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Volumn 53, Issue 25-26, 2010, Pages 5815-5826

Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method

Author keywords

Anisotropic heat conduction; Inverse geometric problem; Method of fundamental solutions (MFS); Regularization

Indexed keywords

ANISOTROPIC HEAT CONDUCTION; BOUNDARY RECONSTRUCTION; CAUCHY DATA; DIRICHLET; INVERSE GEOMETRIC PROBLEMS; L-CURVE CRITERION; MESH-LESS METHODS; METHOD OF FUNDAMENTAL SOLUTIONS; OPTIMAL VALUES; PIECEWISE SMOOTH; REGULARIZATION; REGULARIZATION PARAMETERS; ROBIN BOUNDARY CONDITIONS; STEADY STATE; TIKHONOV REGULARIZATION METHOD; TWO-DIMENSIONAL DOMAIN;

EID: 77957302221     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.08.002     Document Type: Article
Times cited : (18)

References (59)
  • 1
    • 0001965230 scopus 로고    scopus 로고
    • The boundary inverse problem for the Laplace equation in two dimensions
    • N.D. Aparicio, and M.K. Pidcock The boundary inverse problem for the Laplace equation in two dimensions Inverse Prob. 12 1996 565 577
    • (1996) Inverse Prob. , vol.12 , pp. 565-577
    • Aparicio, N.D.1    Pidcock, M.K.2
  • 2
    • 0032271479 scopus 로고    scopus 로고
    • Stable determination of boundaries from Cauchy data
    • E. Beretta, and S. Vessela Stable determination of boundaries from Cauchy data SIAM J. Math. Anal. 30 1998 220 232
    • (1998) SIAM J. Math. Anal. , vol.30 , pp. 220-232
    • Beretta, E.1    Vessela, S.2
  • 3
    • 0001191809 scopus 로고    scopus 로고
    • Stability for an inverse problem of determining a part of the boundary
    • A.L. Bukhgeim, J. Cheng, and M. Yamamoto Stability for an inverse problem of determining a part of the boundary Inverse Prob. 15 1999 1021 1032
    • (1999) Inverse Prob. , vol.15 , pp. 1021-1032
    • Bukhgeim, A.L.1    Cheng, J.2    Yamamoto, M.3
  • 4
    • 0015679005 scopus 로고
    • The use of fundamental Green's functions for the solution of heat conduction in anisotropic media
    • Y.P. Chang, C.S. Kang, and D.J. Chen The use of fundamental Green's functions for the solution of heat conduction in anisotropic media Int. J. Heat Mass Transfer 16 1973 1905 1918
    • (1973) Int. J. Heat Mass Transfer , vol.16 , pp. 1905-1918
    • Chang, Y.P.1    Kang, C.S.2    Chen, D.J.3
  • 5
    • 0029479618 scopus 로고
    • Application of Cesro mean and the L-curve for the deconvolution problem
    • L.Y. Chen, J.T. Chen, H.K. Hong, and C.H. Chen Application of Cesro mean and the L-curve for the deconvolution problem Soil Dyn. Earthquake Eng. 14 1995 361 373
    • (1995) Soil Dyn. Earthquake Eng. , vol.14 , pp. 361-373
    • Chen, L.Y.1    Chen, J.T.2    Hong, H.K.3    Chen, C.H.4
  • 6
    • 27244459403 scopus 로고    scopus 로고
    • The method of fundamental solutions for inverse 2D Stokes problems
    • DOI 10.1007/s00466-005-0692-3
    • C.W. Chen, D.L. Young, C.C. Tsai, and K. Murugesan The method of fundamental solutions for inverse 2D Stokes problems Comput. Mech. 37 2005 2 14 (Pubitemid 41521401)
    • (2005) Computational Mechanics , vol.37 , Issue.1 , pp. 2-14
    • Chen, C.W.1    Young, D.L.2    Tsai, C.C.3    Murugesan, K.4
  • 8
    • 33845336478 scopus 로고    scopus 로고
    • A method of fundamental solutions for inverse heat conduction problems in an anisotropic medium
    • C.F. Dong, F.Y. Sun, and B.Q. Meng A method of fundamental solutions for inverse heat conduction problems in an anisotropic medium Eng. Anal. with Boundary Elem. 31 2007 75 82
    • (2007) Eng. Anal. with Boundary Elem. , vol.31 , pp. 75-82
    • Dong, C.F.1    Sun, F.Y.2    Meng, B.Q.3
  • 10
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems
    • G. Fairweather, and A. Karageorghis The method of fundamental solutions for elliptic boundary value problems Adv. Comput. Math. 9 1998 69 95 (Pubitemid 128403959)
    • (1998) Advances in Computational Mathematics , vol.9 , Issue.1-2 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 12
    • 58149487636 scopus 로고    scopus 로고
    • The method of fundamental solutions applied to 3D elasticity problems using a continuous collocation scheme
