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Volumn 11, Issue 1, 2018, Pages 734-769

Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. Part II: Iterative method

Author keywords

Electromagnetism; Inverse obstacle scattering problems; Shape reconstruction; Topological derivative

Indexed keywords

ELECTROMAGNETISM; ITERATIVE METHODS; NUMERICAL METHODS; TOPOLOGY;

EID: 85045682039     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/17M1148359     Document Type: Article
Times cited : (15)

References (46)
  • 1
    • 0003851729 scopus 로고
    • Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
    • U.S. Government Printing Office, Washington, D.C
    • M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55, U.S. Government Printing Office, Washington, D.C., 1964.
    • (1964) National Bureau of Standards Applied Mathematics Series , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 84907704492 scopus 로고    scopus 로고
    • A study on the topological derivative-based imaging of thin electromagnetic inhomogeneities in limited-aperture problems
    • C.Y. Ahn, K. Jeon, Y.-K. Ma, and W.-K. Park, A study on the topological derivative-based imaging of thin electromagnetic inhomogeneities in limited-aperture problems, Inverse Problems, 30 (2014), 105004, https://doi.org/10.1088/0266-5611/30/10/105004.
    • (2014) Inverse Problems , vol.30
    • Ahn, C.Y.1    Jeon, K.2    Ma, Y.-K.3    Park, W.-K.4
  • 3
    • 84858696570 scopus 로고    scopus 로고
    • Stability and resolution analysis for a topological derivative based imaging functional
    • H. Ammari, J. Garnier, V. Jugnon, and H. Kang, Stability and resolution analysis for a topological derivative based imaging functional, SIAM J. Control Optim., 50 (2012), pp. 48-76, https://doi.org/10.1137/100812501.
    • (2012) SIAM J. Control Optim , vol.50 , pp. 48-76
    • Ammari, H.1    Garnier, J.2    Jugnon, V.3    Kang, H.4
  • 4
    • 0033355191 scopus 로고    scopus 로고
    • A boundary-element solution of the Leontovitch problem
    • A. Bendali, M. Fares, and J. Gay, A boundary-element solution of the Leontovitch problem, IEEE Trans. Antennas and Propagation, 47 (1999), pp. 1597-1605, https://doi.org/10.1109/8.805905.
    • (1999) IEEE Trans. Antennas and Propagation , vol.47 , pp. 1597-1605
    • Bendali, A.1    Fares, M.2    Gay, J.3
  • 5
    • 77958090329 scopus 로고    scopus 로고
    • Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems
    • M. Bonnet, Fast identification of cracks using higher-order topological sensitivity for 2-D potential problems, Eng. Anal. Bound. Elem., 35 (2011), pp. 223-235, https://doi.org/10.1016/j.enganabound.2010.08.007.
    • (2011) Eng. Anal. Bound. Elem , vol.35 , pp. 223-235
    • Bonnet, M.1
  • 6
    • 63249132989 scopus 로고    scopus 로고
    • Higher-order topological sensitivity for 2-D potential problems
    • M. Bonnet, Higher-order topological sensitivity for 2-D potential problems, Internat. J. Solids Structures, 46 (2009), pp. 2275-2292, https://doi.org/10.1016/j.ijsolstr.2009.01.021.
    • (2009) Internat. J. Solids Structures , vol.46 , pp. 2275-2292
    • Bonnet, M.1
  • 7
    • 84900816697 scopus 로고    scopus 로고
    • Fast non-iterative methods for defect identification
    • M. Bonnet, B. Guzina, and N. Nemitz, Fast non-iterative methods for defect identification, Rev. Eur. Mecan. Num., 17 (2008), pp. 571-582, https://www.tandfonline.com/doi/abs/10.3166/remn.17.571-582.
    • (2008) Rev. Eur. Mecan. Num , vol.17 , pp. 571-582
    • Bonnet, M.1    Guzina, B.2    Nemitz, N.3
  • 8
    • 0345060038 scopus 로고    scopus 로고
    • Boundary element methods for Maxwell transmission problems in Lipschitz domains
    • A. Buffa, R. Hiptmair, T. von Petersdorff, and C. Schwab, Boundary element methods for Maxwell transmission problems in Lipschitz domains, Numer. Math., 95 (2003), pp. 459-485, https://doi.org/10.1007/s00211-002-0407-z.
