992BerlinSpringer-Verlag0761.73003 BurgerMOsherSJA survey on level set methods for inverse problems and optimal designEur J Appl Math2005162263301215529310.1017/S09567925050061821091.49001 KharmandaGOlhoffNMohamedALemaireMReliability-based topology optimizationStruct Multidiscip Optim200426529530710.1007/s00158-003-0322-7 WangSYLimKMKhooBCWangMYAn extended level set method for shape and topology optimizationJ Comput Phys20072211395421229057710.1016/j.jcp.2006.06.0291110.65058 ZhaoHKChanTMerrimanBOsherSA variational level set approach to multiphase motionJ Comput Phys1996127179195140806910.1006/jcph.1996.01670860.65050 Wang MY, Chen SK, Xia Q (2004) TOPLSM, 199-line version. http://ihome.ust.hk/~mywang/download/TOPLSM_199.m XiaLBreitkopfPDesign of materials using topology optimization and energy-based homogenization approach in MATLABStruct Multidiscip Optim201552612291241343333110.1007/s00158-015-1294-0 AndreassenEClausenASchevenelsMLazarovBSSigmundOEfficient topology optimization in MATLAB using 88 lines of codeStruct Multidiscip Optim201143111610.1007/s00158-010-0594-71274.74310 WeiPWangMYPiecewise constant level set method for structural topology optimizationInt J Numer Methods Eng2009784379402250947110.1002/nme.24781183.74222 CecilTQianJOsherSNumerical methods for high dimensional Hamilton-Jacobi equations using radial basis functionsJ Comput Phys20041961327347205434610.1016/j.jcp.2003.11.0101053.65086 ChanTFVeseLAActive contours without edgesIEEE Trans Image Process200110226627710.1109/83.9022911039.68779 HuangXXieYMEvolutionary Topology Optimization of Continuum Structures: Methods and Applications2010New YorkWiley10.1002/97804706894861279.90001 WangSYWangMYRadial basis functions and level set method for structural topology optimizationInt J Numer Meth Engng20066520602090220894010.1002/nme.15361174.74331 RochafellarRTThe multiplier method of Hestenes and Powell applied to convex programmingJ Optim Theory Appl19731255556233495310.1007/BF00934777 SethianJAWiegmannAStructural boundary design via level set and immersed interface methodsJ Comput Phys20001632489528178355910.1006/jcph.2000.65810994.74082 TalischiCPaulinoGHPereiraAMenezesIFMPolytop: a MATLAB implementation of a general topology optimization framework using unstructured polygonal finite element meshesStruct Multidiscip Optim2012453329357289711610.1007/s00158-011-0696-x1274.74402 AllaireGJouveFToaderAMStructural optimization using sensitivity analysis and a level-set methodJ Comput Phys20041941363393203339010.1016/j.jcp.2003.09.0321136.74368 ChoiKKKimNHStructural sensitivity analysis and optimization 12005BerlinSpringer SchmidtSSchulzVA 2589 line topology optimization code written for the graphics cardComput Vis Sci2011146249256297225010.1007/s00791-012-0180-11380.74100 WendlandHPiecewise polynomial, positive definite and compactly supported radial functions of minimal degreeAdv Comput Math199541389396136651010.1007/BF021234820838.41014 WangSYWangMYStructural shape and topology optimization using an implicit free boundary parameterization methodComput Model Eng Sci200613211914722261351232.74084 ZhangWYuanJZhangJGuoXA new topology optimization approach based on moving Morphable components (MMC) and the ersatz material modelStruct Multidiscip Optim201653612431260349888510.1007/s00158-015-1372-3 WangMYWangXGuoDA level set method for structural topology optimizationComput Methods Appl Mech Eng20031921–2227246195140810.1016/S0045-7825(02)00559-51083.74573 SureshKA 199-line MATLAB code for Pareto-optimal tracing in topology optimizationStruct Multidiscip Optim2010425665679272027410.1007/s00158-010-0534-61274.74005 