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Volumn 18, Issue 5, 2002, Pages 1229-1246

On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE SCATTERING; ALGORITHMS; OPTIMIZATION; PROBLEM SOLVING; SUBMARINES;

EID: 0036798098     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/18/5/302     Document Type: Article
Times cited : (41)

References (56)
  • 1
    • 0003275409 scopus 로고
    • Inverse acoustic and electromagnetic scattering theory
    • New York: Springer
    • Colton D. and Kress R. 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences vol 93) (New York: Springer).
    • (1992) Applied Mathematical Sciences , vol.93
    • Colton, D.1    Kress, R.2
  • 3
    • 0019539685 scopus 로고
    • Newton-Kantorovich algorithm applied to an electromagnetic inverse problem
    • Roger A. 1981 Newton-Kantorovich algorithm applied to an electromagnetic inverse problem IEEE Trans. Antennas Propag. 29 232-8.
    • (1981) IEEE Trans. Antennas Propag. , vol.29 , pp. 232-238
    • Roger, A.1
  • 4
    • 0011003853 scopus 로고
    • Newton-Kantorovitch method applied to two-dimensional inverse scattering for an exterior Helmholtz problem
    • Murch R.D., Tan D.G.H. and Wall D.J.N. 1988 Newton-Kantorovitch method applied to two-dimensional inverse scattering for an exterior Helmholtz problem Inverse Problems 4 1117-28.
    • (1988) Inverse Problems , vol.4 , pp. 1117-1128
    • Murch, R.D.1    Tan, D.G.H.2    Wall, D.J.N.3
  • 5
    • 0024933116 scopus 로고
    • Inverse acoustic wave scattering in two dimensions from impenetrable targets
    • Tobocman W. 1989 Inverse acoustic wave scattering in two dimensions from impenetrable targets Inverse Problems 5 1131-44.
    • (1989) Inverse Problems , vol.5 , pp. 1131-1144
    • Tobocman, W.1
  • 6
    • 0011003854 scopus 로고
    • An efficient numerical method for exterior and interior inverse problems of Hemholtz equation
    • Wang S.L. and Chen Y.M. 1991 An efficient numerical method for exterior and interior inverse problems of Hemholtz equation Wave Motion 13 387-99.
    • (1991) Wave Motion , vol.13 , pp. 387-399
    • Wang, S.L.1    Chen, Y.M.2
  • 7
    • 4243333658 scopus 로고    scopus 로고
    • A Newton method for solving the inverse scattering problem for a sound-hard obstacle
    • Monk L. 1996 A Newton method for solving the inverse scattering problem for a sound-hard obstacle Inverse Problems 12 309-23.
    • (1996) Inverse Problems , vol.12 , pp. 309-323
    • Monk, L.1
  • 8
    • 0000865204 scopus 로고
    • A quasi-Newton method in inverse obstacle scattering
    • Kress R. and Rundell W. 1994 A quasi-Newton method in inverse obstacle scattering Inverse Problems 10 1145-57.
    • (1994) Inverse Problems , vol.10 , pp. 1145-1157
    • Kress, R.1    Rundell, W.2
  • 10
    • 0010991803 scopus 로고
    • The three dimensional inverse scattering problem for acoustic waves
    • Angel T.S., Colton D. and Kirsch A. 1982 The three dimensional inverse scattering problem for acoustic waves J. Diff. Eq. 46 46-58.
    • (1982) J. Diff. Eq. , vol.46 , pp. 46-58
    • Angel, T.S.1    Colton, D.2    Kirsch, A.3
  • 11
    • 0010962317 scopus 로고
    • Inverse problems for acoustic waves using penalized likelihood method
    • Kristenssen G. and Vogel C.R. 1986 Inverse problems for acoustic waves using penalized likelihood method Inverse Problems 2 461-79.
