Application of the meshless generalized finite difference method to inverse heat source problems
•Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data. The generalized finite difference method (GFDM) is a relatively new...
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| Vydáno v: | International journal of heat and mass transfer Ročník 108; s. 721 - 729 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.05.2017
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| Témata: | |
| ISSN: | 0017-9310, 1879-2189 |
| On-line přístup: | Získat plný text |
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| Abstract | •Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data.
The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems. |
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| AbstractList | •Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data.
The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems. |
| Author | Zhang, Chuanzeng Gu, Yan Wang, Lei He, Xiaoqiao Chen, Wen |
| Author_xml | – sequence: 1 givenname: Yan surname: Gu fullname: Gu, Yan email: guyan1913@163.com organization: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China – sequence: 2 givenname: Lei orcidid: 0000-0002-2104-6169 surname: Wang fullname: Wang, Lei email: shywanglei@126.com organization: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, PR China – sequence: 3 givenname: Wen surname: Chen fullname: Chen, Wen organization: Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, PR China – sequence: 4 givenname: Chuanzeng surname: Zhang fullname: Zhang, Chuanzeng organization: Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, D-57076 Siegen, Germany – sequence: 5 givenname: Xiaoqiao surname: He fullname: He, Xiaoqiao organization: Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong |
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| Cites_doi | 10.1002/nme.5154 10.1016/j.ijheatmasstransfer.2015.01.003 10.1016/S0307-904X(03)00091-X 10.1002/nme.1826 10.1080/1068276031000074267 10.1080/10407790600710184 10.1002/nme.1620200905 10.1016/S0307-904X(01)00029-4 10.1016/S0898-1221(01)00292-9 10.1016/0045-7949(80)90149-2 10.1016/S0045-7825(02)00594-7 10.1016/j.enganabound.2006.01.001 10.1016/j.compstruc.2008.09.003 10.1016/j.jcp.2005.03.007 10.1137/060658618 10.1080/17415977.2014.933831 10.1007/s00466-010-0480-6 10.1029/2003RS002973 10.1023/A:1018981221740 10.1016/j.compstruc.2015.01.002 10.1080/00207160.2011.587871 10.1016/j.compfluid.2012.08.017 10.1016/j.camwa.2006.04.013 10.1016/0021-9991(87)90176-8 10.1016/j.enganabound.2010.11.010 10.1088/0266-5611/27/10/105001 10.1016/j.enganabound.2004.12.001 10.1080/10407790.2013.849979 10.1016/j.enganabound.2013.05.004 10.1016/j.ijsolstr.2013.06.018 10.1016/j.ijsolstr.2006.10.025 10.1016/j.amc.2012.03.101 10.1364/JOSAA.17.000034 10.1016/j.matcom.2008.01.003 10.1088/0266-5611/21/5/001 10.1002/nme.2398 |
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| References | Gu, Chen, Zhang, He (b0055) 2015; 84 Chan, Fan, Kuo (b0025) 2013; 37 Liu, Zhang, Wang, Zhong, Li, Han (b0065) 2007; 44 Sadat, Dubus, Gbahoué, Sophy (b0120) 2006; 50 Ang, Yeo, Chew, Shu (b0170) 2008; 76 Chen, Cho, Golberg (b0085) 2006; 30 Karageorghis, Lesnic, Marin (b0040) 2015; 151 Liszka, Orkisz (b0095) 1980; 11 Sadat, Wang, Le Dez (b0125) 2012; 218 Marin (b0050) 2010; 45 Karageorghis, Lesnic (b0070) 2011; 35 Benito, Urena, Gavete (b0100) 2001; 25 Abdellatif El (b0165) 2005; 21 Gavete, Gavete, Benito (b0105) 2003; 27 Gu, Chen, Gao, Zhang (b0035) 2016; 107 Jin, Marin (b0145) 2007; 69 Sarler, Vertnik (b0075) 2006; 51 Fairweather, Karageorghis (b0030) 1998; 9 Gu, Chen, Zhang (b0010) 2013; 50 Devaney, Marengo, Li (b0140) 2007; 67 Liszka (b0090) 1984; 20 Fan, Li, Yeih (b0155) 2015; 23 Farcas, Elliott, Ingham, Lesnic, Mera (b0160) 2003; 11 Benito, Urena, Gavete, Alvarez (b0110) 2003; 192 Young, Chen, Lee (b0015) 2005; 209 Abdellatif El, Nara (b0135) 2011; 27 Cheng, Cheng (b0005) 2005; 29 