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Volumn 20, Issue 1, 2004, Pages 199-228

An application of shape optimization in the solution of inverse acoustic scattering problems

Author keywords

[No Author keywords available]

Indexed keywords

GRADIENT BASED ALGORITHM; HELMHOLTZ EQUATION; INVERSE ACOUSTIC SCATTERING; SOMMERFELD CONDITION;

EID: 1342308459     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/20/1/012     Document Type: Article
Times cited : (52)

References (36)
  • 1
  • 2
    • 0000753548 scopus 로고
    • Boundary conditions for the numerical solution of elliptic equations in exterior domains
    • Bayliss A, Gunzburger M and Turkel E 1982 Boundary conditions for the numerical solution of elliptic equations in exterior domains SIAM J. Appl. Math. 42 439-51
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 439-451
    • Bayliss, A.1    Gunzburger, M.2    Turkel, E.3
  • 4
    • 0035668125 scopus 로고    scopus 로고
    • A comparison of the Colton-Kirsch inverse scattering methods with tomographic inverse scattering
    • Brandfass M, Langerman A D and Warnick K F 2001 A comparison of the Colton-Kirsch inverse scattering methods with tomographic inverse scattering Inverse Problems 17 1797-816
    • (2001) Inverse Problems , vol.17 , pp. 1797-1816
    • Brandfass, M.1    Langerman, A.D.2    Warnick, K.F.3
  • 5
    • 0028099393 scopus 로고
    • A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion
    • Burnett D S 1994 A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion J. Acoust. Soc. Am. 96 2798-816
    • (1994) J. Acoust. Soc. Am. , vol.96 , pp. 2798-2816
    • Burnett, D.S.1
  • 6
    • 0037465759 scopus 로고    scopus 로고
    • Combined far-field operators in electromagnetic inverse scattering theory
    • Cakoni F and Colton D 2003 Combined far-field operators in electromagnetic inverse scattering theory Math. Methods Appl. Sci. 26 413-29
    • (2003) Math. Methods Appl. Sci. , vol.26 , pp. 413-429
    • Cakoni, F.1    Colton, D.2
  • 7
    • 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
  • 8
    • 0034497173 scopus 로고    scopus 로고
    • A regularized sampling method for solving three-dimensional inverse scattering problems
    • Colton D, Giebermann K and Monk P 2000 A regularized sampling method for solving three-dimensional inverse scattering problems SIAM J. Sci. Comput. 21 2316-30
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2316-2330
    • Colton, D.1    Giebermann, K.2    Monk, P.3
  • 9
    • 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
  • 10
    • 0000340316 scopus 로고    scopus 로고
    • The simple method for solving the electromagnetic inverse scattering problem: The case of the polarized waves
    • Colton D and Piana M 1998 The simple method for solving the electromagnetic inverse scattering problem: the case of the polarized waves Inverse Problems 14 597-614
    • (1998) Inverse Problems , vol.14 , pp. 597-614
    • Colton, D.1    Piana, M.2
  • 11
    • 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
  • 12
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets
    • Dorn O, Miller E L and Rappaport C M 2000 A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets Inverse Problems 16 1119-56
    • (2000) Inverse Problems , vol.16 , pp. 1119-1156
    • Dorn, O.1    Miller, E.L.2    Rappaport, C.M.3
  • 13
    • 0034914944 scopus 로고    scopus 로고
    • Shape sensitivity calculations for exterior acoustics problems
    • Feijóo G R, Malhotra M, Oberai A A and Pinsky P M 2001 Shape sensitivity calculations for exterior acoustics problems Eng. Comput. 18 376-91
    • (2001) Eng. Comput. , vol.18 , pp. 376-391
    • Feijóo, G.R.1    Malhotra, M.2    Oberai, A.A.3    Pinsky, P.M.4
  • 17
    • 0000907608 scopus 로고
    • On non-reflecting boundary conditions
    • Grote M J and Keller J B 1995 On non-reflecting boundary conditions J. Comput. Phys. 122, 231-43
    • (1995) J. Comput. Phys. , vol.122 , pp. 231-243
    • Grote, M.J.1    Keller, J.B.2
  • 20
    • 0000271460 scopus 로고
    • Exact non-reflecting boundary conditions