    • (2003) Numer. Math , vol.95 , pp. 459-485
    • Buffa, A.1    Hiptmair, R.2    Von Petersdorff, T.3    Schwab, C.4
  • 9
    • 84989298263 scopus 로고    scopus 로고
    • Noninvasive imaging of three-dimensional micro and nanostructures by topological methods
    • A. Carpio, T.G. Dimiduk, M.L. Rapún, and V. Selgas, Noninvasive imaging of three-dimensional micro and nanostructures by topological methods, SIAM J. Imaging Sci., 9 (2016), pp. 1324-1354, https://doi.org/10.1137/16M1068669.
    • (2016) SIAM J. Imaging Sci , vol.9 , pp. 1324-1354
    • Carpio, A.1    Dimiduk, T.G.2    Rapún, M.L.3    Selgas, V.4
  • 10
    • 77949264849 scopus 로고    scopus 로고
    • Determining planar multiple sound-soft obstacles from scattered acoustic fields
    • A. Carpio, B.T. Johansson, and M.-L. Rapún, Determining planar multiple sound-soft obstacles from scattered acoustic fields, J. Math. Imaging Vision, 36 (2010), pp. 185-199, https://doi.org/10.1007/s10851-009-0182-x.
    • (2010) J. Math. Imaging Vision , vol.36 , pp. 185-199
    • Carpio, A.1    Johansson, B.T.2    Rapún, M.-L.3
  • 11
    • 49749113620 scopus 로고    scopus 로고
    • Solving inhomogeneous inverse problems by topological derivative methods
    • A. Carpio and M.L. Rapún, Solving inhomogeneous inverse problems by topological derivative methods, Inverse Problems, 24 (2008), 045014, https://doi.org/10.1088/0266-5611/24/4/045014.
    • (2008) Inverse Problems , vol.24
    • Carpio, A.1    Rapún, M.L.2
  • 12
    • 47049097350 scopus 로고    scopus 로고
    • Topological derivatives for shape reconstruction
    • Springer, Berlin
    • A. Carpio and M.L. Rapún, Topological derivatives for shape reconstruction, in Inverse Problems and Imaging, Lecture Notes in Math. 1943, Springer, Berlin, 2008, pp. 83-133, https://doi.org/10.1007/978-3-540-78547-7_5.
    • (2008) Inverse Problems and Imaging, Lecture Notes in Math , vol.1943 , pp. 83-133
    • Carpio, A.1    Rapún, M.L.2
  • 13
    • 47049119542 scopus 로고    scopus 로고
    • Domain reconstruction using photothermal techniques
    • A. Carpio and M.L. Rapún, Domain reconstruction using photothermal techniques, J. Comput. Phys., 227 (2008), pp. 8083-8106, https://doi.org/10.1016/j.jcp.2008.05.014.
    • (2008) J. Comput. Phys , vol.227 , pp. 8083-8106
    • Carpio, A.1    Rapún, M.L.2
  • 14
    • 84866328135 scopus 로고    scopus 로고
    • Hybrid topological derivative and gradient-based methods for electrical impedance tomography
    • A. Carpio and M.L. Rapún, Hybrid topological derivative and gradient-based methods for electrical impedance tomography, Inverse Problems, 28 (2012), 095010, https://doi.org/10.1088/0266-5611/28/9/095010.
    • (2012) Inverse Problems , vol.28
    • Carpio, A.1    Rapún, M.L.2
  • 15
    • 52749087179 scopus 로고    scopus 로고
    • Generalized topological derivative for the Navier equation and inverse scattering in time domain
    • I. Chikichev and B.B. Guzina, Generalized topological derivative for the Navier equation and inverse scattering in time domain, Comput. Methods Appl. Mech. Engrg., 197 (2008), pp. 4467-4484, https://doi.org/10.1016/j.cma.2008.05.019.
    • (2008) Comput. Methods Appl. Mech. Engrg , vol.197 , pp. 4467-4484
    • Chikichev, I.1    Guzina, B.B.2
  • 16
    • 84962274409 scopus 로고    scopus 로고
    • Inverse Acoustic and Electromagnetic Scattering Theory
    • Springer, New York
    • D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed., Appl. Math. Sci. 93, Springer, New York, 2013.
    • (2013) 3Rd Ed., Appl. Math. Sci , vol.93
    • Colton, D.1    Kress, R.2
  • 17
    • 84860219490 scopus 로고    scopus 로고
    • Shape derivatives of boundary integral operators in electromagnetic scattering. Part II: Application to scattering by a homogeneous dielectric obstacle
    • M. Costabel and F. Le Louër, Shape derivatives of boundary integral operators in electromagnetic scattering. Part II: Application to scattering by a homogeneous dielectric obstacle, Integral Equations Operator Theory, 73 (2012), pp. 17-48, https://doi.org/10.1007/s00020-012-1955-y.