Chen, Ganesh, Golberg, Cheng (b0045) 2002; 43 Nguyen, Rabczuk, Bordas, Duflot (b0080) 2008; 79 Karageorghis, Fairweather (b0060) 1987; 69 Liu, Nguyen-Thoi, Nguyen-Xuan, Lam (b0020) 2009; 87 Fan, Huang, Li, Chiu (b0150) 2014; 65 Sten (b0180) 2004; 39 Ureña, Salete, Benito, Gavete (b0115) 2012; 89 Wang, Sadat, Prax (b0130) 2012; 69 Marengo, Devaney, Ziolkowski (b0175) 2000; 17 Karageorghis (10.1016/j.ijheatmasstransfer.2016.12.084_b0040) 2015; 151 Liszka (10.1016/j.ijheatmasstransfer.2016.12.084_b0090) 1984; 20 Devaney (10.1016/j.ijheatmasstransfer.2016.12.084_b0140) 2007; 67 Nguyen (10.1016/j.ijheatmasstransfer.2016.12.084_b0080) 2008; 79 Benito (10.1016/j.ijheatmasstransfer.2016.12.084_b0110) 2003; 192 Karageorghis (10.1016/j.ijheatmasstransfer.2016.12.084_b0060) 1987; 69 Liu (10.1016/j.ijheatmasstransfer.2016.12.084_b0020) 2009; 87 Ang (10.1016/j.ijheatmasstransfer.2016.12.084_b0170) 2008; 76 Benito (10.1016/j.ijheatmasstransfer.2016.12.084_b0100) 2001; 25 Marin (10.1016/j.ijheatmasstransfer.2016.12.084_b0050) 2010; 45 Ureña (10.1016/j.ijheatmasstransfer.2016.12.084_b0115) 2012; 89 Abdellatif El (10.1016/j.ijheatmasstransfer.2016.12.084_b0135) 2011; 27 Sarler (10.1016/j.ijheatmasstransfer.2016.12.084_b0075) 2006; 51 Marengo (10.1016/j.ijheatmasstransfer.2016.12.084_b0175) 2000; 17 Young (10.1016/j.ijheatmasstransfer.2016.12.084_b0015) 2005; 209 Farcas (10.1016/j.ijheatmasstransfer.2016.12.084_b0160) 2003; 11 Gavete (10.1016/j.ijheatmasstransfer.2016.12.084_b0105) 2003; 27 Sadat (10.1016/j.ijheatmasstransfer.2016.12.084_b0120) 2006; 50 Sten (10.1016/j.ijheatmasstransfer.2016.12.084_b0180) 2004; 39 Liu (10.1016/j.ijheatmasstransfer.2016.12.084_b0065) 2007; 44 Chen (10.1016/j.ijheatmasstransfer.2016.12.084_b0045) 2002; 43 Liszka (10.1016/j.ijheatmasstransfer.2016.12.084_b0095) 1980; 11 Gu (10.1016/j.ijheatmasstransfer.2016.12.084_b0035) 2016; 107 Jin (10.1016/j.ijheatmasstransfer.2016.12.084_b0145) 2007; 69 Fan (10.1016/j.ijheatmasstransfer.2016.12.084_b0150) 2014; 65 Fan (10.1016/j.ijheatmasstransfer.2016.12.084_b0155) 2015; 23 Chan (10.1016/j.ijheatmasstransfer.2016.12.084_b0025) 2013; 37 Chen (10.1016/j.ijheatmasstransfer.2016.12.084_b0085) 2006; 30 Sadat (10.1016/j.ijheatmasstransfer.2016.12.084_b0125) 2012; 218 Cheng (10.1016/j.ijheatmasstransfer.2016.12.084_b0005) 2005; 29 Karageorghis (10.1016/j.ijheatmasstransfer.2016.12.084_b0070) 2011; 35 Gu (10.1016/j.ijheatmasstransfer.2016.12.084_b0010) 2013; 50 Wang (10.1016/j.ijheatmasstransfer.2016.12.084_b0130) 2012; 69 Gu (10.1016/j.ijheatmasstransfer.2016.12.084_b0055) 2015; 84 Fairweather (10.1016/j.ijheatmasstransfer.2016.12.084_b0030) 1998; 9 Abdellatif El (10.1016/j.ijheatmasstransfer.2016.12.084_b0165) 2005; 21 |
| References_xml | – volume: 35 start-page: 631 year: 2011 end-page: 638 ident: b0070 article-title: Application of the MFS to inverse obstacle scattering problems publication-title: Eng. Anal. Bound. Elem. – volume: 192 start-page: 735 year: 2003 end-page: 759 ident: b0110 article-title: An h-adaptive method in the generalized finite differences publication-title: Comput. Methods Appl. Mech. Eng. – volume: 27 start-page: 831 year: 2003 end-page: 847 ident: b0105 article-title: Improvements of generalized finite difference method and comparison with other meshless method publication-title: Appl. Math. Model. – volume: 107 start-page: 109 year: 2016 end-page: 126 ident: b0035 article-title: A meshless singular boundary method for three-dimensional elasticity problems publication-title: Int. J. Numer. Methods Eng. – volume: 11 start-page: 83 year: 1980 end-page: 95 ident: b0095 article-title: The finite difference method at arbitrary irregular grids and its application in applied mechanics publication-title: Comput. Struct. – volume: 218 start-page: 10211 year: 2012 end-page: 10225 ident: b0125 article-title: Meshless method for solving coupled radiative and conductive heat transfer in complex multi-dimensional geometries publication-title: Appl. Math. Comput. – volume: 50 start-page: 491 year: 2006 end-page: 498 ident: b0120 article-title: On the solution of heterogeneous heat conduction problems by a diffuse approximation meshless method publication-title: Numer. Heat Transf., Part B – volume: 67 start-page: 1353 year: 2007 end-page: 1378 ident: b0140 article-title: Inverse source problem in nonhomogeneous background media publication-title: SIAM J. Appl. Math. – volume: 89 start-page: 366 year: 2012 end-page: 376 ident: b0115 article-title: Solving third- and fourth-order partial differential equations using GFDM: application to solve problems of plates publication-title: Int. J. Comp. Math. – volume: 209 start-page: 290 year: 2005 end-page: 321 ident: b0015 article-title: Novel meshless method for solving the potential problems with arbitrary domain publication-title: J. Comput. Phys. – volume: 65 start-page: 129 year: 2014 end-page: 154 ident: b0150 article-title: Application of the generalized finite-difference method to inverse biharmonic boundary-value problems publication-title: Numer. Heat Transf., Part B – volume: 25 start-page: 1039 year: 2001 end-page: 1053 ident: b0100 article-title: Influence of several factors in the generalized finite difference method publication-title: Appl. Math. Model. – volume: 151 start-page: 11 year: 2015 end-page: 19 ident: b0040 article-title: The method of fundamental solutions for solving direct and inverse Signorini problems publication-title: Comput. Struct. – volume: 21 start-page: 1487 year: 2005 ident: b0165 article-title: Inverse source problem in an anisotropic medium by boundary measurements publication-title: Inverse. Probl. – volume: 44 start-page: 3840 year: 2007 end-page: 3860 ident: b0065 article-title: A nodal integration technique for meshfree radial point interpolation method (NI-RPIM) publication-title: Int. J. Solids. Struct. – volume: 69 start-page: 136 year: 2012 end-page: 146 ident: b0130 article-title: A new meshless approach for three dimensional fluid flow and related heat transfer problems publication-title: Comp. Fluids – volume: 11 start-page: 123 year: 2003 end-page: 139 ident: b0160 article-title: A dual reciprocity boundary element method for the regularized numerical solution of the inverse source problem associated to the poisson equation publication-title: Inverse. Probl. Sci. Eng. – volume: 17 start-page: 34 year: 2000 end-page: 45 ident: b0175 article-title: Inverse source problem and minimum-energy sources publication-title: J. Opt. Soc. Am. – volume: 50 start-page: 3460 year: 2013 end-page: 3471 ident: b0010 article-title: Stress analysis for thin multilayered coating systems using a sinh transformed boundary element method publication-title: Int. J. Solids. Struct. – volume: 37 start-page: 1189 year: 2013 end-page: 1196 ident: b0025 article-title: Generalized finite difference method for solving two-dimensional non-linear obstacle problems publication-title: Eng. Anal. Bound. Elem. – volume: 43 start-page: 359 year: 2002 end-page: 378 ident: b0045 article-title: Multilevel compact radial functions based computational schemes for some elliptic problems publication-title: Comput. Math. Appl. – volume: 27 start-page: 105001 year: 2011 end-page: 105015 ident: b0135 article-title: An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number publication-title: Inverse. Probl. – volume: 23 start-page: 737 year: 2015 end-page: 759 ident: b0155 article-title: Generalized finite difference method for solving two-dimensional inverse Cauchy problems publication-title: Inverse. Probl. Sci. Eng. – volume: 39 start-page: 1 year: 2004 end-page: 10 ident: b0180 article-title: Reconstruction of electromagnetic minimum energy sources in a prolate spheroid publication-title: Radio. Sci. – volume: 87 start-page: 14 year: 2009 end-page: 26 ident: b0020 article-title: A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems publication-title: Comput. Struct. – volume: 45 start-page: 665 year: 2010 end-page: 