    • G.S.A. Fam, and Y.F. Rashed The method of fundamental solutions applied to 3D elasticity problems using a continuous collocation scheme Eng. Anal. with Boundary Elem. 33 2009 330 341
    • (2009) Eng. Anal. with Boundary Elem. , vol.33 , pp. 330-341
    • Fam, G.S.A.1    Rashed, Y.F.2
  • 14
    • 0000776101 scopus 로고    scopus 로고
    • The method of fundamental solutions for potential, Helmholtz and diffusion problems
    • M.A. Golberg, and C.S. Chen The method of fundamental solutions for potential, Helmholtz and diffusion problems M.A. Golberg, Boundary Integral Methods: Numerical and Mathematical Aspects 1999 WIT Press and Computational Mechanics Publications Boston 105 176
    • (1999) Boundary Integral Methods: Numerical and Mathematical Aspects , pp. 105-176
    • Golberg, M.A.1    Chen, C.S.2
  • 16
    • 1542498779 scopus 로고    scopus 로고
    • Limitations of the L-curve method in ill-posed problems
    • M. Hanke Limitations of the L-curve method in ill-posed problems BIT 36 1996 287 301
    • (1996) BIT , vol.36 , pp. 287-301
    • Hanke, M.1
  • 18
    • 39849100253 scopus 로고    scopus 로고
    • A computational method for inverse free boundary determination problem
    • Y.C. Hon, and M. Li A computational method for inverse free boundary determination problem Int. J. Numer. Methods Eng. 73 2008 1291 1309
    • (2008) Int. J. Numer. Methods Eng. , vol.73 , pp. 1291-1309
    • Hon, Y.C.1    Li, M.2
  • 19
    • 1842842972 scopus 로고    scopus 로고
    • A fundamental solution method for inverse heat conduction problems
    • Y.C. Hon, and T. Wei A fundamental solution method for inverse heat conduction problems Eng. Anal. with Boundary Elem. 28 2004 489 495
    • (2004) Eng. Anal. with Boundary Elem. , vol.28 , pp. 489-495
    • Hon, Y.C.1    Wei, T.2
  • 20
    • 15544363903 scopus 로고    scopus 로고
    • The method of fundamental solutions for solving multidimensional heat conduction problems
    • Y.C. Hon, and T. Wei The method of fundamental solutions for solving multidimensional heat conduction problems CMES: Comput. Model. Eng. Sci. 13 2005 219 228
    • (2005) CMES: Comput. Model. Eng. Sci. , vol.13 , pp. 219-228
    • Hon, Y.C.1    Wei, T.2
  • 21
    • 0342955473 scopus 로고    scopus 로고
    • A numerical computation for inverse boundary determination problem
    • Y.C. Hon, and Z. Wu A numerical computation for inverse boundary determination problem Eng. Anal. with Boundary Elem. 24 2000 599 606
    • (2000) Eng. Anal. with Boundary Elem. , vol.24 , pp. 599-606
    • Hon, Y.C.1    Wu, Z.2
  • 22
    • 0022510006 scopus 로고
    • A general method for the solution of inverse heat conduction problem with partially unknown system geometries
    • C.K. Hsieh, and A.J. Kassab A general method for the solution of inverse heat conduction problem with partially unknown system geometries Int. J. Heat Mass Transfer 29 1986 47 58
    • (1986) Int. J. Heat Mass Transfer , vol.29 , pp. 47-58
    • Hsieh, C.K.1    Kassab, A.J.2
  • 23
    • 0031170037 scopus 로고    scopus 로고
    • An inverse geometry problem for identifying irregular boundary configurations
    • C.H. Huang, and B.H. Chao An inverse geometry problem for identifying irregular boundary configurations Int. J. Heat Mass Transfer 40 1997 2045 2053
    • (1997) Int. J. Heat Mass Transfer , vol.40 , pp. 2045-2053
    • Huang, C.H.1    Chao, B.H.2
  • 24
    • 0032102509 scopus 로고    scopus 로고
    • A transient inverse two-dimensional geometry problem in estimating time-dependent irregular boundary configurations
    • C.H. Huang, and C.C. Tsai A transient inverse two-dimensional geometry problem in estimating time-dependent irregular boundary configurations Int. J. Heat Mass Transfer 41 1997 1707 1718
    • (1997) Int. J. Heat Mass Transfer , vol.41 , pp. 1707-1718
    • Huang, C.H.1    Tsai, C.C.2
  • 25
    • 33846990077 scopus 로고    scopus 로고
    • The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction
    • B. Jin, and L. Marin The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction Int. J. Numer. Methods Eng. 69 2007 1570 1589
    • (2007) Int. J. Numer. Methods Eng. , vol.69 , pp. 1570-1589
    • Jin, B.1    Marin, L.2
  • 26
