메뉴 건너뛰기




Volumn 62, Issue 12, 2005, Pages 1636-1651

Boundary knot method for some inverse problems associated with the Helmholtz equation

Author keywords

Boundary knot method; Cauchy problem; Helmholtz equation; Inverse problem; L curve method; Truncated singular value decomposition

Indexed keywords

COMPUTER SIMULATION; FUNCTIONS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 15844371536     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1240     Document Type: Article
Times cited : (69)

References (28)
  • 1
    • 0026694593 scopus 로고
    • Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries
    • Bai MR. Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries. Journal of the Acoustical Society of America 1992; 92(1):533-549.
    • (1992) Journal of the Acoustical Society of America , vol.92 , Issue.1 , pp. 533-549
    • Bai, M.R.1
  • 2
    • 0001185788 scopus 로고    scopus 로고
    • An inverse problem for the Helmholtz equation
    • Fredderick G-G. An inverse problem for the Helmholtz equation. Inverse Problems 1996; 12(2):139-156.
    • (1996) Inverse Problems , vol.12 , Issue.2 , pp. 139-156
    • Fredderick, G.-G.1
  • 3
    • 0031260260 scopus 로고    scopus 로고
    • Helmholtz equation-least-squares method for reconstructing the acoustic pressure field
    • Wang Z, Wu SF. Helmholtz equation-least-squares method for reconstructing the acoustic pressure field. Journal of the Acoustical Society of America 1997; 102(4):2020-2032.
    • (1997) Journal of the Acoustical Society of America , vol.102 , Issue.4 , pp. 2020-2032
    • Wang, Z.1    Wu, S.F.2
  • 4
    • 0031707703 scopus 로고    scopus 로고
    • Reconstructing interior acoustic pressure fields via Helmholtz equation-least-squares method
    • Wu SF, Yu J. Reconstructing interior acoustic pressure fields via Helmholtz equation-least-squares method. Journal of the Acoustical Society of America 1998; 104(4):2054-2060.
    • (1998) Journal of the Acoustical Society of America , vol.104 , Issue.4 , pp. 2054-2060
    • Wu, S.F.1    Yu, J.2
  • 5
    • 0036684754 scopus 로고    scopus 로고
    • On the theory and application of the Helmholtz equation least squares method in inverse acoustics
    • Isakov V, Wu SF. On the theory and application of the Helmholtz equation least squares method in inverse acoustics. Inverse Problems 2002; 18(4):1147-1159.
    • (2002) Inverse Problems , vol.18 , Issue.4 , pp. 1147-1159
    • Isakov, V.1    Wu, S.F.2
  • 7
    • 0037286693 scopus 로고    scopus 로고
    • Two numerical methods for an inverse problem for the 2-D Helmholtz equation
    • Gryzin YA, Klibanov MV, Lucas TR. Two numerical methods for an inverse problem for the 2-D Helmholtz equation. Journal of Computational Physics 2003; 184(1):122-148.
    • (2003) Journal of Computational Physics , vol.184 , Issue.1 , pp. 122-148
    • Gryzin, Y.A.1    Klibanov, M.V.2    Lucas, T.R.3
  • 8
    • 0025210711 scopus 로고
    • Multiquadratic - A scattered data approximation scheme with applications to computational fluid dynamics II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations
    • Kansa EJ. Multiquadratic-a scattered data approximation scheme with applications to computational fluid dynamics II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations. Computers and Mathematics with Applications 1990; 19 (8-9):147-161.
    • (1990) Computers and Mathematics With Applications , vol.19 , Issue.8-9 , pp. 147-161
    • Kansa, E.J.1
  • 9
    • 0000776101 scopus 로고    scopus 로고
    • The method of fundamental solution for potential, Helmholtz and diffusion equation
    • Golberg MA (ed.). Computational Mechanics Publications: Southampton, U.K
    • Golberg MA, Chen CS. The method of fundamental solution for potential, Helmholtz and diffusion equation. In Boundary Integral Methods-Numerical and Mathematical Aspects, Golberg MA (ed.). Computational Mechanics Publications: Southampton, U.K., 1998; 103-176.
    • (1998) Boundary Integral Methods - Numerical and Mathematical Aspects , pp. 103-176
    • Golberg, M.A.1    Chen, C.S.2
  • 10
    • 0008107767 scopus 로고    scopus 로고
    • New advances in dual reciprocity and boundary-only RBF methods
    • Tanaka M (ed.), Tokyo, Japan
    • Chen W, Tanaka M. New advances in dual reciprocity and boundary-only RBF methods. In Proceeding of BEM Technique Conference, Tanaka M (ed.), vol. 10. Tokyo, Japan, 2000; 17-22.
    • (2000) Proceeding of BEM Technique Conference , vol.10 , pp. 17-22
    • Chen, W.1    Tanaka, M.2
  • 12
    • 0036467593 scopus 로고    scopus 로고
    • A meshless, integration-free, and boundary-only RBF technique
    • Chen W, Tanaka M. A meshless, integration-free, and boundary-only RBF technique. Computers and Mathematics with Applications 2002; 43(3-5):379-391.
