메뉴 건너뛰기




Volumn 31, Issue 4, 2007, Pages 373-385

Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators

Author keywords

Cauchy problems; Inverse problems; Method of fundamental solutions; Regularization methods

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIATION (CALCULUS); LINEAR SYSTEMS; MATRIX ALGEBRA; PARAMETER ESTIMATION; PROBLEM SOLVING;

EID: 33847032040     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2006.07.010     Document Type: Article
Times cited : (186)

References (49)
  • 1
    • 0022107918 scopus 로고
    • Fundamental solutions method for elliptic boundary value problems
    • Bogomolny A. Fundamental solutions method for elliptic boundary value problems. SIAM J Numer Anal 22 4 (1985) 644-669
    • (1985) SIAM J Numer Anal , vol.22 , Issue.4 , pp. 644-669
    • Bogomolny, A.1
  • 2
    • 0001167301 scopus 로고    scopus 로고
    • The collocation points of the fundamental solution method for the potential problem
    • Katsurada M., and Okamoto H. The collocation points of the fundamental solution method for the potential problem. Comput Math Appl 31 1 (1996) 123-137
    • (1996) Comput Math Appl , vol.31 , Issue.1 , pp. 123-137
    • Katsurada, M.1    Okamoto, H.2
  • 3
    • 0000678579 scopus 로고
    • The approximate solution of elliptic boundary-value problems by fundamental solutions
    • Mathon R., and Johnston R.L. The approximate solution of elliptic boundary-value problems by fundamental solutions. SIAM J Numer Anal 14 4 (1977) 638-650
    • (1977) SIAM J Numer Anal , vol.14 , Issue.4 , pp. 638-650
    • Mathon, R.1    Johnston, R.L.2
  • 4
    • 0001705710 scopus 로고
    • The method of fundamental solutions for the numerical solution of the biharmonic equation
    • Karageorghis A., and Fairweather G. The method of fundamental solutions for the numerical solution of the biharmonic equation. J Comput Phys 69 (1987) 433-459
    • (1987) J Comput Phys , vol.69 , pp. 433-459
    • Karageorghis, A.1    Fairweather, G.2
  • 5
    • 8344281356 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain biharmonic problems
    • Smyrlis Y.-S., and Karageorghis A. Some aspects of the method of fundamental solutions for certain biharmonic problems. CMES Comput Model Eng Sci 4 5 (2003) 535-550
    • (2003) CMES Comput Model Eng Sci , vol.4 , Issue.5 , pp. 535-550
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 6
    • 0036465594 scopus 로고    scopus 로고
    • The method of fundamental solutions for three-dimensional elastostatics problems
    • Poullikkas A., Karageorghis A., and Georgiou G. The method of fundamental solutions for three-dimensional elastostatics problems. Comput Struct 80 3-4 (2002) 365-370
    • (2002) Comput Struct , vol.80 , Issue.3-4 , pp. 365-370
    • Poullikkas, A.1    Karageorghis, A.2    Georgiou, G.3
  • 7
    • 0026651666 scopus 로고
    • Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions
    • Kondapalli P.S., Shippy D.J., and Fairweather G. Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions. J Acoust Soc Am 91 4 Part 1 (1992) 1844-1854
    • (1992) J Acoust Soc Am , vol.91 , Issue.4 PART 1 , pp. 1844-1854
    • Kondapalli, P.S.1    Shippy, D.J.2    Fairweather, G.3
  • 8
    • 0026852090 scopus 로고
    • The method of fundamental solutions for transmission and scattering of elastic waves
    • Kondapalli P.S., Shippy D.J., and Fairweather G. The method of fundamental solutions for transmission and scattering of elastic waves. Comput Methods Appl Mech Eng 96 2 (1992) 255-269
    • (1992) Comput Methods Appl Mech Eng , vol.96 , Issue.2 , pp. 255-269
    • Kondapalli, P.S.1    Shippy, D.J.2    Fairweather, G.3