OsherSSantosaFLevel set methods for optimization problems involving geometry and constraints: i. Frequencies of a two-density inhomogeneous drumJ Comput Phys20011711272288184364810.1006/jcph.2001.67891056.74061 ZegardTPaulinoGHGRAND3 - ground structure based topology optimization for arbitrary 3D domains using MATLABStruct Multidiscip Optim20155261161118410.1007/s00158-015-1284-2 DijkNPVMauteKLangelaarMvan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y BendsøeMSigmundOTopology optimization. Theory, methods and applications2003BerlinSpringer1059.74001 MorseBSYooTSChenDTRheingansPSubramanianKRInterpolating implicit surfaces from scattered surface data using compactly supported radial basis functionsInt Conf Shape Model Appl2001152899810.1109/SMA.2001.923379 OsherSSethianJAFronts propagating with curvature-dependent speed: algorithms based on HamiltonJacobi formulationsJ Comput Phys1988791124996586010.1016/0021-9991(88)90002-20659.65132 Allaire G (2009) A 2-d Scilab Code for shape and topology optimization by the level set method. http://www.cmap.polytechnique.fr/∼allaire/levelset_en.html YamadaTIzuiKNishiwakiSTakezawaAA topology optimization method based on the level set method incorporating a fictitious interface energyComput Methods Appl Mech Eng201019945–4828762891274076510.1016/j.cma.2010.05.0131231.74365 ZhouSCadmanJChenYLiWXieYMHuangXDesign and fabrication of biphasic cellular materials with transport properties – a modified bidirectional evolutionary structural optimization procedure and MATLAB programInt J Heat Mass Transf20125525–268149816210.1016/j.ijheatmasstransfer.2012.08.028 KansaEJPowerHFasshauerGELingLA volumetric integral radial basis function method for time-dependent partial differential equations. I. FormulationEng Anal Bound Elem200428101191120610.1016/j.enganabound.2004.01.0041159.76363 LiuKTovarAAn efficient 3d topology optimization code written in MATLABStruct Multidiscip Optim201450611751196331242510.1007/s00158-014-1107-x PengDMerrimanBOsherSZhao H.& Kang M.A PDE-based fast local level set methodJ Comput Phys19991552410438172332110.1006/jcph.1999.63450964.76069 SigmundOMauteKTopology optimization approachesStruct Multidiscip Optim201348610311055313812410.1007/s00158-013-0978-6 AllaireGDe GournayFJouveFToaderAMStructural optimization using topological and shape sensitivity via a level set methodControl Cybern2005341598022110631167.49324 Wang MY, Wei P (2005) Topology optimization with level set method incorporating topological derivative. 6th World Congress on Structural & Multidisciplinary Optimization, Rio de Janeiro, Brazil BurgerMHacklBRingWIncorporating topological derivatives into level set methodsJ Comput Phys20041941344362203338910.1016/j.jcp.2003.09.0331044.65053 ChallisVJA discrete level-set topology optimization code written in MATLABStruct Multidiscip Optim2010413453464260213610.1007/s00158-009-0430-01274.74322 SokołowskiJŻochowskiAOn the topological derivative in shape optimizationSIAM J Control Optim199937412511272169194010.1137/S03630129973232300940.49026 X Huang (1904_CR16) 2010 JA Sethian (1904_CR30) 1999 ZH Zuo (1904_CR56) 2015; 85 C Talischi (1904_CR37) 2012; 45 NP Dijk Van (1904_CR39) 2013; 48 BS Morse (1904_CR21) 2001; 15 1904_CR46 S Osher (1904_CR24) 2001; 171 1904_CR42 X Xie (1904_CR50) 2011; 29 1904_CR44 M Burger (1904_CR6) 2005; 16 O Sigmund (1904_CR32) 2001; 21 G Allaire (1904_CR3) 2005; 34 MY Wang (1904_CR43) 2003; 192 E Andreassen (1904_CR4) 2011; 43 EJ Kansa (1904_CR17) 2004; 28 J Sokołowski (1904_CR35) 1992 H Wendland (1904_CR48) 1995; 4 S Osher (1904_CR25) 1988; 79 RT Rochafellar (1904_CR28) 