    • (1986) Inverse Problems , vol.2 , pp. 461-479
    • Kristenssen, G.1    Vogel, C.R.2
  • 12
    • 0022388472 scopus 로고
    • A novel method for solving the inverse scattering problem for time acoustic waves in the resonance region I
    • Colton D. and Monk L. 1985 A novel method for solving the inverse scattering problem for time acoustic waves in the resonance region I SIAM J. Appl. Math. 45 1039-53.
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 1039-1053
    • Colton, D.1    Monk, L.2
  • 13
    • 0022734499 scopus 로고
    • A novel method for solving the inverse scattering problem for time acoustic waves in the resonance region II
    • Colton D. and Monk L. 1986 A novel method for solving the inverse scattering problem for time acoustic waves in the resonance region II SIAM J. Appl. Math. 46 506-23.
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 506-523
    • Colton, D.1    Monk, L.2
  • 14
    • 0001695976 scopus 로고
    • The numerical solution of the three-dimensional inverse scattering problem for time harmonic acoustic waves
    • Colton D. and Monk P. 1987 The numerical solution of the three-dimensional inverse scattering problem for time harmonic acoustic waves SIAM J. Sci. Stat. Comput. 8 278-91.
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 278-291
    • Colton, D.1    Monk, P.2
  • 15
    • 0011007601 scopus 로고
    • A numerical method for an inverse scattering problem
    • ed E. Groetzch (New York: Academic)
    • Kirsch A. and Kress R. 1987 A numerical method for an inverse scattering problem Inverse Problems ed E. Groetzch (New York: Academic) pp 279-90.
    • (1987) Inverse Problems , pp. 279-290
    • Kirsch, A.1    Kress, R.2
  • 16
    • 0002595876 scopus 로고
    • An optimization method in inverse acoustic scattering problem
    • ed Brebia, Wendland and Kuhn
    • Kirsch A. and Kress R. 1987 An optimization method in inverse acoustic scattering problem Boundary Elements IX, Fluid Flow and Potential Applications vol 13, ed Brebia, Wendland and Kuhn pp 3-18.
    • (1987) Boundary Elements IX, Fluid Flow and Potential Applications , vol.13 , pp. 3-18
    • Kirsch, A.1    Kress, R.2
  • 17
    • 0009617085 scopus 로고
    • An inverse transmission problem for Helmholtz equation
    • Angell T.S., Kleinman R.E. and Roach G.F. 1987 An inverse transmission problem for Helmholtz equation Inverse Problems 3 1149-180.
    • (1987) Inverse Problems , vol.3 , pp. 1149-1180
    • Angell, T.S.1    Kleinman, R.E.2    Roach, G.F.3
  • 18
    • 0001570046 scopus 로고
    • Two methods for solving the inverse acoustic scattering problem
    • Kirsch A., Kress R., Monk P. and Zinn A. 1988 Two methods for solving the inverse acoustic scattering problem Inverse Problems 4 749-70.
    • (1988) Inverse Problems , vol.4 , pp. 749-770
    • Kirsch, A.1    Kress, R.2    Monk, P.3    Zinn, A.4
  • 19
    • 0001011250 scopus 로고
    • The inverse problem in hard acoustic scattering
    • Jones D.S. and Mao X.Q. 1989 The inverse problem in hard acoustic scattering Inverse Problems 5 731-48.
    • (1989) Inverse Problems , vol.5 , pp. 731-748
    • Jones, D.S.1    Mao, X.Q.2
  • 20
    • 0025539162 scopus 로고
    • A method for solving the inverse problem in soft acoustic scattering
    • Jones D.S. and Mao X.Q. 1990 A method for solving the inverse problem in soft acoustic scattering IMA J. Appl. Math. 44 127-43.