    • (2012) Integral Equations Operator Theory , vol.73 , pp. 17-48
    • Costabel, M.1    Le Louër, F.2
  • 18
    • 34249772762 scopus 로고
    • Bubble method for topology and shape optimization of structures
    • H.A. Eschenauer, V.V. Kobolev, and A. Schumacher, Bubble method for topology and shape optimization of structures, Struct. Optim., 8 (1994), pp. 42-51, https://doi.org/10.1007/BF01742933.
    • (1994) Struct. Optim , vol.8 , pp. 42-51
    • Eschenauer, H.A.1    Kobolev, V.V.2    Schumacher, A.3
  • 19
    • 10844274795 scopus 로고    scopus 로고
    • A new method in inverse scattering based on the topological derivative
    • G.R. Feijoo, A new method in inverse scattering based on the topological derivative, Inverse Problems, 20 (2004), pp. 1819-1840, https://doi.org/10.1088/0266-5611/20/6/008.
    • (2004) Inverse Problems , vol.20 , pp. 1819-1840
    • Feijoo, G.R.1
  • 20
    • 3042858769 scopus 로고    scopus 로고
    • A high-order algorithm for obstacle scattering in three dimensions
    • M. Ganesh and I.G. Graham, A high-order algorithm for obstacle scattering in three dimensions, J. Comput. Phys., 198 (2004), pp. 211-242, https://doi.org/10.1016/j.jcp.2004.01.007.
    • (2004) J. Comput. Phys , vol.198 , pp. 211-242
    • Ganesh, M.1    Graham, I.G.2
  • 21
    • 40849094989 scopus 로고    scopus 로고
    • A hybrid high-order algorithm for radar cross section computations, SIAM
    • M. Ganesh and S.C. Hawkins, A hybrid high-order algorithm for radar cross section computations, SIAM J. Sci. Comput., 29 (2007), pp. 1217-1243, https://doi.org/10.1137/060664859.
    • (2007) J. Sci. Comput , vol.29 , pp. 1217-1243
    • Ganesh, M.1    Hawkins, S.C.2
  • 22
    • 40849115944 scopus 로고    scopus 로고
    • A high-order tangential basis algorithm for electromagnetic scattering by curved surfaces
    • M. Ganesh and S.C. Hawkins, A high-order tangential basis algorithm for electromagnetic scattering by curved surfaces, J. Comput. Phys., 227 (2008), pp. 4543-4562, https://doi.org/10.1016/j.jcp.2008.01.016.
    • (2008) J. Comput. Phys , vol.227 , pp. 4543-4562
    • Ganesh, M.1    Hawkins, S.C.2
  • 23
    • 63349097608 scopus 로고    scopus 로고
    • A high-order algorithm for multiple electromagnetic scattering in three dimensions
    • M. Ganesh and S.C. Hawkins, A high-order algorithm for multiple electromagnetic scattering in three dimensions, Numer. Algorithms, 50 (2009), pp. 469-510, https://doi.org/10.1007/s11075-008-9238-z.
    • (2009) Numer. Algorithms , vol.50 , pp. 469-510
    • Ganesh, M.1    Hawkins, S.C.2
  • 24
    • 0035665129 scopus 로고    scopus 로고
    • The topological asymptotic for PDE systems: The elasticity case
    • S. Garreau, P. Guillaume, and M. Masmoudi, The topological asymptotic for PDE systems: The elasticity case, SIAM J. Control Optim., 39 (2001), pp. 1756-1778, https://doi.org/10.1137/S0363012900369538.
    • (2001) SIAM J. Control Optim , vol.39 , pp. 1756-1778
    • Garreau, S.1    Guillaume, P.2    Masmoudi, M.3
  • 25
    • 33845230843 scopus 로고    scopus 로고
    • From imaging to material identification: A generalized concept of topological sensitivity
    • B.B. Guzina and I. Chikichev, From imaging to material identification: A generalized concept of topological sensitivity, J. Mech. Phys. Solids, 55 (2007), pp. 245-279, https://doi.org/10.1016/j.jmps.2006.07.009.
    • (2007) J. Mech. Phys. Solids , vol.55 , pp. 245-279
    • Guzina, B.B.1    Chikichev, I.2
  • 26
    • 84937112037 scopus 로고    scopus 로고
    • Why the high-frequency inverse scattering by topological sensitivity may work
    • B.B. Guzina and F. Pourahmadian, Why the high-frequency inverse scattering by topological sensitivity may work, Proc. A., 471 (2015), 20150187, https://doi.org/10.1098/rspa.2015.0187.
