메뉴 건너뛰기




Volumn 53, Issue 23-24, 2010, Pages 5552-5569

A new algorithm for direct and backward problems of heat conduction equation

Author keywords

Backward heat conduction problem; Fictitious time integration method (FTIM); Group preserving scheme; Heat conduction equation; Strongly ill posed problem

Indexed keywords

FICTITIOUS TIME INTEGRATION METHODS; GROUP PRESERVING SCHEME; HEAT CONDUCTION EQUATION; HEAT CONDUCTION PROBLEMS; ILL POSED PROBLEM;

EID: 77956057028     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2010.06.050     Document Type: Article
Times cited : (29)

References (51)
  • 3
    • 0031651128 scopus 로고    scopus 로고
    • Solving transient diffusion problems: Time-dependent fundamental solution approaches versus LTDRM approaches
    • S.P. Zhu Solving transient diffusion problems: time-dependent fundamental solution approaches versus LTDRM approaches Eng. Anal. Bound. Elem. 21 1998 87 90
    • (1998) Eng. Anal. Bound. Elem. , vol.21 , pp. 87-90
    • Zhu, S.P.1
  • 4
    • 0032044811 scopus 로고    scopus 로고
    • A combination of LTDRM and ATPS in solving diffusion problems
    • S.P. Zhu, H.W. Liu, and X.P. Lu A combination of LTDRM and ATPS in solving diffusion problems Eng. Anal. Bound. Elem. 21 1998 285 289
    • (1998) Eng. Anal. Bound. Elem. , vol.21 , pp. 285-289
    • Zhu, S.P.1    Liu, H.W.2    Lu, X.P.3
  • 5
    • 0032184318 scopus 로고    scopus 로고
    • Iterative solution of systems of equations in the dual reciprocity boundary element method for the diffusion equation
    • V. Bulgakov, B. Sarler, and G. Kuhn Iterative solution of systems of equations in the dual reciprocity boundary element method for the diffusion equation Int. J. Numer. Meth. Eng. 43 1998 713 732
    • (1998) Int. J. Numer. Meth. Eng. , vol.43 , pp. 713-732
    • Bulgakov, V.1    Sarler, B.2    Kuhn, G.3
  • 6
    • 0033101571 scopus 로고    scopus 로고
    • A boundary element scheme for diffusion problems using compactly supported radial basis functions
    • M. Zerroukat A boundary element scheme for diffusion problems using compactly supported radial basis functions Eng. Anal. Bound. Elem. 23 1999 201 209
    • (1999) Eng. Anal. Bound. Elem. , vol.23 , pp. 201-209
    • Zerroukat, M.1
  • 7
    • 0036466997 scopus 로고    scopus 로고
    • Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method
    • A. Sutradhar, G.H. Paulino, and L.J. Gray Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method Eng. Anal. Bound. Elem. 26 2002 119 132
    • (2002) Eng. Anal. Bound. Elem. , vol.26 , pp. 119-132
    • Sutradhar, A.1    Paulino, G.H.2    Gray, L.J.3
  • 8
    • 0036498110 scopus 로고    scopus 로고
    • Dual reciprocity BEM without matrix inversion for transient heat conduction
    • R.A. Bialecki, P. Jurgas, and G. Kuhn Dual reciprocity BEM without matrix inversion for transient heat conduction Eng. Anal. Bound. Elem. 26 2002 227 236
    • (2002) Eng. Anal. Bound. Elem. , vol.26 , pp. 227-236
    • Bialecki, R.A.1    Jurgas, P.2    Kuhn, G.3
  • 9
    • 0026884582 scopus 로고
    • Diffusion problems using transient discrete source superposition
    • S.P. Walker Diffusion problems using transient discrete source superposition Int. J. Numer. Meth. Eng. 35 1992 165 178
    • (1992) Int. J. Numer. Meth. Eng. , vol.35 , pp. 165-178
    • Walker, S.P.1
  • 10
    • 0345369390 scopus 로고    scopus 로고
    • The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations
    • C.S. Chen, M.A. Golberg, and Y.C. Hon The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations Int. J. Numer. Meth. Eng. 43 1998 1421 1435
    • (1998) Int. J. Numer. Meth. Eng. , vol.43 , pp. 1421-1435
    • Chen, C.S.1    Golberg, M.A.2    Hon, Y.C.3