    • (1990) IMA J. Appl. Math. , vol.44 , pp. 127-143
    • Jones, D.S.1    Mao, X.Q.2
  • 22
    • 0010961768 scopus 로고
    • An inverse problem for the three dimensional Helmholtz equation with Neumann or mixed boundary conditions: A numerical method
    • ed G. Cohen et al. Philadelphia, PA: SLAM
    • Misici L. and Zirilli F. 1991 An inverse problem for the three dimensional Helmholtz equation with Neumann or mixed boundary conditions: a numerical method Mathematical and Numerical Aspects of Wave Propagation Phenomena ed G. Cohen et al. (Philadelphia, PA: SLAM) pp 497-505.
    • (1991) Mathematical and Numerical Aspects of Wave Propagation Phenomena , pp. 497-505
    • Misici, L.1    Zirilli, F.2
  • 23
    • 38249008128 scopus 로고
    • On the numerical solution of the three-dimensional inverse obstacle scattering problem
    • Kress R. and Zinn A. 1992 On the numerical solution of the three-dimensional inverse obstacle scattering problem J. Comput. Appl. Math. 42 49-61.
    • (1992) J. Comput. Appl. Math. , vol.42 , pp. 49-61
    • Kress, R.1    Zinn, A.2
  • 24
    • 0001748645 scopus 로고
    • Three-dimensional inverse obstacle scattering for time harmonic acoustic waves: A numerical method
    • Misici L. and Zirilli F. 1994 Three-dimensional inverse obstacle scattering for time harmonic acoustic waves: a numerical method SIAM J. Sci. Comput. 15 1174-89.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1174-1189
    • Misici, L.1    Zirilli, F.2
  • 25
    • 0000978411 scopus 로고    scopus 로고
    • A simple method for solving inverse scattering problems in the resonance region
    • Colton D. and Kirsch A. 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-93.
    • (1996) Inverse Problems , vol.12 , pp. 383-393
    • Colton, D.1    Kirsch, A.2
  • 26
    • 0000459796 scopus 로고    scopus 로고
    • A fast new method to solve inverse scattering problems
    • Potthast R. 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731-42.
    • (1996) Inverse Problems , vol.12 , pp. 731-742
    • Potthast, R.1
  • 27
    • 3343011404 scopus 로고    scopus 로고
    • A simple method using Morozov's discrepancy principle for solving inverse scattering problems
    • Colton D., Piana M. and Potthast R. 1997 A simple method using Morozov's discrepancy principle for solving inverse scattering problems Inverse Problems 13 1477-93.
    • (1997) Inverse Problems , vol.13 , pp. 1477-1493
    • Colton, D.1    Piana, M.2    Potthast, R.3
  • 28
    • 0034266332 scopus 로고    scopus 로고
    • Recent developments in inverse acoustic scattering theory
    • Colton D., Coyle J. and Monk P. 2000 Recent developments in inverse acoustic scattering theory SIAM Rev. 42 369-414.
    • (2000) SIAM Rev. , vol.42 , pp. 369-414
    • Colton, D.1    Coyle, J.2    Monk, P.3
  • 29
    • 85057686420 scopus 로고    scopus 로고
    • Point sources and multipoles in inverse scattering theory
    • London: Chapman and Hall
    • Potthast R. 2001 Point Sources and Multipoles in Inverse Scattering Theory (Research Notes in Mathematics vol 427) (London: Chapman and Hall).
    • (2001) Research Notes in Mathematics , vol.427
    • Potthast, R.1
  • 30
    • 0000153088 scopus 로고    scopus 로고
    • Scattering and inverse scattering of sound-hard obstacles via shape deformation
    • Ghosh D.N., Couchman L. and Warner J. 1997 Scattering and inverse scattering of sound-hard obstacles via shape deformation Inverse Problems 13 585-606.
    • (1997) Inverse Problems , vol.13 , pp. 585-606
    • Ghosh, D.N.1    Couchman, L.2    Warner, J.3
  • 31
    • 0031124439 scopus 로고    scopus 로고
    • A distributed source method for inverse acoustic scattering
    • Angell T.S., Jiang X. and Kleinman R.E. 1997 A distributed source method for inverse acoustic scattering Inverse Problems 13 531-45.