    • (2015) Proc. A , vol.471
    • Guzina, B.B.1    Pourahmadian, F.2
  • 27
    • 16244379216 scopus 로고    scopus 로고
    • On the Fréchet derivative for obstacle scattering with an impedance boundary condition
    • H. Haddar and R. Kress, On the Fréchet derivative for obstacle scattering with an impedance boundary condition, SIAM J. Appl. Math., 65 (2004), pp. 194-208, https://doi.org/10.1137/S0036139903435413.
    • (2004) SIAM J. Appl. Math , vol.65 , pp. 194-208
    • Haddar, H.1    Kress, R.2
  • 28
    • 84865860888 scopus 로고    scopus 로고
    • The domain derivative of time-harmonic electromagnetic waves at interfaces
    • F. Hettlich, The domain derivative of time-harmonic electromagnetic waves at interfaces, Math. Methods Appl. Sci., 35 (2012), pp. 1681-1689, https://doi.org/10.1002/mma.2548.
    • (2012) Math. Methods Appl. Sci , vol.35 , pp. 1681-1689
    • Hettlich, F.1
  • 29
    • 84923264547 scopus 로고    scopus 로고
    • Topological sensitivity analysis for the modified Helmholtz equation under an impedance condition on the boundary of a hole
    • M. Jleli, B. Samet, and G. Vial, Topological sensitivity analysis for the modified Helmholtz equation under an impedance condition on the boundary of a hole, J. Math. Pures Appl. (9), 103 (2015), pp. 557-574, https://doi.org/10.1016/j.matpur.2014.07.003.
    • (2015) J. Math. Pures Appl , vol.103 , Issue.9 , pp. 557-574
    • Jleli, M.1    Samet, B.2    Vial, G.3
  • 30
    • 0002695655 scopus 로고    scopus 로고
    • Electromagnetic waves scattering: Scattering by obstacles
    • E.R. Pike and P.C. Sabatier, eds., Academic Press, London
    • R. Kress, Electromagnetic waves scattering: Scattering by obstacles, in Scattering, E.R. Pike and P.C. Sabatier, eds., Academic Press, London, 2001, pp. 191-210.
    • (2001) Scattering , pp. 191-210
    • Kress, R.1
  • 31
    • 84905251470 scopus 로고    scopus 로고
    • Spectrally accurate numerical solution of hypersingular boundary integral equations for three-dimensional electromagnetic wave scattering problems
    • F. Le Louër, Spectrally accurate numerical solution of hypersingular boundary integral equations for three-dimensional electromagnetic wave scattering problems, J. Comput. Phys., 275 (2014), pp. 662-666, https://doi.org/10.1016/j.jcp.2014.07.022.
    • (2014) J. Comput. Phys , vol.275 , pp. 662-666
    • Le Louër, F.1
  • 32
    • 85045661223 scopus 로고    scopus 로고
    • A spectrally accurate method for the direct and inverse scattering problems by multiple 3d dielectric obstacles
    • F. Le Louër, A spectrally accurate method for the direct and inverse scattering problems by multiple 3d dielectric obstacles, ANZIAM e-Journal, 59 (2018), pp. E1-E49, https://doi.org/10.21914/anziamj.v59i0.11534.
    • (2018) ANZIAM E-Journal , vol.59 , pp. EE1-E49
    • Le Louër, F.1
  • 33
    • 85032922717 scopus 로고    scopus 로고
    • Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. Part I: One step method
    • F. Le Louër and M.-L. Rapún, Topological sensitivity for solving inverse multiple scattering problems in three-dimensional electromagnetism. Part I: One step method, SIAM J. Imaging Sci., 10 (2017), pp. 1291-1321, https://doi.org/10.1137/17M1113850.
    • (2017) SIAM J. Imaging Sci , vol.10 , pp. 1291-1321
    • Le Louër, F.1    Rapún, M.-L.2
  • 34
    • 0001225320 scopus 로고
    • Analysis of radiative scattering for multiple sphere configurations
    • D.W. Mackowski, Analysis of radiative scattering for multiple sphere configurations, Proc. Roy. Soc. London Ser. A, 433 (1991), pp. 599-614, https://doi.org/10.1098/rspa.1991.0066.
    • (1991) Proc. Roy. Soc. London Ser. A , vol.433 , pp. 599-614
    • Mackowski, D.W.1
  • 35
    • 84971961740 scopus 로고
    • Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle
    • P.A. Martin and P. Ola, Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 185-208, https://doi.org/10.1017/S0308210500021296.