  • 12
    • 33645461386 scopus 로고    scopus 로고
    • Methods of fundamental solutions for time-dependent heat conduction problems
    • S. Chantasiriwan Methods of fundamental solutions for time-dependent heat conduction problems Int. J. Numer. Meth. Eng. 66 2006 147 165
    • (2006) Int. J. Numer. Meth. Eng. , vol.66 , pp. 147-165
    • Chantasiriwan, S.1
  • 13
    • 47049117962 scopus 로고    scopus 로고
    • A method of fundamental solutions for transient heat conduction
    • B.T. Johansson, and D. Lesnic A method of fundamental solutions for transient heat conduction Eng. Anal. Bound. Elem. 32 2008 697 703
    • (2008) Eng. Anal. Bound. Elem. , vol.32 , pp. 697-703
    • Johansson, B.T.1    Lesnic, D.2
  • 14
    • 0001293247 scopus 로고
    • The boundary element method for the solution of the backward heat conduction equation
    • H. Han, D.B. Ingham, and Y. Yuan The boundary element method for the solution of the backward heat conduction equation J. Comput. Phys. 116 1995 292 299
    • (1995) J. Comput. Phys. , vol.116 , pp. 292-299
    • Han, H.1    Ingham, D.B.2    Yuan, Y.3
  • 15
    • 0034744604 scopus 로고    scopus 로고
    • An iterative boundary element method for solving the one-dimensional backward heat conduction problem
    • N.S. Mera, L. Elliott, D.B. Ingham, and D. Lesnic An iterative boundary element method for solving the one-dimensional backward heat conduction problem Int. J. Heat Mass Transfer 44 2001 1937 1946
    • (2001) Int. J. Heat Mass Transfer , vol.44 , pp. 1937-1946
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3    Lesnic, D.4
  • 16
    • 0036749217 scopus 로고    scopus 로고
    • An inversion method with decreasing regularization for the backward heat conduction problem
    • N.S. Mera, L. Elliott, and D.B. Ingham An inversion method with decreasing regularization for the backward heat conduction problem Numer. Heat Transfer B 42 2002 215 230
    • (2002) Numer. Heat Transfer B , vol.42 , pp. 215-230
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3
  • 17
    • 0036697675 scopus 로고    scopus 로고
    • An iterative algorithm for the backward heat conduction problem based on variable relaxation factors
    • M. Jourhmane, and N.S. Mera An iterative algorithm for the backward heat conduction problem based on variable relaxation factors Inv. Prob. Eng. 10 2002 293 308
    • (2002) Inv. Prob. Eng. , vol.10 , pp. 293-308
    • Jourhmane, M.1    Mera, N.S.2
  • 18
    • 0033096606 scopus 로고    scopus 로고
    • A comparison of some inverse methods for estimating the initial condition of the heat equation
    • W.B. Muniz, H.F. de Campos Velho, and F.M. Ramos A comparison of some inverse methods for estimating the initial condition of the heat equation J. Comput. Appl. Math. 103 1999 145 163
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 145-163
    • Muniz, W.B.1    De Campos Velho, H.F.2    Ramos, F.M.3
  • 19
    • 0342520839 scopus 로고    scopus 로고
    • Entropy- and Tikhonov-based regularization techniques applied to the backward heat equation
    • W.B. Muniz, F.M. Ramos, and H.F. de Campos Velho Entropy- and Tikhonov-based regularization techniques applied to the backward heat equation Int. J. Comput. Math. 40 2000 1071 1084
    • (2000) Int. J. Comput. Math. , vol.40 , pp. 1071-1084
    • Muniz, W.B.1    Ramos, F.M.2    De Campos Velho, H.F.3
  • 20
    • 0344514171 scopus 로고    scopus 로고
    • Solution of inverse diffusion problems by operator-splitting methods
    • S.M. Kirkup, and M. Wadsworth Solution of inverse diffusion problems by operator-splitting methods Appl. Math. Model. 26 2002 1003 1018
    • (2002) Appl. Math. Model. , vol.26 , pp. 1003-1018