  • 9
    • 0033996710 scopus 로고    scopus 로고
    • The method of fundamental solutions for linear diffusion-reaction equations
    • Balakrishnan K., and Ramachandran P.A. The method of fundamental solutions for linear diffusion-reaction equations. Math Comput Model 31 2-3 (2000) 221-237
    • (2000) Math Comput Model , vol.31 , Issue.2-3 , pp. 221-237
    • Balakrishnan, K.1    Ramachandran, P.A.2
  • 10
    • 0035455999 scopus 로고    scopus 로고
    • Osculatory interpolation in the method of fundamental solution for nonlinear possion problems
    • Balakrishnan K., and Ramachandran P.A. Osculatory interpolation in the method of fundamental solution for nonlinear possion problems. J Comput Phys 172 1 (2001) 1-18
    • (2001) J Comput Phys , vol.172 , Issue.1 , pp. 1-18
    • Balakrishnan, K.1    Ramachandran, P.A.2
  • 11
    • 0029388503 scopus 로고
    • The method of fundamental solutions for Poisson's equation
    • Golberg M.A. The method of fundamental solutions for Poisson's equation. Eng Anal Boundary Elem 16 3 (1995) 205-213
    • (1995) Eng Anal Boundary Elem , vol.16 , Issue.3 , pp. 205-213
    • Golberg, M.A.1
  • 12
    • 0034297885 scopus 로고    scopus 로고
    • The method of fundamental solutions with dual reciprocity for diffusion and diffusion convection using subdomains
    • Partridge P.W., and Sensale B. The method of fundamental solutions with dual reciprocity for diffusion and diffusion convection using subdomains. Eng Anal Boundary Elem 24 9 (2000) 633-641
    • (2000) Eng Anal Boundary Elem , vol.24 , Issue.9 , pp. 633-641
    • Partridge, P.W.1    Sensale, B.2
  • 13
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems
    • Fairweather G., and Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math 9 1-2 (1998) 69-95
    • (1998) Adv Comput Math , vol.9 , Issue.1-2 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 14
    • 0000776101 scopus 로고    scopus 로고
    • The method of fundamental solutions for potential, Helmholtz and diffusion problems
    • WIT Press, Computational Mechanics Publications, Boston, MA
    • Golberg M.A., and Chen C.S. The method of fundamental solutions for potential, Helmholtz and diffusion problems. Boundary integral methods: numerical and mathematical aspects. Computational Engineering vol. 1 (1999), WIT Press, Computational Mechanics Publications, Boston, MA 103-176
    • (1999) Boundary integral methods: numerical and mathematical aspects. Computational Engineering , vol.1 , pp. 103-176
    • Golberg, M.A.1    Chen, C.S.2
  • 15
    • 84971151488 scopus 로고
    • Stable determination of a crack from boundary measurements
    • Alessandrini G. Stable determination of a crack from boundary measurements. Proc Roy Soc Edinburgh Sect A 123 3 (1993) 497-516
    • (1993) Proc Roy Soc Edinburgh Sect A , vol.123 , Issue.3 , pp. 497-516
    • Alessandrini, G.1
  • 17
    • 51249182572 scopus 로고
    • On the inverse potential problem of electrocardiology
    • Franzone P.C., and Magenes E. On the inverse potential problem of electrocardiology. Calcolo 16 4 (1980) 459-538
    • (1980) Calcolo , vol.16 , Issue.4 , pp. 459-538
    • Franzone, P.C.1    Magenes, E.2
  • 18
    • 1542356613 scopus 로고    scopus 로고
    • Regularized solutions of cauchy problem for the laplace equation in an irregular layer: a three dimensional case
    • Ang D.D., Nghia N.H., and Tam N.C. Regularized solutions of cauchy problem for the laplace equation in an irregular layer: a three dimensional case. Acta Math Vietnam 23 (1998) 65-74
    • (1998) Acta Math Vietnam , vol.23 , pp. 65-74
    • Ang, D.D.1    Nghia, N.H.2    Tam, N.C.3
