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Volumn 184, Issue 1, 2003, Pages 122-148

Two numerical methods for an inverse problem for the 2-D Helmholtz equation

Author keywords

Elliptic systems method; Helmholtz equation; Land mines; PCG; Preconditioners; Subsurface imaging

Indexed keywords

CONJUGATE GRADIENT METHOD; FINITE DIFFERENCE METHOD; INVERSE PROBLEMS; NUMERICAL METHODS;

EID: 0037286693     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(02)00023-2     Document Type: Article
Times cited : (15)

References (22)
  • 1
    • 0032638277 scopus 로고    scopus 로고
    • Optical tomography in medical imaging, Topical review
    • S. Arridge, Optical tomography in medical imaging, Topical review, Inverse Problems 15 (1999) R41.
    • (1999) Inverse Problems , vol.15
    • Arridge, S.1
  • 3
    • 84984086678 scopus 로고
    • A finite-difference method of high-order accuracy for the solution of three-dimensional transient heat conduction problems
    • P.L.T. Brian, A finite-difference method of high-order accuracy for the solution of three-dimensional transient heat conduction problems, AIChE J. 1 (1961) 367.
    • (1961) AIChE J. , vol.1 , pp. 367
    • Brian, P.L.T.1
  • 4
    • 0000228116 scopus 로고
    • Inverse problems for a perturbed dissipative half-space
    • M. Cheney, D. Isaacson, Inverse problems for a perturbed dissipative half-space, Inverse Problems 11 (1995) 865.
    • (1995) Inverse Problems , vol.11 , pp. 865
    • Cheney, M.1    Isaacson, D.2
  • 5
    • 0001297471 scopus 로고
    • Three-dimensional inverse scattering for the wave equation: Weak scattering approximation with error estimation
    • M. Cheney, J.H. Rose, Three-dimensional inverse scattering for the wave equation: weak scattering approximation with error estimation, Inverse Problems 4 (1988) 435.
    • (1988) Inverse Problems , vol.4 , pp. 435
    • Cheney, M.1    Rose, J.H.2
  • 7
    • 85190569058 scopus 로고    scopus 로고
    • Dielectric Constant and Loss Tangent of Explosives, Data from U.S. Army Belvoir RD&E Center (unpublished)
    • Dielectric Constant and Loss Tangent of Explosives, Data from U.S. Army Belvoir RD&E Center (unpublished).
  • 9
  • 10
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
    • O. Dorn, E.L. Miller, C.M. Rappaport, A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets, Inverse Problems 16 (2000) 1119.
    • (2000) Inverse Problems , vol.16 , pp. 1119
    • Dorn, O.1    Miller, E.L.2    Rappaport, C.M.3
  • 11
    • 0003514653 scopus 로고    scopus 로고
    • Sparse numerical linear algebra: Direct methods and preconditioning
    • I.S. Duff, G.A. Watson (Eds.), Oxford University Press, Oxford
    • I.S. Duff, Sparse numerical linear algebra: direct methods and preconditioning, in: I.S. Duff, G.A. Watson (Eds.), The State of the Art in Numerical Analysis, Oxford University Press, Oxford, 1997.
    • (1997) The State of the Art in Numerical Analysis
    • Duff, I.S.1
  • 14
    • 0001925237 scopus 로고    scopus 로고
    • GMRES computation of high frequency electrical field propagation in land mine detection
    • Y.A. Gryazin, M.V. Klibanov, T.R. Lucas, GMRES computation of high frequency electrical field propagation in land mine detection, J. Comp. Phys. 158 (2000) 98.
    • (2000) J. Comp. Phys. , vol.158 , pp. 98
    • Gryazin, Y.A.1    Klibanov, M.V.2    Lucas, T.R.3
  • 15
    • 0032681466 scopus 로고    scopus 로고
    • Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography
    • Y.A. Gryazin, M.V. Klibanov, T.R. Lucas, Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography, Inverse Problems 15 (1999) 373.
    • (1999) Inverse Problems , vol.15 , pp. 373
    • Gryazin, Y.A.1    Klibanov, M.V.2    Lucas, T.R.3
  • 16
    • 0036252068 scopus 로고    scopus 로고
    • Numerical solution of a subsurface imaging inverse problem
    • Y.A. Gryazin, M.V. Klibanov, T.R. Lucas, Numerical solution of a subsurface imaging inverse problem, SIAM J. Appl. Math. 62 (2001) 664.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 664
    • Gryazin, Y.A.1    Klibanov, M.V.2    Lucas, T.R.3
  • 18
    • 0033340575 scopus 로고    scopus 로고
    • Numerical solution of a parabolic inverse problem in optical tomography using experimental data
    • M.V. Klibanov, T.R. Lucas, Numerical solution of a parabolic inverse problem in optical tomography using experimental data, SIAM J. Appl. Math. 59 (1999) 1763.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 1763
    • Klibanov, M.V.1    Lucas, T.R.2
  • 19
    • 0031247253 scopus 로고    scopus 로고
    • A fast and accurate imaging algorithm in optical/diffusion tomography
    • M.V. Klibanov, T.R, Lucas, R.M. Frank, A fast and accurate imaging algorithm in optical/diffusion tomography, Inverse Problems 13 (1997) 1341.
    • (1997) Inverse Problems , vol.13 , pp. 1341
    • Klibanov, M.V.1    Lucas, T.R.2    Frank, R.M.3
  • 20
    • 0000543253 scopus 로고
    • A propagation-backpropogation method for ultrasound tomography
    • F. Natterer, F. Wuebbeling, A propagation-backpropogation method for ultrasound tomography, Inverse Problems 11 (1995) 1225.
    • (1995) Inverse Problems , vol.11 , pp. 1225
    • Natterer, F.1    Wuebbeling, F.2
  • 21
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad, M.H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Star. Comput. 7 (1986) 856.
    • (1986) SIAM J. Sci. Star. Comput. , vol.7 , pp. 856
    • Saad, Y.1    Schultz, M.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.