    • (2002) Computers and Mathematics With Applications , vol.43 , Issue.3-5 , pp. 379-391
    • Chen, W.1    Tanaka, M.2
  • 14
    • 0346226587 scopus 로고    scopus 로고
    • Recent research at Cambridge on radial basis functions
    • (Durtmund, 1998), Müller MW, Buhmann MD, Mache DH, Felten M (eds), International Series in Numerical Mathematics, Birkhäuser: Basel
    • Powell MJD. Recent research at Cambridge on radial basis functions. In New Developments in Approximation Theory (Durtmund, 1998), Müller MW, Buhmann MD, Mache DH, Felten M (eds), International Series in Numerical Mathematics, vol. 132. Birkhäuser: Basel, 1999; 215-232.
    • (1999) New Developments in Approximation Theory , vol.132 , pp. 215-232
    • Powell, M.J.D.1
  • 15
    • 0037432707 scopus 로고    scopus 로고
    • Numerical convergence of boundary knot method in the analysis of Helmholtz, modified Helmholtz, and convection-diffusion problems
    • Chen W, Hon YC. Numerical convergence of boundary knot method in the analysis of Helmholtz, modified Helmholtz, and convection-diffusion problems. Computer Methods in Applied Mechanics and Engineering 2003; 192(15):1859-1875.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , Issue.15 , pp. 1859-1875
    • Chen, W.1    Hon, Y.C.2
  • 16
    • 0037424959 scopus 로고    scopus 로고
    • Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry
    • Hon YC, Chen W. Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry. International Journal for Numerical Methods in Engineering 2003; 56(13):1931-1948.
    • (2003) International Journal for Numerical Methods in Engineering , vol.56 , Issue.13 , pp. 1931-1948
    • Hon, Y.C.1    Chen, W.2
  • 18
    • 0034173976 scopus 로고    scopus 로고
    • Circumventing the ill-conditioning problem with multiquadratic radial basis functions: Applications to elliptic partial differential equations
    • Kansa EJ, Hon YC. Circumventing the ill-conditioning problem with multiquadratic radial basis functions: applications to elliptic partial differential equations. Computers and Mathematics with Applications 2000; 39(7-8):123-137.
    • (2000) Computers and Mathematics With Applications , vol.39 , Issue.7-8 , pp. 123-137
    • Kansa, E.J.1    Hon, Y.C.2
  • 19
    • 0023570429 scopus 로고
    • The truncated SVD as a method for regularization
    • Hansen PC. The truncated SVD as a method for regularization. BIT 1987; 27(4):533-534.
    • (1987) BIT , vol.27 , Issue.4 , pp. 533-534
    • Hansen, P.C.1
  • 20
    • 0001840812 scopus 로고
    • Regularization methods for the stable solution of inverse problems
    • Engl HW. Regularization methods for the stable solution of inverse problems. Surveys on Mathematics for Industry 1993; 3 (2):71-142.
    • (1993) Surveys on Mathematics for Industry , vol.3 , Issue.2 , pp. 71-142
    • Engl, H.W.1
  • 22
    • 0000570697 scopus 로고
    • Analysis of the discrete ill-posed problems by means of the L-curve
    • Hansen PC. Analysis of the discrete ill-posed problems by means of the L-curve. SIAM Review 1992; 34(4):561-580.
    • (1992) SIAM Review , vol.34 , Issue.4 , pp. 561-580
    • Hansen, P.C.1
  • 23
    • 0001632418 scopus 로고
    • The use of the L-curve in the regularization of discrete ill-posed problems
    • Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal of Scientific Computing 1993; 14(6):1487-1503.
    • (1993) SIAM Journal of Scientific Computing , vol.14 , Issue.6 , pp. 1487-1503
    • Hansen, P.C.1    O'Leary, D.P.2
  • 24
    • 32044449925 scopus 로고
    • Generalized cross-validation as a method for choosing a good ridge parameter
    • Golub G, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 1979; 21 (2):215-223.
    • (1979) Technometrics , vol.21 , Issue.2 , pp. 215-223
    • Golub, G.1    Heath, M.2    Wahba, G.3
  • 26
    • 0001476575 scopus 로고
    • A new approach for free vibration analysis using boundary elements
    • Brebbia CA (ed.). Springer: Berlin
    • Nardini D, Brebbia CA. A new approach for free vibration analysis using boundary elements. In Boundary Element Methods in Engineering, Brebbia CA (ed.). Springer: Berlin, 1982; 312-326.
    • (1982) Boundary Element Methods in Engineering , pp. 312-326
    • Nardini, D.1    Brebbia, C.A.2
  • 28
    • 0033442485 scopus 로고    scopus 로고
    • Fast fitting of radial basis functions: Methods based on preconditioned GMRES iteration
    • Beatson RK, Cherrie JB, Mouat CT. Fast fitting of radial basis functions: methods based on preconditioned GMRES iteration. Advances in Computational Mathematics 1999; 11(2-3):253-270.
    • (1999) Advances in Computational Mathematics , vol.11 , Issue.2-3 , pp. 253-270
    • Beatson, R.K.1    Cherrie, J.B.2    Mouat, C.T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.