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Volumn 35, Issue 2, 2008, Pages 91-111

A highly accurate MCTM for inverse Cauchy problems of Laplace equation in arbitrary plane domains

Author keywords

Inverse Cauchy problem; Laplace equation; Modified collocation Trefftz method (MCTM); Modified Trefftz method

Indexed keywords

INTEGRODIFFERENTIAL EQUATIONS; INVERSE PROBLEMS; LAPLACE TRANSFORMS; NUMBER THEORY;

EID: 58149525832     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (60)

References (32)
  • 1
    • 0036904428 scopus 로고    scopus 로고
    • Electrostatic imaging via conformal mapping
    • Akduman, I.; Kress, R. (2002): Electrostatic imaging via conformal mapping. Inverse Problems, vol. 18, pp. 1659-1672.
    • (2002) Inverse Problems , vol.18 , pp. 1659-1672
    • Akduman, I.1    Kress, R.2
  • 2
    • 31844434943 scopus 로고    scopus 로고
    • Solving Cauchy problems by minimizing an energy-like functional
    • Andrieux, S.; Baranger, T. N.; Ben Abda, A. (2006): Solving Cauchy problems by minimizing an energy-like functional. Inverse Problems, vol. 22, pp. 115-133.
    • (2006) Inverse Problems , vol.22 , pp. 115-133
    • Andrieux, S.1    Baranger, T.N.2    Ben Abda, A.3
  • 3
    • 0001965230 scopus 로고    scopus 로고
    • The boundary inverse problem for the Laplace equation in two dimensions
    • Aparicio, N. D.; Pidcock, M. K. (1996): The boundary inverse problem for the Laplace equation in two dimensions. Inverse Problems, vol. 12, pp. 565-577.
    • (1996) Inverse Problems , vol.12 , pp. 565-577
    • Aparicio, N.D.1    Pidcock, M.K.2
  • 4
    • 28544445998 scopus 로고    scopus 로고
    • On Cauchy's problem. I. a variational Steklov-Poincaré theory
    • Ben Belgacem, F.; El Fekih, H. (2005): On Cauchy's problem. I. a variational Steklov-Poincaré theory. Inverse Problems, vol. 21, pp. 1915-1936.
    • (2005) Inverse Problems , vol.21 , pp. 1915-1936
    • Ben Belgacem, F.1    El Fekih, H.2
  • 5
    • 0343772980 scopus 로고    scopus 로고
    • Numerical solution of a Cauchy problem for the Laplace equation
    • Berntsson, F.; Eiden, L. (2001): Numerical solution of a Cauchy problem for the Laplace equation. Inverse Problems, vol. 17, pp. 839-854.
    • (2001) Inverse Problems , vol.17 , pp. 839-854
    • Berntsson, F.1    Eiden, L.2
  • 6
    • 18744373648 scopus 로고    scopus 로고
    • A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
    • Bourgeois, L. (2005): A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation. Inverse Problems, vol. 21, pp. 1087-1104.
    • (2005) Inverse Problems , vol.21 , pp. 1087-1104
    • Bourgeois, L.1
  • 7
    • 33645303206 scopus 로고    scopus 로고
    • Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
    • Bourgeois, L. (2006): Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation. Inverse Problems, vol. 22, pp. 413-430.
    • (2006) Inverse Problems , vol.22 , pp. 413-430
    • Bourgeois, L.1
  • 8
    • 0242516794 scopus 로고    scopus 로고
    • On the modified Tikhonov's regularization method for the Cauchy problem of the Laplace equation
    • Chang, J. R.; Yeih, W.; Shieh, M. H. (2001): On the modified Tikhonov's regularization method for the Cauchy problem of the Laplace equation. J. Mar. Sci. Tech., vol. 9, pp. 113-121.
    • (2001) J. Mar. Sci. Tech , vol.9 , pp. 113-121
    • Chang, J.R.1    Yeih, W.2    Shieh, M.H.3
  • 9
    • 14844290885 scopus 로고    scopus 로고
    • A hybrid method for inverse boundary value problems in potential theory
    • Chapko, R.; Kress, R. (2005): A hybrid method for inverse boundary value problems in potential theory. J. Inv. Ill-Posed Problems, vol. 13, pp. 27-40.
    • (2005) J. Inv. Ill-Posed Problems , vol.13 , pp. 27-40
    • Chapko, R.1    Kress, R.2
  • 10
    • 56949108322 scopus 로고    scopus 로고
    • Applications of the modified Trefftz method for the Laplace equation
    • Chen, Y. W.; Liu, C.-S.; Chang, J. R. (2008): Applications of the modified Trefftz method for the Laplace equation. Engng. Anal. Bound. Elem., vol. 33, pp. 137-146.
    • (2008) Engng. Anal. Bound. Elem , vol.33 , pp. 137-146
    • Chen, Y.W.1    Liu, C.-S.2    Chang, J.R.3
  • 11