677 ident: b0050 article-title: An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation publication-title: Comput. Mech. – volume: 20 start-page: 1599 year: 1984 end-page: 1612 ident: b0090 article-title: An interpolation method for an irregular net of nodes publication-title: Int. J. Numer. Methods Eng. – volume: 51 start-page: 1269 year: 2006 end-page: 1282 ident: b0075 article-title: Meshfree explicit local radial basis function collocation method for diffusion problems publication-title: Comput. Math. Appl. – volume: 79 start-page: 763 year: 2008 end-page: 813 ident: b0080 article-title: Meshless methods: a review and computer implementation aspects publication-title: Math. Comput. Simul. – volume: 9 start-page: 69 year: 1998 end-page: 95 ident: b0030 article-title: The method of fundamental solutions for elliptic boundary value problems publication-title: Adv. Comput. Math. – volume: 29 start-page: 268 year: 2005 end-page: 302 ident: b0005 article-title: Heritage and early history of the boundary element method publication-title: Eng. Anal. Bound. Elem. – volume: 30 start-page: 405 year: 2006 end-page: 410 ident: b0085 article-title: Some comments on the ill-conditioning of the method of fundamental solutions publication-title: Eng. Anal. Bound. Elem. – volume: 76 start-page: 1892 year: 2008 end-page: 1929 ident: b0170 article-title: A singular-value decomposition (SVD)-based generalized finite difference (GFD) method for close-interaction moving boundary flow problems publication-title: Int. J. Numer. Methods Eng. – volume: 84 start-page: 91 year: 2015 end-page: 102 ident: b0055 article-title: A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media publication-title: Int. J. Heat. Mass. Transf. – volume: 69 start-page: 1570 year: 2007 end-page: 1589 ident: b0145 article-title: The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction publication-title: Int. J. Numer. Methods Eng. – volume: 69 start-page: 434 year: 1987 end-page: 459 ident: b0060 article-title: The method of fundamental solutions for the numerical solution of the biharmonic equation publication-title: J. Comput. Phys. – volume: 107 start-page: 109 issue: 2 year: 2016 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0035 article-title: A meshless singular boundary method for three-dimensional elasticity problems publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.5154 – volume: 84 start-page: 91 year: 2015 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0055 article-title: A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media publication-title: Int. J. Heat. Mass. Transf. doi: 10.1016/j.ijheatmasstransfer.2015.01.003 – volume: 27 start-page: 831 issue: 10 year: 2003 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0105 article-title: Improvements of generalized finite difference method and comparison with other meshless method publication-title: Appl. Math. Model. doi: 10.1016/S0307-904X(03)00091-X – volume: 69 start-page: 1570 issue: 8 year: 2007 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0145 article-title: The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1826 – volume: 11 start-page: 123 issue: 2 year: 2003 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0160 article-title: A dual reciprocity boundary element method for the regularized numerical solution of the inverse source problem associated to the poisson equation publication-title: Inverse. Probl. Sci. Eng. doi: 10.1080/1068276031000074267 – volume: 50 start-page: 491 issue: 6 year: 2006 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0120 article-title: On the solution of heterogeneous heat conduction problems by a diffuse approximation meshless method publication-title: Numer. Heat Transf., Part B doi: 10.1080/10407790600710184 – volume: 20 start-page: 1599 issue: 9 year: 1984 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0090 article-title: An interpolation method for an irregular net of nodes publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620200905 – volume: 25 start-page: 1039 issue: 12 year: 2001 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0100 article-title: Influence of several factors in the generalized finite difference method publication-title: Appl. Math. Model. doi: 10.1016/S0307-904X(01)00029-4 – volume: 43 start-page: 359 issue: 3–5 year: 2002 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0045 article-title: Multilevel compact radial functions based computational schemes for some elliptic problems publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(01)00292-9 – volume: 11 start-page: 83 issue: 1 year: 1980 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0095 article-title: The finite difference method at arbitrary irregular grids and its application in applied mechanics publication-title: Comput. Struct. doi: 10.1016/0045-7949(80)90149-2 – volume: 192 start-page: 735 issue: 5–6 year: 2003 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0110 article-title: An h-adaptive method in the generalized finite differences publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/S0045-7825(02)00594-7 – volume: 30 start-page: 405 issue: 5 year: 2006 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0085 article-title: Some comments on the ill-conditioning of the method of fundamental solutions publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2006.01.001 – volume: 87 start-page: 14 issue: 1–2 year: 2009 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0020 article-title: A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2008.09.003 – volume: 209 start-page: 290 issue: 1 year: 2005 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0015 article-title: Novel meshless method for solving the potential problems with arbitrary domain publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.03.007 – volume: 67 start-page: 1353 issue: 5 year: 2007 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0140 article-title: Inverse source problem in nonhomogeneous background media publication-title: SIAM J. Appl. Math. doi: 10.1137/060658618 – volume: 23 start-page: 737 issue: 5 year: 2015 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0155 article-title: Generalized finite difference method for solving two-dimensional inverse Cauchy problems publication-title: Inverse. Probl. Sci. Eng. doi: 10.1080/17415977.2014.933831 – volume: 45 start-page: 665 issue: 6 year: 2010 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0050 article-title: An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation publication-title: Comput. Mech. doi: 10.1007/s00466-010-0480-6 – volume: 39 start-page: 1 issue: 2 year: 2004 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0180 article-title: Reconstruction of electromagnetic minimum energy sources in a prolate spheroid publication-title: Radio. Sci. doi: 10.1029/2003RS002973 – volume: 9 start-page: 69 issue: 1 year: 1998 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0030 article-title: The method of fundamental solutions for elliptic boundary value problems publication-title: Adv. Comput. Math. doi: 10.1023/A:1018981221740 – volume: 151 start-page: 11 year: 2015 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0040 article-title: The method of fundamental solutions for solving direct and inverse Signorini problems publication-title: Comput. Struct. doi: 10.1016/j.compstruc.2015.01.002 – volume: 89 start-page: 366 issue: 3 year: 2012 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0115 article-title: Solving third- and fourth-order partial differential equations using GFDM: application to solve problems of plates publication-title: Int. J. Comp. Math. doi: 10.1080/00207160.2011.587871 – volume: 69 start-page: 136 year: 2012 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0130 article-title: A new meshless approach for three dimensional fluid flow and related heat transfer problems publication-title: Comp. Fluids doi: 10.1016/j.compfluid.2012.08.017 – volume: 51 start-page: 1269 issue: 8 year: 2006 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0075 article-title: Meshfree explicit local radial basis function collocation method for diffusion problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.04.013 – volume: 69 start-page: 434 issue: 2 year: 1987 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0060 article-title: The method of fundamental solutions for the numerical solution of the biharmonic equation publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(87)90176-8 – volume: 35 start-page: 631 issue: 4 year: 2011 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0070 article-title: Application of the MFS to inverse obstacle scattering problems publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2010.11.010 – volume: 27 start-page: 105001 issue: 10 year: 2011 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0135 article-title: An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number publication-title: Inverse. Probl. doi: 10.1088/0266-5611/27/10/105001 – volume: 29 start-page: 268 issue: 3 year: 2005 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0005 article-title: Heritage and early history of the boundary element method publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2004.12.001 – volume: 65 start-page: 129 issue: 2 year: 2014 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0150 article-title: Application of the generalized finite-difference method to inverse biharmonic boundary-value problems publication-title: Numer. Heat Transf., Part B doi: 10.1080/10407790.2013.849979 – volume: 37 start-page: 1189 issue: 9 year: 2013 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0025 article-title: Generalized finite difference method for solving two-dimensional non-linear obstacle problems publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2013.05.004 – volume: 50 start-page: 3460 issue: 20–21 year: 2013 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0010 article-title: Stress analysis for thin multilayered coating systems using a sinh transformed boundary element method publication-title: Int. J. Solids. Struct. doi: 10.1016/j.ijsolstr.2013.06.018 – volume: 44 start-page: 3840 issue: 11–12 year: 2007 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0065 article-title: A nodal integration technique for meshfree radial point interpolation method (NI-RPIM) publication-title: Int. J. Solids. Struct. doi: 10.1016/j.ijsolstr.2006.10.025 – volume: 218 start-page: 10211 issue: 20 year: 2012 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0125 article-title: Meshless method for solving coupled radiative and conductive heat transfer in complex multi-dimensional geometries publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.03.101 – volume: 17 start-page: 34 issue: 1 year: 2000 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0175 article-title: Inverse source problem and minimum-energy sources publication-title: J. Opt. Soc. Am. doi: 10.1364/JOSAA.17.000034 – volume: 79 start-page: 763 issue: 3 year: 2008 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0080 article-title: Meshless methods: a review and computer implementation aspects publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2008.01.003 – volume: 21 start-page: 1487 issue: 5 year: 2005 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0165 article-title: Inverse source problem in an anisotropic medium by boundary measurements publication-title: Inverse. Probl. doi: 10.1088/0266-5611/21/5/001 – volume: 76 start-page: 1892 issue: 12 year: 2008 ident: 10.1016/j.ijheatmasstransfer.2016.12.084_b0170 article-title: A singular-value decomposition (SVD)-based generalized finite difference (GFD) method for close-interaction moving boundary flow problems publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.2398 |
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