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Volumn 43, Issue 6, 2009, Pages 827-837

Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

Author keywords

Desingularized meshless method; Inverse problem; Subtracting and adding back technique; Tikhonov method; Truncated singular value decomposition method

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; PROBLEM SOLVING; SINGULAR VALUE DECOMPOSITION;

EID: 60449101220     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-008-0348-1     Document Type: Article
Times cited : (21)

References (26)
  • 1
    • 0034323326 scopus 로고    scopus 로고
    • Tikhonov regularization and the L-curve for large discrete ill-posed problems
    • D Calvetti S Morigi L Reichel F Sgallari 2000 Tikhonov regularization and the L-curve for large discrete ill-posed problems J Comput Appl Math 123 423 446
    • (2000) J Comput Appl Math , vol.123 , pp. 423-446
    • Calvetti, D.1    Morigi, S.2    Reichel, L.3    Sgallari, F.4
  • 2
    • 0242516794 scopus 로고    scopus 로고
    • On the modified Tikhonov's regularization method for the Cauchy problem of the Laplace equation
    • JR Chang W Yeih MH Shieh 2001 On the modified Tikhonov's regularization method for the Cauchy problem of the Laplace equation J Mar Sci Technol 9 113 121
    • (2001) J Mar Sci Technol , vol.9 , pp. 113-121
    • Chang, J.R.1    Yeih, W.2    Shieh, M.H.3
  • 3
    • 0345369390 scopus 로고    scopus 로고
    • The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations
    • CS Chen MA Golberg YC Hon 1998 The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations Int J Numer Methods Eng 43 1421 1435
    • (1998) Int J Numer Methods Eng , vol.43 , pp. 1421-1435
    • Chen, C.S.1    Golberg, M.A.2    Hon, Y.C.3
  • 4
    • 0032155239 scopus 로고    scopus 로고
    • Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions
    • JT Chen KH Chen 1998 Analytical study and numerical experiments for Laplace equation with overspecified boundary conditions Appl Math Model 22 703 725
    • (1998) Appl Math Model , vol.22 , pp. 703-725
    • Chen, J.T.1    Chen, K.H.2
  • 5
    • 33748450782 scopus 로고    scopus 로고
    • Regularized meshless method for multiply-connected-domain Laplace problems
    • 10
    • KH Chen JH Kao JT Chen DL Young MC Lu 2006 Regularized meshless method for multiply-connected-domain Laplace problems Eng Anal Bound Elem 30 10 882 896
    • (2006) Eng Anal Bound Elem , vol.30 , pp. 882-896
    • Chen, K.H.1    Kao, J.H.2    Chen, J.T.3    Young, D.L.4    Lu, M.C.5
  • 6
    • 0036467593 scopus 로고    scopus 로고
    • A meshfree integration-free and boundary-only RBF technique
    • W Chen M Tanaka 2002 A meshfree integration-free and boundary-only RBF technique Comput Math Appl 43 379 391
    • (2002) Comput Math Appl , vol.43 , pp. 379-391
    • Chen, W.1    Tanaka, M.2
  • 7
    • 24944556284 scopus 로고    scopus 로고
    • Direct solution of ill-posed boundary value problems by radial basis function collocation method
    • AHD Cheng JJSP Cabral 2005 Direct solution of ill-posed boundary value problems by radial basis function collocation method Int J Numer Methods Eng 64 45 64
    • (2005) Int J Numer Methods Eng , vol.64 , pp. 45-64
    • Cheng, A.H.D.1    Jjsp, C.2
  • 8
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems
    • G Fairweather A Karageorghis 1998 The method of fundamental solutions for elliptic boundary value problems Adv Comput Math 9 69 95
    • (1998) Adv Comput Math , vol.9 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 9
    • 39749105274 scopus 로고    scopus 로고
    • A first order method for the Cauchy problem for the Laplace equation using BEM
    • doi: 10.1007/s00466-007-0157-y
    • Franck D, Alain C (2007) A first order method for the Cauchy problem for the Laplace equation using BEM. Comput Mech. doi: 10.1007/s00466-007-0157-y
    • (2007) Comput Mech.
    • Franck, D.1    Alain, C.2
  • 11
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • 4
    • PC Hansen 1992 Analysis of discrete ill-posed problems by means of the L-curve SIAM Rev 34 4 561 580
    • (1992) SIAM Rev , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 12
    • 1842842972 scopus 로고    scopus 로고
    • A fundamental solution method for inverse heat conduction problem
    • YC Hon T Wei 2004 A fundamental solution method for inverse heat conduction problem Eng Anal Bound Elem 28 489 495