    • 33644595481 scopus 로고    scopus 로고
    • A meshless method for some inverse problems associated with the Helmholtz equation
    • B. Jin, and Y. Zheng A meshless method for some inverse problems associated with the Helmholtz equation Comput. Methods Appl. Mech. Eng. 195 2006 2270 2280
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.195 , pp. 2270-2280
    • Jin, B.1    Zheng, Y.2
  • 27
    • 0001410167 scopus 로고    scopus 로고
    • Iterative choices of regularization parameters in linear inverse problems
    • K. Kunisch, and J. Zou Iterative choices of regularization parameters in linear inverse problems Inverse Prob. 14 1998 1247 1264
    • (1998) Inverse Prob. , vol.14 , pp. 1247-1264
    • Kunisch, K.1    Zou, J.2
  • 28
    • 33748444430 scopus 로고
    • The method of functional equations for the approximate solution of certain boundary value problems
    • V.D. Kupradze, and M.A. Aleksidze The method of functional equations for the approximate solution of certain boundary value problems USSR Comput. Math. Math. Phys. 4 1964 82 126
    • (1964) USSR Comput. Math. Math. Phys. , vol.4 , pp. 82-126
    • Kupradze, V.D.1    Aleksidze, M.A.2
  • 29
    • 0036554090 scopus 로고    scopus 로고
    • A boundary element regularization method for the boundary determination in potential corrosion damage
    • D. Lesnic, J.R. Berger, and P.A. Martin A boundary element regularization method for the boundary determination in potential corrosion damage Inverse Prob. Eng. 10 2002 163 182
    • (2002) Inverse Prob. Eng. , vol.10 , pp. 163-182
    • Lesnic, D.1    Berger, J.R.2    Martin, P.A.3
  • 30
    • 49749085551 scopus 로고    scopus 로고
    • Boundary control for inverse Cauchy problems of the Laplace equations
    • L. Ling, and T. Takeuchi Boundary control for inverse Cauchy problems of the Laplace equations CMES: Comput. Model. Eng. Sci. 29 2008 45 54
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.29 , pp. 45-54
    • Ling, L.1    Takeuchi, T.2
  • 31
    • 51349169389 scopus 로고    scopus 로고
    • A regularized integral equation method for the inverse geometry heat conduction problem
    • C.S. Liu, C.W. Chang, and C.Y. Chiang A regularized integral equation method for the inverse geometry heat conduction problem Int. J. Heat Transfer 51 2008 5380 5388
    • (2008) Int. J. Heat Transfer , vol.51 , pp. 5380-5388
    • Liu, C.S.1    Chang, C.W.2    Chiang, C.Y.3
  • 32
    • 27544445360 scopus 로고    scopus 로고
    • A meshless method for solving the Cauchy problem in three-dimensional elastostatics
    • L. Marin A meshless method for solving the Cauchy problem in three-dimensional elastostatics Comput. Math. Appl. 50 2005 73 92
    • (2005) Comput. Math. Appl. , vol.50 , pp. 73-92
    • Marin, L.1
  • 33
    • 16344395168 scopus 로고    scopus 로고
    • Numerical solutions of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials
    • L. Marin Numerical solutions of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials Int. J. Solids Struct. 42 2005 4338 4351
    • (2005) Int. J. Solids Struct. , vol.42 , pp. 4338-4351
    • Marin, L.1
  • 34
    • 17644417110 scopus 로고    scopus 로고
    • A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations
    • DOI 10.1016/j.amc.2004.04.052, PII S009630030400387X
    • L. Marin A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations Appl. Math. Comput. 165 2005 355 374 (Pubitemid 40567737)
    • (2005) Applied Mathematics and Computation , vol.165 , Issue.2 , pp. 355-374
    • Marin, L.1
  • 35
    • 33749000622 scopus 로고    scopus 로고
    • Numerical boundary identification for Helmholtz-type equations
    • L. Marin Numerical boundary identification for Helmholtz-type equations Comput. Mech. 39 2006 25 40
    • (2006) Comput. Mech. , vol.39 , pp. 25-40
    • Marin, L.1
  • 36
    • 55549084883 scopus 로고    scopus 로고
    • The method of fundamental solutions for inverse problems associated with the steady-state heat conduction in the presence of sources
    • L. Marin The method of fundamental solutions for inverse problems associated with the steady-state heat conduction in the presence of sources CMES: Comput. Model. Eng. Sci. 30 2008 99 122