  • 19
    • 0343772980 scopus 로고    scopus 로고
    • Numerical solution of a Cauchy problem for the Laplace equation
    • Berntsson F., and Eldén L. Numerical solution of a Cauchy problem for the Laplace equation. Inverse Probl 17 4 (2001) 839-853
    • (2001) Inverse Probl , vol.17 , Issue.4 , pp. 839-853
    • Berntsson, F.1    Eldén, L.2
  • 20
    • 23044529471 scopus 로고    scopus 로고
    • Numerical computation of a Cauchy problem for Laplace's equation
    • Cheng J., Hon Y.C., Wei T., and Yamamoto M. Numerical computation of a Cauchy problem for Laplace's equation. ZAMM Z Angew Math Mech 81 10 (2001) 665-674
    • (2001) ZAMM Z Angew Math Mech , vol.81 , Issue.10 , pp. 665-674
    • Cheng, J.1    Hon, Y.C.2    Wei, T.3    Yamamoto, M.4
  • 21
    • 0342572571 scopus 로고    scopus 로고
    • The Cauchy problem for Laplace's equation via the conjugate gradient method
    • Hào D.N., and Lesnic D. The Cauchy problem for Laplace's equation via the conjugate gradient method. IMA J Appl Math 65 2 (2000) 199-217
    • (2000) IMA J Appl Math , vol.65 , Issue.2 , pp. 199-217
    • Hào, D.N.1    Lesnic, D.2
  • 22
    • 0035306176 scopus 로고    scopus 로고
    • Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
    • Hon Y.C., and Wei T. Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation. Inverse Probl 17 2 (2001) 261-271
    • (2001) Inverse Probl , vol.17 , Issue.2 , pp. 261-271
    • Hon, Y.C.1    Wei, T.2
  • 23
    • 0342955473 scopus 로고    scopus 로고
    • A numerical computation for inverse boundary determination problem
    • Hon Y.C., and Wu Z. A numerical computation for inverse boundary determination problem. Eng Anal Boundary Elem 24 7-8 (2000) 599-606
    • (2000) Eng Anal Boundary Elem , vol.24 , Issue.7-8 , pp. 599-606
    • Hon, Y.C.1    Wu, Z.2
  • 24
    • 0001189418 scopus 로고    scopus 로고
    • Stability and regularization of a discrete approximation to the Cauchy problem for Laplace's equation
    • (electronic)
    • Reinhardt H.-J., Han H., and Hào D.N. Stability and regularization of a discrete approximation to the Cauchy problem for Laplace's equation. SIAM J Numer Anal 36 3 (1999) 890-905 (electronic)
    • (1999) SIAM J Numer Anal , vol.36 , Issue.3 , pp. 890-905
    • Reinhardt, H.-J.1    Han, H.2    Hào, D.N.3
  • 25
    • 33644595481 scopus 로고    scopus 로고
    • Jin B, Zheng Y. A meshless method for some inverse problems associated with the helmholtz equation. Comput Methods Appl Mech Eng 2006; 195 (19-22): 2270-88.
  • 26
    • 17644417110 scopus 로고    scopus 로고
    • A meshless method for the numerical solution of cauchy problem associated with three-dimensional helmholtz-type equations
    • Marin L. A meshless method for the numerical solution of cauchy problem associated with three-dimensional helmholtz-type equations. Appl Math Comput 165 (2005) 355-374
    • (2005) Appl Math Comput , vol.165 , pp. 355-374
    • Marin, L.1
  • 27
    • 11344277052 scopus 로고    scopus 로고
    • The method of fundamental solutions for the cauchy problem associated with two-dimensional helmholtz-type equations
    • Marin L., and Lesnic D. The method of fundamental solutions for the cauchy problem associated with two-dimensional helmholtz-type equations. Comput Struct 83 (2005) 267-278
    • (2005) Comput Struct , vol.83 , pp. 267-278
    • Marin, L.1    Lesnic, D.2
  • 29
    • 33847035981 scopus 로고    scopus 로고
    • Tikhonov AN, Arsenin VY. Solutions of ill-posed problems, Washington, DC, New York: V.H. Winston, Wiley; 1977. Translated from the Russian, Preface by translation editor Fritz J, Scripta Series in Mathematics.