    • (2004) Eng Anal Bound Elem , vol.28 , pp. 489-495
    • Hon, Y.C.1    Wei, T.2
  • 13
    • 0034283123 scopus 로고    scopus 로고
    • Selecting the Corner in the Curve Approach to Tikhonov regularization
    • 9
    • PR Johnston RM Gulrajani 2000 Selecting the Corner in the Curve Approach to Tikhonov regularization IEEE Trans Biomed Eng 47 9 1293 1296
    • (2000) IEEE Trans Biomed Eng , vol.47 , pp. 1293-1296
    • Johnston, P.R.1    Gulrajani, R.M.2
  • 14
    • 8344280951 scopus 로고    scopus 로고
    • A meshless method for the Laplace and Biharmonic equations subjected to noisy boundary data
    • 3
    • B Jin 2004 A meshless method for the Laplace and Biharmonic equations subjected to noisy boundary data Comput Model Eng Sci 6 3 253 261
    • (2004) Comput Model Eng Sci , vol.6 , pp. 253-261
    • Jin, B.1
  • 15
    • 0023994993 scopus 로고    scopus 로고
    • Inverse problems related to the mechanics and fracture of solids structure
    • 2
    • S Kubo 1998 Inverse problems related to the mechanics and fracture of solids structure JSME Int J Ser I 31 2 157 166
    • (1998) JSME Int J ser i , vol.31 , pp. 157-166
    • Kubo, S.1
  • 16
    • 0008215313 scopus 로고
    • The method of functional equations for the approximate solution of certain boundary value problems
    • VD Kupradze MA Aleksidze 1964 The method of functional equations for the approximate solution of certain boundary value problems USSR Comput Math Math Phys 4 199 205
    • (1964) USSR Comput Math Math Phys , vol.4 , pp. 199-205
    • Kupradze, V.D.1    Aleksidze, M.A.2
  • 17
    • 0742289128 scopus 로고    scopus 로고
    • A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition
    • GL Lagier H Lemonnier N Coutris 2004 A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition Int J Therm Sci 43 145 155
    • (2004) Int J Therm Sci , vol.43 , pp. 145-155
    • Lagier, G.L.1    Lemonnier, H.2    Coutris, N.3
  • 18
    • 0031219785 scopus 로고    scopus 로고
    • An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation
    • D Lesnic L Elliott DB Ingham 1997 An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation Eng Anal Bound Elem 20 123 133
    • (1997) Eng Anal Bound Elem , vol.20 , pp. 123-133
    • Lesnic, D.1    Elliott, L.2    Ingham, D.B.3
  • 19
    • 0035080394 scopus 로고    scopus 로고
    • A minimal product method and its application to cortical imaging
    • J Lian B He 2001 A minimal product method and its application to cortical imaging Brain Topogr 13 209 217
    • (2001) Brain Topogr , vol.13 , pp. 209-217
    • Lian, J.1    He, B.2
  • 20
    • 16344395168 scopus 로고    scopus 로고
    • Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials
    • L Marin 2005 Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials Int J Solids Struct 42 4338 4351
    • (2005) Int J Solids Struct , vol.42 , pp. 4338-4351
    • Marin, L.1
  • 21
    • 33749000622 scopus 로고    scopus 로고
    • Numerical boundary identification for Helmholtz-type equations
    • L Marin 2006 Numerical boundary identification for Helmholtz-type equations Comput Mech 39 25 40
    • (2006) Comput Mech , vol.39 , pp. 25-40
    • Marin, L.1
  • 22
    • 38849130746 scopus 로고
    • Short communications: A method of choosing the regularization parameter for the numerical solution of ill-posed problems
    • 3
    • AR Poluektov 1992 Short communications: a method of choosing the regularization parameter for the numerical solution of ill-posed problems Comput Math Math Phys 32 3 397 401
    • (1992) Comput Math Math Phys , vol.32 , pp. 397-401
    • Poluektov, A.R.1
  • 25
    • 33847032040 scopus 로고    scopus 로고
    • Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators
    • T Wei YC Hon L Ling 2007 Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators Eng Anal Bound Elem 31 373 385
    • (2007) Eng Anal Bound Elem , vol.31 , pp. 373-385
    • Wei, T.1    Hon, Y.C.2    Ling, L.3
  • 26
    • 20344402529 scopus 로고    scopus 로고
    • Novel meshless method for solving the potential problems with arbitrary domain
    • DL Young KH Chen CW Lee 2005 Novel meshless method for solving the potential problems with arbitrary domain J Comput Phys 209 290 321
    • (2005) J Comput Phys , vol.209 , pp. 290-321
    • Young, D.L.1    Chen, K.H.2    Lee, C.W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.