    • Kirkup, S.M.1    Wadsworth, M.2
  • 21
    • 0037102596 scopus 로고    scopus 로고
    • Numerical solution of forward and backward problem for 2-D heat conduction equation
    • J. Liu Numerical solution of forward and backward problem for 2-D heat conduction equation J. Comput. Appl. Math. 145 2002 459 482
    • (2002) J. Comput. Appl. Math. , vol.145 , pp. 459-482
    • Liu, J.1
  • 22
    • 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 Inv. Prob. Sci. Eng. 13 2005 65 78
    • (2005) Inv. Prob. Sci. Eng. , vol.13 , pp. 65-78
    • Mera, N.S.1
  • 23
    • 3142679353 scopus 로고    scopus 로고
    • Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method
    • K. Iijima Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method J. Chin. Inst. Eng. 27 2004 611 620
    • (2004) J. Chin. Inst. Eng. , vol.27 , pp. 611-620
    • Iijima, K.1
  • 24
    • 33646850601 scopus 로고    scopus 로고
    • Past cone dynamics and backward group preserving schemes for backward heat conduction problems
    • C.-S. Liu, C.-W. Chang, and J.-R. Chang Past cone dynamics and backward group preserving schemes for backward heat conduction problems CMES: Comput. Model. Eng. Sci. 12 2006 67 81
    • (2006) CMES: Comput. Model. Eng. Sci. , vol.12 , pp. 67-81
    • Liu, C.-S.1    Chang, C.-W.2    Chang, J.-R.3
  • 25
    • 1842534840 scopus 로고    scopus 로고
    • Group preserving scheme for backward heat conduction problems
    • C.-S. Liu Group preserving scheme for backward heat conduction problems Int. J. Heat Mass Transfer 47 2004 2567 2576
    • (2004) Int. J. Heat Mass Transfer , vol.47 , pp. 2567-2576
    • Liu, C.-S.1
  • 26
    • 0035480574 scopus 로고    scopus 로고
    • Cone of non-linear dynamical system and group preserving schemes
    • C.-S. Liu Cone of non-linear dynamical system and group preserving schemes Int. J. Non-Linear Mech. 36 2001 1047 1068
    • (2001) Int. J. Non-Linear Mech. , vol.36 , pp. 1047-1068
    • Liu, C.-S.1
  • 27
    • 33847712471 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of backward heat conduction problems
    • J.-R. Chang, C.-S. Liu, and C.-W. Chang A new shooting method for quasi-boundary regularization of backward heat conduction problems Int. J. Heat Mass Transfer 50 2007 2325 2332
    • (2007) Int. J. Heat Mass Transfer , vol.50 , pp. 2325-2332
    • Chang, J.-R.1    Liu, C.-S.2    Chang, C.-W.3
  • 28
    • 67249148129 scopus 로고    scopus 로고
    • A new shooting method for quasi-boundary regularization of multi-dimensional backward heat conduction problems
    • C.-W. Chang, C.-S. Liu, and J.-R. Chang A new shooting method for quasi-boundary regularization of multi-dimensional backward heat conduction problems J. Chin. Inst. Eng. 32 2009 307 318
    • (2009) J. Chin. Inst. Eng. , vol.32 , pp. 307-318
    • Chang, C.-W.1    Liu, C.-S.2    Chang, J.-R.3
  • 29
    • 77950798676 scopus 로고    scopus 로고
    • A quasi-boundary semi-analytical method for backward heat conduction problems
    • C.-W. Chang, C.-S. Liu, and J.-R. Chang A quasi-boundary semi-analytical method for backward heat conduction problems J. Chin. Inst. Eng. 33 2010 163 175
    • (2010) J. Chin. Inst. Eng. , vol.33 , pp. 163-175
    • Chang, C.-W.1    Liu, C.-S.2    Chang, J.-R.3
  • 30
    • 77952843312 scopus 로고    scopus 로고
    • A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems
    • C.-W. Chang, C.-S. Liu, and J.-R. Chang A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems CMC: Comput. Mater. Contin. 15 2010 45 66
    • (2010) CMC: Comput. Mater. Contin. , vol.15 , pp. 45-66
    • Chang, C.-W.1    Liu, C.-S.2    Chang, J.-R.3
  • 31
    • 77954535504 scopus 로고    scopus 로고
    • A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data