    • 2942733336 scopus 로고    scopus 로고
    • Two iterative boundary element methods for inverse Cauchy problems
    • Brebbia, C. A. and Power, H, Eds, WIT Press
    • Delvare, F.; Cimetiére, A.; Pons, F. (2000): Two iterative boundary element methods for inverse Cauchy problems. In Brebbia, C. A. and Power, H., Eds., Boundary Elements, vol. XXII, pp. 211-20, WIT Press.
    • (2000) Boundary Elements , vol.22 , pp. 211-220
    • Delvare, F.1    Cimetiére, A.2    Pons, F.3
  • 12
    • 0036353774 scopus 로고    scopus 로고
    • Direct method of solution for general boundary value problem of the Laplace equation
    • Hayashi, K.; Ohura, Y.; Onishi, K. (2002): Direct method of solution for general boundary value problem of the Laplace equation. Engng. Anal. Bound. Elem., vol. 26, pp. 763-771.
    • (2002) Engng. Anal. Bound. Elem , vol.26 , pp. 763-771
    • Hayashi, K.1    Ohura, Y.2    Onishi, K.3
  • 13
    • 0031212101 scopus 로고    scopus 로고
    • An inverse problem in corrosion detection
    • Inglese, G. (1997): An inverse problem in corrosion detection. Inverse Problems, vol. 13, pp. 1425-1438.
    • (1997) Inverse Problems , vol.13 , pp. 1425-1438
    • Inglese, G.1
  • 14
    • 33644595481 scopus 로고    scopus 로고
    • A meshless method for some inverse problems associated with the Helmholtz equation
    • Jin, B.; Zheng, Y. (2006): A meshless method for some inverse problems associated with the Helmholtz equation. Comp. Meth. Appl. Mech. Engng., vol. 195, pp. 2270-2288.
    • (2006) Comp. Meth. Appl. Mech. Engng , vol.195 , pp. 2270-2288
    • Jin, B.1    Zheng, Y.2
  • 16
    • 0003003643 scopus 로고    scopus 로고
    • Method for imaging corrosion damage in thin plates from electrostatic data
    • Kaup, P. G.; Santosa, F.; Vogelius, M. (1996): Method for imaging corrosion damage in thin plates from electrostatic data. Inverse Problems, vol. 12, pp. 279-293.
    • (1996) Inverse Problems , vol.12 , pp. 279-293
    • Kaup, P.G.1    Santosa, F.2    Vogelius, M.3
  • 17
    • 3042730181 scopus 로고    scopus 로고
    • Inverse Dirichlet problem and conformal mapping
    • Kress, R. (2004): Inverse Dirichlet problem and conformal mapping. Math. Comp. Simul., vol. 66, pp. 255-265.
    • (2004) Math. Comp. Simul , vol.66 , pp. 255-265
    • Kress, R.1
  • 18
    • 0031219785 scopus 로고    scopus 로고
    • An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation
    • Lesnic, D.; Elliott, L.; Ingham, D. B. (1997): An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation. Engng. Anal. Bound. Elem., vol. 20, pp. 123-133.
    • (1997) Engng. Anal. Bound. Elem , vol.20 , pp. 123-133
    • Lesnic, D.1    Elliott, L.2    Ingham, D.B.3
  • 19
    • 49749085551 scopus 로고    scopus 로고
    • Boundary control for inverse Cauchy problems of the Laplace equations
    • Ling, L.; Takeuchi, T. (2008): Boundary control for inverse Cauchy problems of the Laplace equations. CMES: Computer Modeling in Engineering & Sciences, vol. 29, pp. 45-54.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.29 , pp. 45-54
    • Ling, L.1    Takeuchi, T.2
  • 20
    • 35348966933 scopus 로고    scopus 로고
    • A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length
    • Liu, C.-S. (2007a): A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length. CMES: Computer Modeling in Engineering & Sciences, vol. 21, pp. 53-66.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.21 , pp. 53-66
    • Liu, C.-S.1
  • 21
    • 34547764810 scopus 로고    scopus 로고
    • A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain
    • Liu, C.-S. (2007b): A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain. CMES: Computer Modeling in Engineering & Sciences, vol. 20, pp. 111-122.
    • (2007) CMES: Computer Modeling in Engineering & Sciences , vol.20 , pp. 111-122
    • Liu, C.-S.1
  • 22
    • 34547777321 scopus 로고    scopus 로고
    • An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length
    • Liu, C.-S. (2007c): An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length. Engng. Anal. Bound. Elem., vol. 31, pp. 983-993.
    • (2007) Engng. Anal. Bound. Elem , vol.31 , pp. 983-993
    • Liu, C.-S.1
  • 23