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.30 , pp. 99-122
    • Marin, L.1
  • 37
    • 76449098701 scopus 로고    scopus 로고
    • Boundary reconstruction in two-dimensional functionally graded materials using a regularized MFS
    • L. Marin Boundary reconstruction in two-dimensional functionally graded materials using a regularized MFS CMES: Comput. Model. Eng. Sci. 46 2009 221 253
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.46 , pp. 221-253
    • Marin, L.1
  • 38
    • 77649162340 scopus 로고    scopus 로고
    • Regularized MFS-based boundary identification in two-dimensional Helmholtz-type equations
    • L. Marin, and A. Karageorghis Regularized MFS-based boundary identification in two-dimensional Helmholtz-type equations CMC: Comput. Mater. Continua 10 2009 259 293
    • (2009) CMC: Comput. Mater. Continua , vol.10 , pp. 259-293
    • Marin, L.1    Karageorghis, A.2
  • 39
    • 0038364172 scopus 로고    scopus 로고
    • BEM first-order regularisation method in linear elasticity for boundary identification
    • L. Marin, and D. Lesnic BEM first-order regularisation method in linear elasticity for boundary identification Comput. Methods Appl. Mech. Eng. 192 2003 2059 2071
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 2059-2071
    • Marin, L.1    Lesnic, D.2
  • 40
    • 2342463081 scopus 로고    scopus 로고
    • The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
    • L. Marin, and D. Lesnic The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity Int. J. Solids Struct. 41 2004 3425 3438
    • (2004) Int. J. Solids Struct. , vol.41 , pp. 3425-3438
    • Marin, L.1    Lesnic, D.2
  • 41
    • 11344277052 scopus 로고    scopus 로고
    • The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations
    • DOI 10.1016/j.compstruc.2004.10.005, PII S0045794904004031
    • L. Marin, and D. Lesnic The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations Comput. Struct. 83 2005 267 278 (Pubitemid 40072215)
    • (2005) Computers and Structures , vol.83 , Issue.4-5 , pp. 267-278
    • Marin, L.1    Lesnic, D.2
  • 42
    • 26844436520 scopus 로고    scopus 로고
    • The method of fundamental solutions for inverse boundary value problems associated with the two dimensional biharmonic equation
    • L. Marin, and D. Lesnic The method of fundamental solutions for inverse boundary value problems associated with the two dimensional biharmonic equation Math. Comput. Model. 42 2005 261 278
    • (2005) Math. Comput. Model. , vol.42 , pp. 261-278
    • Marin, L.1    Lesnic, D.2
  • 44
    • 0000678579 scopus 로고
    • The approximate solution of elliptic boundary value problems by fundamental solutions
    • R. Mathon, and R.L. Johnston The approximate solution of elliptic boundary value problems by fundamental solutions SIAM J. Numer. Anal. 14 1977 638 650
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 638-650
    • Mathon, R.1    Johnston, R.L.2
  • 45
    • 12344271462 scopus 로고    scopus 로고
    • The method of fundamental solutions for the backward heat conduction problem
    • N.S. Mera The method of fundamental solutions for the backward heat conduction problem Inverse Prob. Sci. Eng. 13 2005 79 98
    • (2005) Inverse Prob. Sci. Eng. , vol.13 , pp. 79-98
    • Mera, N.S.1
  • 46
    • 21144444255 scopus 로고    scopus 로고
    • A three-dimensional boundary determination problem in potential corrosion damage
    • N.S. Mera, and D. Lesnic A three-dimensional boundary determination problem in potential corrosion damage Comput. Mech. 36 2005 129 138
    • (2005) Comput. Mech. , vol.36 , pp. 129-138
    • Mera, N.S.1    Lesnic, D.2
  • 47
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • V.A. Morozov On the solution of functional equations by the method of regularization Doklady Math. 7 1966 414 417
    • (1966) Doklady Math. , vol.7 , pp. 414-417
    • Morozov, V.A.1
  • 48
    • 77957317178 scopus 로고    scopus 로고
    • Numerical Algorithms Group Library Mark 21, NAG(UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK 2007
    • Numerical Algorithms Group Library Mark 21, NAG(UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK, 2007.