    • (1997) Inverse Problems , vol.13 , pp. 531-545
    • Angell, T.S.1    Jiang, X.2    Kleinman, R.E.3
  • 32
    • 0000834834 scopus 로고
    • The problem of the convergence of the iteratively regularized Gauss-Newton method
    • Bakushinskii A.B. 1992 The problem of the convergence of the iteratively regularized Gauss-Newton method Comput. Math. Phys. 32 1353-9.
    • (1992) Comput. Math. Phys. , vol.32 , pp. 1353-1359
    • Bakushinskii, A.B.1
  • 33
    • 0031532935 scopus 로고    scopus 로고
    • On the convergence rates for the iteratively regularized Gauss-Newton method
    • Blaschke B., Nebauer A. and Scherzer O. 1997 On the convergence rates for the iteratively regularized Gauss-Newton method IMA J. Numer. Anal. 17 421-36.
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 421-436
    • Blaschke, B.1    Nebauer, A.2    Scherzer, O.3
  • 35
    • 0001200043 scopus 로고
    • Curvature approximation for triangulated surfaces
    • Hamann B. 1993 Curvature approximation for triangulated surfaces Comput. Suppl. 8 139-53.
    • (1993) Comput. Suppl. , vol.8 , pp. 139-153
    • Hamann, B.1
  • 38
    • 0011052120 scopus 로고
    • Uniqueness theorems for the inverse problem of acoustic scattering
    • Colton D. and Sleeman B.D. 1983 Uniqueness theorems for the inverse problem of acoustic scattering IMA J. Appl. Math. 31 253-9.
    • (1983) IMA J. Appl. Math. , vol.31 , pp. 253-259
    • Colton, D.1    Sleeman, B.D.2
  • 39
    • 0023586355 scopus 로고
    • The limited aperture problem of inverse acoustic scattering: Dirichlet boundary conditions
    • Ochs R.L. 1987 The limited aperture problem of inverse acoustic scattering: Dirichlet boundary conditions SIAM J. Appl. Math. 47 1320-41.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 1320-1341
    • Ochs, R.L.1
  • 40
    • 0000637794 scopus 로고
    • On an optimization method for full- and limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle
    • Zinn A. 1989 On an optimization method for full- and limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle Inverse Problems 5 239-53.
    • (1989) Inverse Problems , vol.5 , pp. 239-253
    • Zinn, A.1
  • 41
    • 0003114885 scopus 로고    scopus 로고
    • Integral equation methods in inverse acoustic and electromagnetic scattering
    • ed Ingham and Wrobel
    • Kress R. 1997 Integral equation methods in inverse acoustic and electromagnetic scattering Boundary Integral Formulation for Inverse Analysis ed Ingham and Wrobel pp 67-92.
    • (1997) Boundary Integral Formulation for Inverse Analysis , pp. 67-92
    • Kress, R.1
  • 42
    • 0032201651 scopus 로고    scopus 로고
    • Inverse obstacle scattering using reduced data
    • Kress R. and Rundell W. 1999 Inverse obstacle scattering using reduced data SIAM J. Appl. Math. 59 442-54.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 442-454
    • Kress, R.1    Rundell, W.2
  • 44
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of the regularization
    • Morozov V.A. 1966 On the solution of functional equations by the method of the regularization Dokl. Akad. Nauk 167 414-17.
    • (1966) Dokl. Akad. Nauk , vol.167 , pp. 414-417
    • Morozov, V.A.1
  • 46
    • 36149033735 scopus 로고
    • The domain derivative and two applications in inverse scattering theory
    • Kirsch A. 1993 The domain derivative and two applications in inverse scattering theory Inverse Problems 9 81-96.