    • 55549132292 scopus 로고    scopus 로고
    • A highly accurate MCTM for direct and inverse problems of biharmonic equation in arbitrary plane domains
    • Liu, C.-S. (2008a): A highly accurate MCTM for direct and inverse problems of biharmonic equation in arbitrary plane domains. CMES: Computer Modeling in Engineering & Sciences, vol. 30, pp. 65-75.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.30 , pp. 65-75
    • Liu, C.-S.1
  • 24
    • 47049098927 scopus 로고    scopus 로고
    • A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation
    • Liu, C.-S. (2008b): A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation. Engng. Anal. Bound. Elem., vol. 32, pp. 778-785.
    • (2008) Engng. Anal. Bound. Elem , vol.32 , pp. 778-785
    • Liu, C.-S.1
  • 25
    • 38049156326 scopus 로고    scopus 로고
    • A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly-connected domains
    • Liu, C.-S. (2008c): A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly-connected domains. Numer. Meth. Partial Diff. Eq., vol. 24, pp. 179-192.
    • (2008) Numer. Meth. Partial Diff. Eq , vol.24 , pp. 179-192
    • Liu, C.-S.1
  • 26
    • 57649213675 scopus 로고    scopus 로고
    • A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization
    • in press
    • Liu, C.-S.; Atluri, S. N. (2008a): A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization. CMES: Computer Modeling in Engineering & Sciences, in press.
    • (2008) CMES: Computer Modeling in Engineering & Sciences
    • Liu, C.-S.1    Atluri, S.N.2
  • 27
    • 55349116390 scopus 로고    scopus 로고
    • A novel time integration method for solving a large system of non-linear algebraic equations
    • Liu, C.-S.; Atluri, S. N. (2008b): A novel time integration method for solving a large system of non-linear algebraic equations. CMES: Computer Modeling in Engineering & Sciences, vol. 31, pp. 71-83.
    • (2008) CMES: Computer Modeling in Engineering & Sciences , vol.31 , pp. 71-83
    • Liu, C.-S.1    Atluri, S.N.2
  • 28
    • 26844436520 scopus 로고    scopus 로고
    • The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
    • Marin, L.; Lesnic, D. (2005): The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation. Math. Comp. Model, vol. 42, pp. 261-278.
    • (2005) Math. Comp. Model , vol.42 , pp. 261-278
    • Marin, L.1    Lesnic, D.2
  • 29
    • 0039925774 scopus 로고    scopus 로고
    • An iterative boundary element method for the solution of a Cauchy steady state heat conduction problem
    • Mera, N. S.; Elliott, L.; Ingham, D. B.; Lesnic, D. (2000): An iterative boundary element method for the solution of a Cauchy steady state heat conduction problem. CMES: Computer Modeling in Engineering & Sciences, vol. 1, pp. 101-106.
    • (2000) CMES: Computer Modeling in Engineering & Sciences , vol.1 , pp. 101-106
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3    Lesnic, D.4
  • 30
    • 0034307952 scopus 로고    scopus 로고
    • The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium
    • Mera, N. S.; Elliott, L.; Ingham, D. B.; Lesnic, D. (2000): The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium. Int. J. Num. Meth. Engng., vol. 49, pp. 481-499.
    • (2000) Int. J. Num. Meth. Engng , vol.49 , pp. 481-499
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3    Lesnic, D.4
  • 31
    • 0037995749 scopus 로고    scopus 로고
    • On the use of genetic algorithms for solving ill-posed problems
    • Mera, N. S.; Elliott, L.; Ingham, D. B. (2003): On the use of genetic algorithms for solving ill-posed problems. Inverse Prob. Engng., vol. 11, pp. 105-121.
    • (2003) Inverse Prob. Engng , vol.11 , pp. 105-121
    • Mera, N.S.1    Elliott, L.2    Ingham, D.B.3
  • 32
    • 17644448457 scopus 로고    scopus 로고
    • A numerical approach for the determination of a missing boundary data in elliptic problems
    • Slodička, M.; Van Keer, R. (2004): A numerical approach for the determination of a missing boundary data in elliptic problems. Appl. Math. Comp., vol. 147, pp. 569-580.
    • (2004) Appl. Math. Comp , vol.147 , pp. 569-580
    • Slodička, M.1    Van Keer, R.2


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