  • 30
    • 0001313501 scopus 로고    scopus 로고
    • Unique continuation on a line for harmonic functions
    • Cheng J., and Yamamoto M. Unique continuation on a line for harmonic functions. Inverse Probl 14 4 (1998) 869-882
    • (1998) Inverse Probl , vol.14 , Issue.4 , pp. 869-882
    • Cheng, J.1    Yamamoto, M.2
  • 31
    • 0009767974 scopus 로고
    • Bounds in the Cauchy problem for the Laplace equation
    • Payne L.E. Bounds in the Cauchy problem for the Laplace equation. Arch Ration Mech Anal 5 (1960) 35-45
    • (1960) Arch Ration Mech Anal , vol.5 , pp. 35-45
    • Payne, L.E.1
  • 32
    • 0026370571 scopus 로고
    • A computational quasi-reversibility method for Cauchy problems for Laplace's equation
    • Klibanov M.V., and Santosa F. A computational quasi-reversibility method for Cauchy problems for Laplace's equation. SIAM J Appl Math 51 6 (1991) 1653-1675
    • (1991) SIAM J Appl Math , vol.51 , Issue.6 , pp. 1653-1675
    • Klibanov, M.V.1    Santosa, F.2
  • 33
    • 33847018141 scopus 로고    scopus 로고
    • Lattès R, Lions J-L. The method of quasi-reversibility. Applications to partial differential equations. Translated from the French edition and edited by Bellman R. Modern analytic and computational methods in science and mathematics, vol. 18. New York: Elsevier; 1969.
  • 34
    • 84966205692 scopus 로고
    • Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson's equation
    • Falk R.S., and Monk P.B. Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson's equation. Math Comput 47 175 (1986) 135-149
    • (1986) Math Comput , vol.47 , Issue.175 , pp. 135-149
    • Falk, R.S.1    Monk, P.B.2
  • 35
    • 0031260260 scopus 로고    scopus 로고
    • Helmholtz equation-least-squares method for reconstructing the acoustic pressure field
    • Wang Z., and Wu S.R. Helmholtz equation-least-squares method for reconstructing the acoustic pressure field. J Acoust Soc Am 102 (1997) 2020-2032
    • (1997) J Acoust Soc Am , vol.102 , pp. 2020-2032
    • Wang, Z.1    Wu, S.R.2
  • 36
    • 0031707703 scopus 로고    scopus 로고
    • Application of bem-based holography to radiation analysis of sound sources with arbitrary geometries
    • Wu S.R., and Yu J. Application of bem-based holography to radiation analysis of sound sources with arbitrary geometries. J Acoust Soc Am 104 (1998) 1054-1060
    • (1998) J Acoust Soc Am , vol.104 , pp. 1054-1060
    • Wu, S.R.1    Yu, J.2
  • 37
    • 0035707434 scopus 로고    scopus 로고
    • The detect of the source of acoustical noise in two dimensions
    • Validivia I.V.N., and Delillo W.L.T. The detect of the source of acoustical noise in two dimensions. SIAM J Appl Math 61 (2001) 2104-2121
    • (2001) SIAM J Appl Math , vol.61 , pp. 2104-2121
    • Validivia, I.V.N.1    Delillo, W.L.T.2
  • 38
    • 0038678004 scopus 로고    scopus 로고
    • The detect of surface vibrations from interior acoustical pressure
    • Validivia I.V.N., and Delillo W.L.T. The detect of surface vibrations from interior acoustical pressure. Inverse Probl 19 (2003) 507-524
    • (2003) Inverse Probl , vol.19 , pp. 507-524
    • Validivia, I.V.N.1    Delillo, W.L.T.2
  • 39
    • 0037474371 scopus 로고    scopus 로고
    • An alternating iterative algorithm for the cauchy problem associated to the helmholtz equation
    • Elliott L., Heggs P.J., Ingham D.B., Lesnic D., Marin L., and Wen X. An alternating iterative algorithm for the cauchy problem associated to the helmholtz equation. Comput Methods Appl Mech Eng 192 (2003) 709-722
    • (2003) Comput Methods Appl Mech Eng , vol.192 , pp. 709-722