    • (1993) Inverse Problems , vol.9 , pp. 81-96
    • Kirsch, A.1
  • 47
    • 0000631543 scopus 로고
    • Fréchet-differentiability of boundary integral operators in inverse acoustic scattering
    • Potthast R. 1994 Fréchet-differentiability of boundary integral operators in inverse acoustic scattering Inverse Problems 10 431-47.
    • (1994) Inverse Problems , vol.10 , pp. 431-447
    • Potthast, R.1
  • 48
    • 36149029023 scopus 로고
    • Fréchet derivatives in inverse obstacle scattering
    • Hettlich F. 1995 Fréchet derivatives in inverse obstacle scattering Inverse Problems 11 371-82.
    • (1995) Inverse Problems , vol.11 , pp. 371-382
    • Hettlich, F.1
  • 49
    • 0010968472 scopus 로고    scopus 로고
    • On the characterization of the Fréchet differentiability with respect to a Lipschitz domain of the acoustic scattered field
    • Djellouli R. and Farhat C. 1999 On the characterization of the Fréchet differentiability with respect to a Lipschitz domain of the acoustic scattered field J. Math. Anal. Appl. 238 259-76.
    • (1999) J. Math. Anal. Appl. , vol.238 , pp. 259-276
    • Djellouli, R.1    Farhat, C.2
  • 50
    • 0001374907 scopus 로고    scopus 로고
    • Bayliss-Turkel like radiation conditions on surfaces of arbitrary shape
    • Antoine X., Barucq H. and Bendali A. 1999 Bayliss-Turkel like radiation conditions on surfaces of arbitrary shape J. Math. Anal. Appl. 229 184-211.
    • (1999) J. Math. Anal. Appl. , vol.229 , pp. 184-211
    • Antoine, X.1    Barucq, H.2    Bendali, A.3
  • 51
    • 0034147879 scopus 로고    scopus 로고
    • Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries
    • Djellouli R., Farhat C., Macedo A. and Tezaur R. 2000 Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries J. Comput. Acoust. 8 81-99.
    • (2000) J. Comput. Acoust. , vol.8 , pp. 81-99
    • Djellouli, R.1    Farhat, C.2    Macedo, A.3    Tezaur, R.4
  • 52
    • 0035839293 scopus 로고    scopus 로고
    • Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries
    • Tezaur R., Macedo A., Farhat C. and Djellouli R. 2001 Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries Int. J. Numer. Methods Eng. 51 1175-93.
    • (2001) Int. J. Numer. Methods Eng. , vol.51 , pp. 1175-1193
    • Tezaur, R.1    Macedo, A.2    Farhat, C.3    Djellouli, R.4
  • 53
    • 0000753548 scopus 로고
    • Boundary conditions for the numerical solution of elliptic equations in exterior regions
    • Bayliss A., Gunzburger M. and Turkel E. 1982 Boundary conditions for the numerical solution of elliptic equations in exterior regions SIAM J. Appl. Math. 42 430-51.
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 430-451
    • Bayliss, A.1    Gunzburger, M.2    Turkel, E.3
  • 54
    • 0034405892 scopus 로고    scopus 로고
    • A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems
    • Farhat C., Macedo A. and Lesoinne M. 2000 A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems Numer. Math. 85 283-308.
    • (2000) Numer. Math. , vol.85 , pp. 283-308
    • Farhat, C.1    Macedo, A.2    Lesoinne, M.3
  • 55
    • 0035839293 scopus 로고    scopus 로고
    • Iterative solution of large-scale acoustic scattering problems with multiple right-hand sides by a domain decomposition method with Lagrange multipliers
    • Tezaur R., Macedo A. and Farhat C. 2001 Iterative solution of large-scale acoustic scattering problems with multiple right-hand sides by a domain decomposition method with Lagrange multipliers Int. J. Numer. Methods Eng. 51 1175-93.
    • (2001) Int. J. Numer. Methods Eng. , vol.51 , pp. 1175-1193
    • Tezaur, R.1    Macedo, A.2    Farhat, C.3


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