1973; 12 R Tavakoli (1904_CR38) 2014; 49 M Burger (1904_CR7) 2004; 194 NPV Dijk (1904_CR13) 2013; 48 T Cecil (1904_CR8) 2004; 196 L Xia (1904_CR49) 2015; 52 TF Chan (1904_CR10) 2001; 10 1904_CR1 M Bendsøe (1904_CR5) 2003 SY Wang (1904_CR45) 2007; 221 D Peng (1904_CR27) 1999; 155 T Yamada (1904_CR51) 2010; 199 O Sigmund (1904_CR33) 2013; 48 AL Gain (1904_CR15) 2013; 48 K Liu (1904_CR19) 2014; 50 LH Olesen (1904_CR22) 2006; 65 K Suresh (1904_CR36) 2010; 42 M Otomori (1904_CR26) 2014; 51 JD Deaton (1904_CR12) 2014; 49 J Sokołowski (1904_CR34) 1999; 37 W Zhang (1904_CR53) 2016; 53 G Allaire (1904_CR2) 2004; 194 SY Wang (1904_CR41) 2006; 13 T Zegard (1904_CR52) 2015; 52 KK Choi (1904_CR11) 2005 SY Wang (1904_CR40) 2006; 65 P Wei (1904_CR47) 2009; 78 B Emre (1904_CR14) 2015; 10 S Osher (1904_CR23) 2002 JA Sethian (1904_CR31) 2000; 163 G Kharmanda (1904_CR18) 2004; 26 VJ Challis (1904_CR9) 2010; 41 S Schmidt (1904_CR29) 2011; 14 Y Mei (1904_CR20) 2004; 35 HK Zhao (1904_CR54) 1996; 127 S Zhou (1904_CR55) 2012; 55
References_xml	– reference: GainALPaulinoGHA critical comparative assessment of differential equation-driven methods for structural topology optimizationStruct Multidiscip Optim2013484685710310759710.1007/s00158-013-0935-4 – reference: LiuKTovarAAn efficient 3d topology optimization code written in MATLABStruct Multidiscip Optim201450611751196331242510.1007/s00158-014-1107-x – reference: OlesenLHOkkelsFBruusHA high-level programming-language implementation of topology optimization applied to steady-state navier-stokes flowInt J Numer Methods Eng20066579751001220169110.1002/nme.14681111.76017 – reference: DeatonJDGrandhiRVA survey of structural and multidisciplinary continuum topology optimization: post 2000Struct Multidiscip Optim2014491138318245010.1007/s00158-013-0956-z – reference: BurgerMOsherSJA survey on level set methods for inverse problems and optimal designEur J Appl Math2005162263301215529310.1017/S09567925050061821091.49001 – reference: MorseBSYooTSChenDTRheingansPSubramanianKRInterpolating implicit surfaces from scattered surface data using compactly supported radial basis functionsInt Conf Shape Model Appl2001152899810.1109/SMA.2001.923379 – reference: BurgerMHacklBRingWIncorporating topological derivatives into level set methodsJ Comput Phys20041941344362203338910.1016/j.jcp.2003.09.0331044.65053 – reference: ZhangWYuanJZhangJGuoXA new topology optimization approach based on moving Morphable components (MMC) and the ersatz material modelStruct Multidiscip Optim201653612431260349888510.1007/s00158-015-1372-3 – reference: SigmundOA 99 line topology optimization code written in MATLABStruct Multidiscip Optim2001212112012710.1007/s001580050176 – reference: TalischiCPaulinoGHPereiraAMenezesIFMPolytop: a MATLAB implementation of a general topology optimization framework using unstructured polygonal finite element meshesStruct Multidiscip Optim2012453329357289711610.1007/s00158-011-0696-x1274.74402 – reference: OtomoriMYamadaTIzuiKNishiwakiSMATLAB code for a level set-based topology optimization method using a reaction diffusion equationStruct Multidiscip Optim201451511591172335386810.1007/s00158-014-1190-z – reference: ZhouSCadmanJChenYLiWXieYMHuangXDesign and fabrication of biphasic cellular materials with transport properties – a modified bidirectional evolutionary structural optimization procedure and MATLAB programInt J Heat Mass Transf20125525–268149816210.1016/j.ijheatmasstransfer.2012.08.028 – reference: SethianJAWiegmannAStructural boundary design via level set and immersed interface methodsJ Comput Phys20001632489528178355910.1006/jcph.2000.65810994.74082 – reference: OsherSSantosaFLevel set methods for optimization problems involving geometry and constraints: i. Frequencies of a two-density inhomogeneous drumJ Comput Phys20011711272288184364810.1006/jcph.2001.67891056.74061 – reference: RochafellarRTThe multiplier method of Hestenes and Powell applied to convex programmingJ Optim Theory Appl19731255556233495310.1007/BF00934777 – reference: AndreassenEClausenASchevenelsMLazarovBSSigmundOEfficient topology optimization in MATLAB using 88 lines of codeStruct Multidiscip Optim201143111610.1007/s00158-010-0594-71274.74310 – reference: Wang MY, Chen SK, Xia Q (2004) TOPLSM, 199-line version. http://ihome.ust.hk/~mywang/download/TOPLSM_199.m – reference: XiaLBreitkopfPDesign of materials using topology optimization and energy-based homogenization approach in MATLABStruct Multidiscip Optim201552612291241343333110.1007/s00158-015-1294-0 – reference: WangSYLimKMKhooBCWangMYAn extended level set method for shape and topology optimizationJ Comput Phys20072211395421229057710.1016/j.jcp.2006.06.0291110.65058 – reference: WangSYWangMYStructural shape and topology optimization using an implicit free boundary parameterization methodComput Model Eng Sci200613211914722261351232.74084 – reference: AllaireGDe GournayFJouveFToaderAMStructural optimization using topological and shape sensitivity via a level set methodControl Cybern2005341598022110631167.49324 – reference: Wang MY, Wei P (2005) Topology optimization with level set method incorporating topological derivative. 6th World Congress on Structural & Multidisciplinary Optimization, Rio de Janeiro, Brazil – reference: HuangXXieYMEvolutionary Topology Optimization of Continuum Structures: Methods and Applications2010New YorkWiley10.1002/97804706894861279.90001 – reference: MeiYWangXA level set method for structural topology optimization and its applicationsAdv Eng Softw200435741544110.1016/j.advengsoft.2004.06.0041067.90153 – reference: ZhaoHKChanTMerrimanBOsherSA variational level set approach to multiphase motionJ Comput Phys1996127179195140806910.1006/jcph.1996.01670860.65050 – reference: SokołowskiJŻochowskiAOn the topological derivative in shape optimizationSIAM J Control Optim199937412511272169194010.1137/S03630129973232300940.49026 – reference: OsherSSethianJAFronts propagating with curvature-dependent speed: algorithms based on HamiltonJacobi formulationsJ Comput Phys1988791124996586010.1016/0021-9991(88)90002-20659.65132 – reference: SchmidtSSchulzVA 2589 line topology optimization code written for the graphics cardComput Vis Sci2011146249256297225010.1007/s00791-012-0180-11380.74100 – reference: SigmundOMauteKTopology optimization approachesStruct Multidiscip Optim201348610311055313812410.1007/s00158-013-0978-6 – reference: ZegardTPaulinoGHGRAND3 - ground structure based topology optimization for arbitrary 3D domains using MATLABStruct Multidiscip Optim20155261161118410.1007/s00158-015-1284-2 – reference: CecilTQianJOsherSNumerical methods for high dimensional Hamilton-Jacobi equations using radial basis functionsJ Comput Phys20041961327347205434610.1016/j.jcp.2003.11.0101053.65086 – reference: WeiPWangMYPiecewise constant level set method for structural topology optimizationInt J Numer Methods Eng2009784379402250947110.1002/nme.24781183.74222 – reference: DijkNPVMauteKLangelaarMvan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y – reference: ChallisVJA discrete level-set topology optimization code written in MATLABStruct Multidiscip Optim2010413453464260213610.1007/s00158-009-0430-01274.74322 – reference: SethianJALevel