    • Elliott, L.1    Heggs, P.J.2    Ingham, D.B.3    Lesnic, D.4    Marin, L.5    Wen, X.6
  • 40
    • 0141853866 scopus 로고    scopus 로고
    • Conjugate gradient-boundary element solution to the cauchy problem for helmholtz-type equations
    • Elliott L., Heggs P.J., Ingham D.B., Lesnic D., Marin L., and Wen X. Conjugate gradient-boundary element solution to the cauchy problem for helmholtz-type equations. Comput Mech 31 (2003) 367-372
    • (2003) Comput Mech , vol.31 , pp. 367-372
    • Elliott, L.1    Heggs, P.J.2    Ingham, D.B.3    Lesnic, D.4    Marin, L.5    Wen, X.6
  • 41
    • 15844371536 scopus 로고    scopus 로고
    • Boundary knot method for some inverse problems associated with the helmholtz equation
    • Jin B., and Zheng Y. Boundary knot method for some inverse problems associated with the helmholtz equation. J Numer Methods Eng 62 (2005) 1636-1651
    • (2005) J Numer Methods Eng , vol.62 , pp. 1636-1651
    • Jin, B.1    Zheng, Y.2
  • 42
    • 26844516611 scopus 로고    scopus 로고
    • Boundary knot method for the cauchy problem associated with the inhomogeneous helmholtz equation
    • Jin B., and Zheng Y. Boundary knot method for the cauchy problem associated with the inhomogeneous helmholtz equation. Eng Anal Boundary Elem 29 (2005) 925-935
    • (2005) Eng Anal Boundary Elem , vol.29 , pp. 925-935
    • Jin, B.1    Zheng, Y.2
  • 43
    • 3142686215 scopus 로고    scopus 로고
    • Bem solution for the cauchy problem associated with helmholtz-type equations by the landweber method
    • Elliott L., Heggs P.J., Ingham D.B., Lesnic D., Marin L., and Wen X. Bem solution for the cauchy problem associated with helmholtz-type equations by the landweber method. Eng Anal Boundary Elem 28 (2004) 1025-1034
    • (2004) Eng Anal Boundary Elem , vol.28 , pp. 1025-1034
    • Elliott, L.1    Heggs, P.J.2    Ingham, D.B.3    Lesnic, D.4    Marin, L.5    Wen, X.6
  • 44
    • 3242796795 scopus 로고    scopus 로고
    • Comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation
    • Elliott L., Heggs P.J., Ingham D.B., Lesnic D., Marin L., and Wen X. Comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation. Int J Numer Mech Eng 60 (2004) 1933-1947
    • (2004) Int J Numer Mech Eng , vol.60 , pp. 1933-1947
    • Elliott, L.1    Heggs, P.J.2    Ingham, D.B.3    Lesnic, D.4    Marin, L.5    Wen, X.6
  • 46
    • 0036860667 scopus 로고    scopus 로고
    • Method of fundamental solutions: singular value decomposition analysis
    • Ramachandran P.A. Method of fundamental solutions: singular value decomposition analysis. Commun Numer Methods Eng 18 11 (2002) 789-801
    • (2002) Commun Numer Methods Eng , vol.18 , Issue.11 , pp. 789-801
    • Ramachandran, P.A.1
  • 47
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • Hansen P.C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev 34 4 (1992) 561-580
    • (1992) SIAM Rev , vol.34 , Issue.4 , pp. 561-580
    • Hansen, P.C.1
  • 48
    • 13344267706 scopus 로고
    • Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems
    • Hansen P.C. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer Algorithms 6 1-2 (1994) 1-35
    • (1994) Numer Algorithms , vol.6 , Issue.1-2 , pp. 1-35
    • Hansen, P.C.1
  • 49
    • 0001632418 scopus 로고
    • The use of the L-curve in the regularization of discrete ill-posed problems
    • Hansen P.C., and O'Leary D.P. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput 14 6 (1993) 1487-1503
    • (1993) SIAM J Sci Comput , vol.14 , Issue.6 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.