    • (1993) Proc. Roy. Soc. Edinburgh Sect. A , vol.123 , pp. 185-208
    • Martin, P.A.1    Ola, P.2
  • 36
    • 17444421198 scopus 로고    scopus 로고
    • The topological asymptotic expansion for the Maxwell equations and some applications
    • M. Masmoudi, J. Pommier, and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, 21 (2005), pp. 547-564, https://doi.org/10.1088/0266-5611/21/2/008.
    • (2005) Inverse Problems , vol.21 , pp. 547-564
    • Masmoudi, M.1    Pommier, J.2    Samet, B.3
  • 37
    • 0012541720 scopus 로고    scopus 로고
    • Finite Element Methods for Maxwell’s Equations
    • Oxford University Press, New York
    • P. Monk, Finite Element Methods for Maxwell’s Equations, Numer. Math. Sci. Comput., Oxford University Press, New York, 2003.
    • (2003) Numer. Math. Sci. Comput
    • Monk, P.1
  • 38
    • 0003807866 scopus 로고    scopus 로고
    • Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems
    • Springer-Verlag, New York
    • J.-C. Nédélec, Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems, Appl. Math. Sci. 144, Springer-Verlag, New York, 2001.
    • (2001) Appl. Math. Sci , vol.144
    • Nédélec, J.-C.1
  • 39
    • 53249111801 scopus 로고    scopus 로고
    • Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering
    • N. Nemitz and M. Bonnet, Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering, Eng. Anal. Bound. Elem., 32 (2008), pp. 957-970, https://doi.org/10.1016/j.enganabound.2007.02.006.
    • (2008) Eng. Anal. Bound. Elem , vol.32 , pp. 957-970
    • Nemitz, N.1    Bonnet, M.2
  • 41
    • 84855192911 scopus 로고    scopus 로고
    • Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions
    • W.K. Park, Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions, J. Comput. Phys., 231 (2012), pp. 1426-1439, https://doi.org/10.1016/j.jcp.2011.10.014.
    • (2012) J. Comput. Phys , vol.231 , pp. 1426-1439
    • Park, W.K.1
  • 42
    • 0032681559 scopus 로고    scopus 로고
    • On the topological derivative in shape optimization
    • J. Sokowłoski and A. Żochowski, On the topological derivative in shape optimization, SIAM J. Control Optim., 37 (1999), pp. 1251-1272, https://doi.org/10.1137/S0363012997323230.
    • (1999) SIAM J. Control Optim , vol.37 , pp. 1251-1272
    • Sokowłoski, J.1    Żochowski, A.2
  • 43
    • 79957477823 scopus 로고    scopus 로고
    • Modified combined field integral equations for electromagnetic scattering
    • O. Steinbach and M. Windisch, Modified combined field integral equations for electromagnetic scattering, SIAM J. Numer. Anal., 47 (2009), pp. 1149-1167, https://doi.org/10.1137/070698063.
    • (2009) SIAM J. Numer. Anal , vol.47 , pp. 1149-1167
    • Steinbach, O.1    Windisch, M.2
  • 44
    • 84943572820 scopus 로고    scopus 로고
    • Stability and resolution analysis of topological derivative based localization of small electromagnetic inclusions
    • A. Wahab, Stability and resolution analysis of topological derivative based localization of small electromagnetic inclusions, SIAM J. Imaging Sci., 8 (2015), pp. 1687-1717, https://doi.org/10.1137/141000567.
    • (2015) SIAM J. Imaging Sci , vol.8 , pp. 1687-1717
    • Wahab, A.1
  • 45
    • 85032943302 scopus 로고    scopus 로고
    • Detection of electromagnetic inclusions using topological sensitivity
    • A. Wahab, T. Abbas, N. Ahmed, and Q.M.Z. Zia, Detection of electromagnetic inclusions using topological sensitivity, J. Comput. Math., 35 (2017), pp. 642-671, https://doi.org/10.4208/jcm.1609-m2016-0498.
    • (2017) J. Comput. Math , vol.35 , pp. 642-671
    • Wahab, A.1    Abbas, T.2    Ahmed, N.3    Zia, Q.M.Z.4
  • 46
    • 84924390005 scopus 로고    scopus 로고
    • Inverse acoustic scattering by solid obstacles: Topological sensitivity and its preliminary application
    • H. Yuan, G. Bracq, and Q. Lin, Inverse acoustic scattering by solid obstacles: Topological sensitivity and its preliminary application, Inverse Probl. Sci. Eng., 24 (2016), pp. 92-126, https://doi.org/10.1080/17415977.2015.1017483.
    • (2016) Inverse Probl. Sci. Eng , vol.24 , pp. 92-126
    • Yuan, H.1    Bracq, G.2    Lin, Q.3


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