set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science1999CambridgeCambridge University Press0973.76003 – reference: SureshKA 199-line MATLAB code for Pareto-optimal tracing in topology optimizationStruct Multidiscip Optim2010425665679272027410.1007/s00158-010-0534-61274.74005 – reference: KansaEJPowerHFasshauerGELingLA volumetric integral radial basis function method for time-dependent partial differential equations. I. FormulationEng Anal Bound Elem200428101191120610.1016/j.enganabound.2004.01.0041159.76363 – reference: TavakoliRMohseniSMAlternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementationStruct Multidiscip Optim2014494621642318339710.1007/s00158-013-0999-1 – reference: Allaire G (2009) A 2-d Scilab Code for shape and topology optimization by the level set method. http://www.cmap.polytechnique.fr/∼allaire/levelset_en.html – reference: XieXMirmehdiMRadial basis function based level set interpolation and evolution for deformable modellingImage Vis Comput2011292–316717710.1016/j.imavis.2010.08.011 – reference: ChoiKKKimNHStructural sensitivity analysis and optimization 12005BerlinSpringer – reference: ChanTFVeseLAActive contours without edgesIEEE Trans Image Process200110226627710.1109/83.9022911039.68779 – reference: AllaireGJouveFToaderAMStructural optimization using sensitivity analysis and a level-set methodJ Comput Phys20041941363393203339010.1016/j.jcp.2003.09.0321136.74368 – reference: WangMYWangXGuoDA level set method for structural topology optimizationComput Methods Appl Mech Eng20031921–2227246195140810.1016/S0045-7825(02)00559-51083.74573 – reference: WendlandHPiecewise polynomial, positive definite and compactly supported radial functions of minimal degreeAdv Comput Math199541389396136651010.1007/BF021234820838.41014 – reference: ZuoZHXieYMA simple and compact python code for complex 3D topology optimizationAdv Eng Softw20158511110.1016/j.advengsoft.2015.02.006 – reference: KharmandaGOlhoffNMohamedALemaireMReliability-based topology optimizationStruct Multidiscip Optim200426529530710.1007/s00158-003-0322-7 – reference: YamadaTIzuiKNishiwakiSTakezawaAA topology optimization method based on the level set method incorporating a fictitious interface energyComput Methods Appl Mech Eng201019945–4828762891274076510.1016/j.cma.2010.05.0131231.74365 – reference: BendsøeMSigmundOTopology optimization. Theory, methods and applications2003BerlinSpringer1059.74001 – reference: WangSYWangMYRadial basis functions and level set method for structural topology optimizationInt J Numer Meth Engng20066520602090220894010.1002/nme.15361174.74331 – reference: OsherSFedkiwRLevel set methods and dynamic implicit surfaces2002New YorkSpringer1026.76001 – reference: PengDMerrimanBOsherSZhao H.& Kang M.A PDE-based fast local level set methodJ Comput Phys19991552410438172332110.1006/jcph.1999.63450964.76069 – reference: Van DijkNPMauteKLangelaarMVan KeulenFLevel-set methods for structural topology optimization: a reviewStruct Multidiscip Optim2013483437472310758310.1007/s00158-013-0912-y – reference: EmreBToACProportional topology optimization: a new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLABPLoS One20151012e014504110.1371/journal.pone.0145041 – reference: SokołowskiJZolésioJPIntroduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis1992BerlinSpringer-Verlag0761.73003 – reference: Wei P, Wang MY (2006) The augmented Lagrangian method in structural shape and topology optimization with RBF based level set method, The 4th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kunming, China – ident: 1904_CR44 – volume: 55 start-page: 8149 issue: 25–26 year: 2012 ident: 