  • 49
    • 67649338397 scopus 로고    scopus 로고
    • The method of fundamental solutions for the inverse space-dependent heat source problem
    • M. Nili Ahmadabadi, M. Arab, and F.M. Maalek Ghaini The method of fundamental solutions for the inverse space-dependent heat source problem Eng. Anal. with Boundary Elem. 33 2009 1231 1235
    • (2009) Eng. Anal. with Boundary Elem. , vol.33 , pp. 1231-1235
    • Nili Ahmadabadi, M.1    Arab, M.2    Maalek Ghaini, F.M.3
  • 50
    • 0035660043 scopus 로고    scopus 로고
    • Shape identification for natural convection problems
    • H.M. Park, and J.H. Ku Shape identification for natural convection problems Commun. Numer. Methods Eng. 17 2001 871 880
    • (2001) Commun. Numer. Methods Eng. , vol.17 , pp. 871-880
    • Park, H.M.1    Ku, J.H.2
  • 51
    • 0010716249 scopus 로고
    • Isotherm shape identification for a two-dimensional heat conduction problem
    • S. Peneau, Y. Jarny, and A. Sarda Isotherm shape identification for a two-dimensional heat conduction problem H.D. Bui, M. Tanaka, M. Bonnet, H. Maigre, E. Luzzato, M. Reynier, Inverse Problems in Engineering Mechanics 1966 Balkema Rotterdam 47 53
    • (1966) Inverse Problems in Engineering Mechanics , pp. 47-53
    • Peneau, S.1    Jarny, Y.2    Sarda, A.3
  • 52
    • 59149098853 scopus 로고    scopus 로고
    • Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points
    • T. Shigeta, and D.L. Young Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points J. Comput. Phys. 228 2009 1903 1915
    • (2009) J. Comput. Phys. , vol.228 , pp. 1903-1915
    • Shigeta, T.1    Young, D.L.2
  • 54
    • 0001041472 scopus 로고    scopus 로고
    • Non-convergence of the L-curve regularization parameter selection method
    • C.R. Vogel Non-convergence of the L-curve regularization parameter selection method Inverse Prob. 12 1996 535 547
    • (1996) Inverse Prob. , vol.12 , pp. 535-547
    • Vogel, C.R.1
  • 55
    • 0000544453 scopus 로고
    • Practical approximate solutions to linear operator equations when the data are noisy
    • G. Wahba Practical approximate solutions to linear operator equations when the data are noisy SIAM J. Numer. Anal. 14 1977 651 667
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 651-667
    • Wahba, G.1
  • 56
    • 38349149734 scopus 로고    scopus 로고
    • The method of fundamental solutions for the inverse heat source problem
    • L. Yan, C.-L. Fu, and F.-L. Yang The method of fundamental solutions for the inverse heat source problem Eng. Anal. with Boundary Elem. 32 2008 216 222
    • (2008) Eng. Anal. with Boundary Elem. , vol.32 , pp. 216-222
    • Yan, L.1    Fu, C.-L.2    Yang, F.-L.3
  • 57
    • 70350751330 scopus 로고    scopus 로고
    • Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solutions
    • F.L. Yang, L. Yan, and T. Wei Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solutions Inverse Prob. Sci. Eng. 17 2009 1113 1128
    • (2009) Inverse Prob. Sci. Eng. , vol.17 , pp. 1113-1128
    • Yang, F.L.1    Yan, L.2    Wei, T.3
  • 58
    • 38849085183 scopus 로고    scopus 로고
    • The method of fundamental solutions and condition number analysis for inverse problems of Laplace equation
    • D.L. Young, C.C. Tsai, C.W. Chen, and C.M. Fan The method of fundamental solutions and condition number analysis for inverse problems of Laplace equation Comput. Math. with Appl. 55 2008 1189 1200
    • (2008) Comput. Math. with Appl. , vol.55 , pp. 1189-1200
    • Young, D.L.1    Tsai, C.C.2    Chen, C.W.3    Fan, C.M.4
  • 59
    • 44449145507 scopus 로고    scopus 로고
    • The method of fundamental solutions for a biharmonic boundary determination
    • A. Zeb, D.B. Ingham, and D. Lesnic The method of fundamental solutions for a biharmonic boundary determination Comput. Mech. 42 2008 371 379
    • (2008) Comput. Mech. , vol.42 , pp. 371-379
    • Zeb, A.1    Ingham, D.B.2    Lesnic, D.3


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