    • C.-S. Liu A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data Int. J. Heat Mass Transfer 53 2010 4132 4140
    • (2010) Int. J. Heat Mass Transfer , vol.53 , pp. 4132-4140
    • Liu, C.-S.1
  • 33
    • 43049107224 scopus 로고    scopus 로고
    • Solving an inverse Sturm-Liouville problem by a Lie-group method
    • C.-S. Liu Solving an inverse Sturm-Liouville problem by a Lie-group method Bound. Value Prob. 2008 2008 Article ID: 749865
    • (2008) Bound. Value Prob. , vol.2008
    • Liu, C.-S.1
  • 34
    • 46449129207 scopus 로고    scopus 로고
    • Identifying time-dependent damping and stiffness functions by a simple and yet accurate method
    • C.-S. Liu Identifying time-dependent damping and stiffness functions by a simple and yet accurate method J. Sound Vib. 318 2008 148 165
    • (2008) J. Sound Vib. , vol.318 , pp. 148-165
    • Liu, C.-S.1
  • 35
    • 49149112956 scopus 로고    scopus 로고
    • A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients
    • C.-S. Liu A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients CMES: Comput. Model. Eng. Sci. 27 2008 137 149
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.27 , pp. 137-149
    • Liu, C.-S.1
  • 36
    • 46449109059 scopus 로고    scopus 로고
    • Simultaneously estimating the time-dependent damping and stiffness coefficients with the aid of vibrational data
    • C.-S. Liu, J.-R. Chang, K.-H. Chang, and Y.-W. Chen Simultaneously estimating the time-dependent damping and stiffness coefficients with the aid of vibrational data CMC: Comput. Mater. Contin. 7 2008 97 107
    • (2008) CMC: Comput. Mater. Contin. , vol.7 , pp. 97-107
    • Liu, C.-S.1    Chang, J.-R.2    Chang, K.-H.3    Chen, Y.-W.4
  • 37
    • 55349116390 scopus 로고    scopus 로고
    • A novel time integration method for solving a large system of non-linear algebraic equations
    • C.-S. Liu, and S.N. Atluri A novel time integration method for solving a large system of non-linear algebraic equations CMES: Comput. Model. Eng. Sci. 31 2008 71 83
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.31 , pp. 71-83
    • Liu, C.-S.1    Atluri, S.N.2
  • 38
    • 58149396461 scopus 로고    scopus 로고
    • A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function
    • C.-S. Liu A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function CMC: Comput. Mater. Contin. 8 2008 53 65
    • (2008) CMC: Comput. Mater. Contin. , vol.8 , pp. 53-65
    • Liu, C.-S.1
  • 39
    • 57349138589 scopus 로고    scopus 로고
    • A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems
    • C.-S. Liu A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems CMES: Comput. Model. Eng. Sci. 33 2008 179 198
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.33 , pp. 179-198
    • Liu, C.-S.1
  • 40
    • 58149503275 scopus 로고    scopus 로고
    • A novel fictitious time integration method for solving the discretized inverse Sturm-Liouville problems, for specified eigenvalues
    • C.-S. Liu, and S.N. Atluri A novel fictitious time integration method for solving the discretized inverse Sturm-Liouville problems, for specified eigenvalues CMES: Comput. Model. Eng. Sci. 36 2008 261 285
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.36 , pp. 261-285
    • Liu, C.-S.1    Atluri, S.N.2
  • 41
    • 57649213675 scopus 로고    scopus 로고
    • A novel time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization
    • C.-S. Liu, and S.N. Atluri A novel time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization CMES: Comput. Model. Eng. Sci. 34 2008 155 178
    • (2008) CMES: Comput. Model. Eng. Sci. , vol.34 , pp. 155-178
    • Liu, C.-S.1    Atluri, S.N.2
  • 42