1904_CR55 publication-title: Int J Heat Mass Transf doi: 10.1016/j.ijheatmasstransfer.2012.08.028 – volume: 194 start-page: 344 issue: 1 year: 2004 ident: 1904_CR7 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.09.033 – volume-title: Level set methods and dynamic implicit surfaces year: 2002 ident: 1904_CR23 – volume: 171 start-page: 272 issue: 1 year: 2001 ident: 1904_CR24 publication-title: J Comput Phys doi: 10.1006/jcph.2001.6789 – volume: 16 start-page: 263 issue: 2 year: 2005 ident: 1904_CR6 publication-title: Eur J Appl Math doi: 10.1017/S0956792505006182 – volume: 53 start-page: 1243 issue: 6 year: 2016 ident: 1904_CR53 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1372-3 – volume: 65 start-page: 2060 year: 2006 ident: 1904_CR40 publication-title: Int J Numer Meth Engng doi: 10.1002/nme.1536 – volume: 192 start-page: 227 issue: 1–2 year: 2003 ident: 1904_CR43 publication-title: Comput Methods Appl Mech Eng doi: 10.1016/S0045-7825(02)00559-5 – volume: 50 start-page: 1175 issue: 6 year: 2014 ident: 1904_CR19 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-014-1107-x – volume: 51 start-page: 1159 issue: 5 year: 2014 ident: 1904_CR26 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-014-1190-z – volume: 127 start-page: 179 year: 1996 ident: 1904_CR54 publication-title: J Comput Phys doi: 10.1006/jcph.1996.0167 – volume: 37 start-page: 1251 issue: 4 year: 1999 ident: 1904_CR34 publication-title: SIAM J Control Optim doi: 10.1137/S0363012997323230 – volume-title: Introduction to shape optimization: shape Sensitity analysis. Introduction to shape optimization : shape sensitivity analysis year: 1992 ident: 1904_CR35 – volume: 49 start-page: 621 issue: 4 year: 2014 ident: 1904_CR38 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0999-1 – volume: 4 start-page: 389 issue: 1 year: 1995 ident: 1904_CR48 publication-title: Adv Comput Math doi: 10.1007/BF02123482 – volume: 52 start-page: 1161 issue: 6 year: 2015 ident: 1904_CR52 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1284-2 – volume: 49 start-page: 1 issue: 1 year: 2014 ident: 1904_CR12 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0956-z – volume: 48 start-page: 437 issue: 3 year: 2013 ident: 1904_CR13 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0912-y – volume: 29 start-page: 167 issue: 2–3 year: 2011 ident: 1904_CR50 publication-title: Image Vis Comput doi: 10.1016/j.imavis.2010.08.011 – volume: 78 start-page: 379 issue: 4 year: 2009 ident: 1904_CR47 publication-title: Int J Numer Methods Eng doi: 10.1002/nme.2478 – volume: 194 start-page: 363 issue: 1 year: 2004 ident: 1904_CR2 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.09.032 – volume: 26 start-page: 295 issue: 5 year: 2004 ident: 1904_CR18 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-003-0322-7 – volume: 199 start-page: 2876 issue: 45–48 year: 2010 ident: 1904_CR51 publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2010.05.013 – volume: 79 start-page: 12 issue: 1 year: 1988 ident: 1904_CR25 publication-title: J Comput Phys doi: 10.1016/0021-9991(88)90002-2 – volume: 14 start-page: 249 issue: 6 year: 2011 ident: 1904_CR29 publication-title: Comput Vis Sci doi: 10.1007/s00791-012-0180-1 – volume: 45 start-page: 329 issue: 3 year: 2012 ident: 1904_CR37 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-011-0696-x – volume: 35 start-page: 415 issue: 7 year: 2004 ident: 1904_CR20 publication-title: Adv Eng Softw doi: 10.1016/j.advengsoft.2004.06.004 – volume: 13 start-page: 119 issue: 2 year: 2006 ident: 1904_CR41 publication-title: Comput Model Eng Sci – volume-title: Topology