    • Keller J B and Givoli D 1989 Exact non-reflecting boundary conditions J. Comput. Phys. 82 172-92
    • (1989) J. Comput. Phys. , vol.82 , pp. 172-192
    • Keller, J.B.1    Givoli, D.2
  • 21
    • 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
  • 22
    • 0000714376 scopus 로고    scopus 로고
    • Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
    • Kirsch A 1998 Characterization of the shape of a scattering obstacle using the spectral data of the far field operator Inverse Problems 14 1489-512
    • (1998) Inverse Problems , vol.14 , pp. 1489-1512
    • Kirsch, A.1
  • 23
    • 0001119601 scopus 로고    scopus 로고
    • Factorization of the far-field operator for the inhomogeneous medium case and an application to inverse scattering theory
    • Kirsch A 1999 Factorization of the far-field operator for the inhomogeneous medium case and an application to inverse scattering theory Inverse Problems 15 413-29
    • (1999) Inverse Problems , vol.15 , pp. 413-429
    • Kirsch, A.1
  • 24
    • 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
  • 25
    • 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
  • 26
    • 0000386587 scopus 로고    scopus 로고
    • Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set
    • Litman A, Lesselier D and Santosa F 1998 Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set Inverse Problems 14 685-706
    • (1998) Inverse Problems , vol.14 , pp. 685-706
    • Litman, A.1    Lesselier, D.2    Santosa, F.3
  • 28
    • 0141478997 scopus 로고    scopus 로고
    • On modeling the large-scale exterior acoustics problem using the finite-element method
    • PhD Thesis Stanford University, CA, USA
    • Oberai A A 1998 On modeling the large-scale exterior acoustics problem using the finite-element method PhD Thesis Stanford University, CA, USA
    • (1998)
    • Oberai, A.A.1
  • 29
    • 0032137480 scopus 로고    scopus 로고
    • On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation
    • Oberai A A, Malhotra M and Pinsky P M 1998 On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation Appl. Numer. Math. 27 443-64
    • (1998) Appl. Numer. Math. , vol.27 , pp. 443-464
    • Oberai, A.A.1    Malhotra, M.2    Pinsky, P.M.3
  • 30
    • 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
  • 31
    • 0008339101 scopus 로고
    • Mathematical programming: The state of the art
    • ed A Bachem, M Grötschel and B Korte (Berlin: Springer)
    • Powell M J D 1983 Mathematical programming: the state of the art Variable Metric Methods for Constrained Optimization ed A Bachem, M Grötschel and B Korte (Berlin: Springer) pp 288-311
    • (1983) Variable Metric Methods for Constrained Optimization , pp. 288-311
    • Powell, M.J.D.1
  • 32
    • 0035419980 scopus 로고    scopus 로고
    • Shape reconstruction of buried obstacles by controlled evolution of a level set: From a min-max formulation to numerical experimentation
    • Ramananjaona C, Lambert M, Lesselier D and Zolesio J P 2001 Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min-max formulation to numerical experimentation Inverse Problems 17 1087-111
    • (2001) Inverse Problems , vol.17 , pp. 1087-1111
    • Ramananjaona, C.1    Lambert, M.2    Lesselier, D.3    Zolesio, J.P.4
  • 33
    • 84996143735 scopus 로고    scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • Santosa F 1996 A level-set approach for inverse problems involving obstacles ESAIM: Control Optim. Calculus Variat. 1 17-33
    • (1996) ESAIM: Control Optim. Calculus Variat. , vol.1 , pp. 17-33
    • Santosa, F.1
  • 35
    • 0001743441 scopus 로고
    • The Green's function of the oscillation equation
    • Sommerfeld A 1912 The Green's function of the oscillation equation Jahresber. Deutsch. Math. Ver. 21 309-53
    • (1912) Jahresber. Deutsch. Math. Ver. , vol.21 , pp. 309-353
    • Sommerfeld, A.1
  • 36
    • 0003909674 scopus 로고    scopus 로고
    • Thompson J F, Soni B K and Weatherill N P (ed); (Boca Raton, FL: CRC Press)
    • Thompson J F, Soni B K and Weatherill N P (ed) 1999 Handbook of Grid Generation (Boca Raton, FL: CRC Press)
    • (1999) Handbook of Grid Generation


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