    • 63349084543 scopus 로고    scopus 로고
    • A fictitious time integration method for solving m-point boundary value problems
    • C.-S. Liu A fictitious time integration method for solving m-point boundary value problems CMES: Comput. Model. Eng. Sci. 39 2009 125 154
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.39 , pp. 125-154
    • Liu, C.-S.1
  • 43
    • 77249118300 scopus 로고    scopus 로고
    • A fictitious time integration method for solving delay ordinary differential equations
    • C.-S. Liu A fictitious time integration method for solving delay ordinary differential equations CMC: Comput. Mater. Contin. 10 2009 97 116
    • (2009) CMC: Comput. Mater. Contin. , vol.10 , pp. 97-116
    • Liu, C.-S.1
  • 44
    • 77449088886 scopus 로고    scopus 로고
    • A fictitious time integration method for a quasilinear elliptic boundary value problems, defined in an arbitrary plane domain
    • C.-S. Liu A fictitious time integration method for a quasilinear elliptic boundary value problems, defined in an arbitrary plane domain CMC: Comput. Mater. Contin. 11 2009 15 32
    • (2009) CMC: Comput. Mater. Contin. , vol.11 , pp. 15-32
    • Liu, C.-S.1
  • 45
    • 67049167147 scopus 로고    scopus 로고
    • A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory
    • C.-S. Liu, and S.N. Atluri A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory CMES: Comput. Model. Eng. Sci. 41 2009 243 261
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.41 , pp. 243-261
    • Liu, C.-S.1    Atluri, S.N.2
  • 46
    • 76249127210 scopus 로고    scopus 로고
    • Applications of the fictitious time integration method using a new time-like function
    • C.-Y. Ku, W. Yeih, C.-S. Liu, and C.C. Chi Applications of the fictitious time integration method using a new time-like function CMES: Comput. Model. Eng. Sci. 43 2009 173 190
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.43 , pp. 173-190
    • Ku, C.-Y.1    Yeih, W.2    Liu, C.-S.3    Chi, C.C.4
  • 47
    • 76449100929 scopus 로고    scopus 로고
    • A novel method for solving the Cauchy problem of Laplace equation using the fictitious time integration method
    • C.-C. Chi, W. Yeih, and C.-S. Liu A novel method for solving the Cauchy problem of Laplace equation using the fictitious time integration method CMES: Comput. Model. Eng. Sci. 47 2009 167 190
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.47 , pp. 167-190
    • Chi, C.-C.1    Yeih, W.2    Liu, C.-S.3
  • 48
    • 77449157576 scopus 로고    scopus 로고
    • A fictitious time integration method for backward advection-dispersion equation
    • C.-W. Chang, and C.-S. Liu A fictitious time integration method for backward advection-dispersion equation CMES: Comput. Model. Eng. Sci. 51 2009 261 276
    • (2009) CMES: Comput. Model. Eng. Sci. , vol.51 , pp. 261-276
    • Chang, C.-W.1    Liu, C.-S.2
  • 50
    • 84953600891 scopus 로고
    • A practical method for numerical evaluation of solution of partial differential equations of the heat conduction type
    • J. Crank, and P. Nicolson A practical method for numerical evaluation of solution of partial differential equations of the heat conduction type Proc. Camb. Phil. Soc. 43 1947 50 67
    • (1947) Proc. Camb. Phil. Soc. , vol.43 , pp. 50-67
    • Crank, J.1    Nicolson, P.2
  • 51
    • 0000898783 scopus 로고    scopus 로고
    • An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation
    • D. Lesnic, L. Elliott, and D.B. Ingham An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation Inv. Prob. Eng. 6 1998 255 279
    • (1998) Inv. Prob. Eng. , vol.6 , pp. 255-279
    • Lesnic, D.1    Elliott, L.2    Ingham, D.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.