optimization. Theory, methods and applications year: 2003 ident: 1904_CR5 – volume: 42 start-page: 665 issue: 5 year: 2010 ident: 1904_CR36 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-010-0534-6 – volume: 163 start-page: 489 issue: 2 year: 2000 ident: 1904_CR31 publication-title: J Comput Phys doi: 10.1006/jcph.2000.6581 – ident: 1904_CR46 doi: 10.1115/DETC2006-99294 – volume: 48 start-page: 1031 issue: 6 year: 2013 ident: 1904_CR33 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0978-6 – volume: 28 start-page: 1191 issue: 10 year: 2004 ident: 1904_CR17 publication-title: Eng Anal Bound Elem doi: 10.1016/j.enganabound.2004.01.004 – volume: 48 start-page: 437 issue: 3 year: 2013 ident: 1904_CR39 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0912-y – volume: 10 start-page: 266 issue: 2 year: 2001 ident: 1904_CR10 publication-title: IEEE Trans Image Process doi: 10.1109/83.902291 – volume: 48 start-page: 685 issue: 4 year: 2013 ident: 1904_CR15 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-013-0935-4 – volume: 43 start-page: 1 issue: 1 year: 2011 ident: 1904_CR4 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-010-0594-7 – volume: 12 start-page: 555 year: 1973 ident: 1904_CR28 publication-title: J Optim Theory Appl doi: 10.1007/BF00934777 – volume-title: Structural sensitivity analysis and optimization 1 year: 2005 ident: 1904_CR11 – volume: 85 start-page: 1 year: 2015 ident: 1904_CR56 publication-title: Adv Eng Softw doi: 10.1016/j.advengsoft.2015.02.006 – volume: 34 start-page: 59 issue: 1 year: 2005 ident: 1904_CR3 publication-title: Control Cybern – volume: 41 start-page: 453 issue: 3 year: 2010 ident: 1904_CR9 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-009-0430-0 – ident: 1904_CR42 – volume-title: Evolutionary Topology Optimization of Continuum Structures: Methods and Applications year: 2010 ident: 1904_CR16 doi: 10.1002/9780470689486 – ident: 1904_CR1 – volume: 10 start-page: e0145041 issue: 12 year: 2015 ident: 1904_CR14 publication-title: PLoS One doi: 10.1371/journal.pone.0145041 – volume: 65 start-page: 975 issue: 7 year: 2006 ident: 1904_CR22 publication-title: Int J Numer Methods Eng doi: 10.1002/nme.1468 – volume: 155 start-page: 410 issue: 2 year: 1999 ident: 1904_CR27 publication-title: J Comput Phys doi: 10.1006/jcph.1999.6345 – volume: 221 start-page: 395 issue: 1 year: 2007 ident: 1904_CR45 publication-title: J Comput Phys doi: 10.1016/j.jcp.2006.06.029 – volume-title: Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science year: 1999 ident: 1904_CR30 – volume: 15 start-page: 89 issue: 2 year: 2001 ident: 1904_CR21 publication-title: Int Conf Shape Model Appl doi: 10.1109/SMA.2001.923379 – volume: 52 start-page: 1229 issue: 6 year: 2015 ident: 1904_CR49 publication-title: Struct Multidiscip Optim doi: 10.1007/s00158-015-1294-0 – volume: 196 start-page: 327 issue: 1 year: 2004 ident: 1904_CR8 publication-title: J Comput Phys doi: 10.1016/j.jcp.2003.11.010 – volume: 21 start-page: 120 issue: 21 year: 2001 ident: 1904_CR32 publication-title: Struct Multidiscip Optim doi: 10.1007/s001580050176
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SubjectTerms	Basis functions Computational Mathematics and Numerical Analysis Dependence Educational Article Engineering Engineering Design Matlab Modulus of elasticity Neural networks Nucleation Parameterization Radial basis function Theoretical and Applied Mechanics Topology optimization
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Title	An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions
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