메뉴 건너뛰기




Volumn 17, Issue 6, 2009, Pages 803-820

Detection of cavities using the method of fundamental solutions

Author keywords

Cavity detection; Inverse problem; Method of fundamental solutions

Indexed keywords

CAVITY DETECTION; CAVITY SHAPE; CONDUCTING MEDIUM; CURRENT FLUX; DISCRETIZATIONS; HARMONIC FUNCTION; ILL-CONDITIONED SYSTEMS; INPUT DATAS; INVERSE BOUNDARY VALUE PROBLEM; METHOD OF FUNDAMENTAL SOLUTIONS; NON-LINEAR; NONLINEAR LEAST-SQUARES; NUMERICAL EXAMPLE; NUMERICAL SOLUTION; NUMERICAL SOLUTION METHOD; PARAMETRIZATIONS; RANDOM NOISE; THREE DIMENSIONS; TWO-DIMENSION;

EID: 70349750097     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970802580263     Document Type: Article
Times cited : (40)

References (52)
  • 1
    • 3042730181 scopus 로고    scopus 로고
    • Inverse Dirichlet problem and conformal mapping
    • R. Kress, Inverse Dirichlet problem and conformal mapping, Math. Comput. Simulation 66 (2004), pp. 255-265.
    • (2004) Math Comput Simulation , vol.66 , pp. 255-265
    • Kress, R.1
  • 2
    • 0142125679 scopus 로고    scopus 로고
    • The point source method for reconstructing an inclusion from boundary measurements in electrical impedence tomography and acoustic scattering
    • K. Erhard and R. Potthast, The point source method for reconstructing an inclusion from boundary measurements in electrical impedence tomography and acoustic scattering, Inverse Probl. 19 (2003), pp. 1139-1157.
    • (2003) Inverse Probl , vol.19 , pp. 1139-1157
    • Erhard, K.1    Potthast, R.2
  • 3
    • 14844290885 scopus 로고    scopus 로고
    • A hybrid method for inverse boundary value problems in potential theory
    • R. Chapko and R. Kress, A hybrid method for inverse boundary value problems in potential theory, J. Inverse Ill-Posed Probl. 13 (2005), pp. 27-40.
    • (2005) J Inverse Ill-Posed Probl , vol.13 , pp. 27-40
    • Chapko, R.1    Kress, R.2
  • 4
    • 3142715247 scopus 로고    scopus 로고
    • An efficient singular superposition technique for cavity detection and shape optimization
    • E. Divo, A.J. Kassab, and F. Rodriguez, An efficient singular superposition technique for cavity detection and shape optimization, Numer. Heat Transfer, Part B: Fundamentals 46 (2004), pp. 1-30.
    • (2004) Numer. Heat Transfer, Part B: Fundamentals , vol.46 , pp. 1-30
    • Divo, E.1    Kassab, A.J.2    Rodriguez, F.3
  • 5
    • 0036551790 scopus 로고    scopus 로고
    • Location search techniques for a grounded conductor
    • S. Kim, O. Kwon, and J.K. Seo, Location search techniques for a grounded conductor, SIAM J. Appl. Math. 62 (2002), pp. 1383-1393.
    • (2002) SIAM J Appl Math , vol.62 , pp. 1383-1393
    • Kim, S.1    Kwon, O.2    Seo, J.K.3
  • 6
    • 23244456330 scopus 로고    scopus 로고
    • Nonlinear integral equations and the iterative solution for an inverse boundary value problem
    • R. Kress and W. Rundell, Nonlinear integral equations and the iterative solution for an inverse boundary value problem, Inverse Prob. 21 (2005), pp. 1207-1223.
    • (2005) Inverse Prob , vol.21 , pp. 1207-1223
    • Kress, R.1    Rundell, W.2
  • 7
    • 0031195160 scopus 로고    scopus 로고
    • Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography
    • R. Duraiswami, G.L. Chahine, and K. Sarkar, Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography, Chem. Eng. Sci. 52 (1997), pp. 2185-2196.
    • (1997) Chem. Eng. Sci. , vol.52 , pp. 2185-2196
    • Duraiswami, R.1    Chahine, G.L.2    Sarkar, K.3
  • 8
    • 33846110386 scopus 로고    scopus 로고
    • Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks
    • O. Ivanyshyn and R. Kress, Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks, J. Integral Eqns. Appl. 18 (2006), pp. 13-38.
    • (2006) J Integral Eqns Appl , vol.18 , pp. 13-38
    • Ivanyshyn, O.1    Kress, R.2
  • 9
    • 0022490545 scopus 로고
    • Boundary element iterative techniques for determining the interface boundary between two Laplace domains - A basic study of impedance plethysmography as an inverse problem
    • T. Murai and Y. Kagawa, Boundary element iterative techniques for determining the interface boundary between two Laplace domains - A basic study of impedance plethysmography as an inverse problem, Internat. J. Numer. Methods Eng. 23 (1986), pp. 35-47.
    • (1986) Internat J Numer Methods Eng , vol.23 , pp. 35-47
    • Murai, T.1    Kagawa, Y.2
  • 10
    • 0033625606 scopus 로고    scopus 로고
    • The boundary element method in the forward and inverse problem of electrical impedance tomography
    • J.C. de Munck, T.J.C. Faes, and R.M. Heethaar, The boundary element method in the forward and inverse problem of electrical impedance tomography, IEEE Trans. Biomed. Eng. 47 (2000), pp. 792-800.
    • (2000) IEEE Trans Biomed Eng , vol.47 , pp. 792-800
    • de Munck, J.C.1    Faes, T.J.C.2    Heethaar, R.M.3
  • 12
    • 27144479756 scopus 로고
    • On the treatment of a Dirichlet-Neumann mixed boundary value problem for harmonic functions by an integral equation method
    • On the treatment of a Dirichlet-Neumann mixed boundary value problem for harmonic functions by an integral equation method, SIAM J. Math. Anal. 8 (1977), pp. 504-517.
    • (1977) SIAM J Math Anal , vol.8 , pp. 504-517
  • 15
    • 0030385058 scopus 로고    scopus 로고
    • Field mice: Extracting hand geometry from electric field measurements
    • J.R. Smith, Field mice: Extracting hand geometry from electric field measurements, IBM Sys. J. 35 (1996), pp. 587-608.
    • (1996) IBM Sys J , vol.35 , pp. 587-608
    • Smith, J.R.1
  • 17
    • 18744366101 scopus 로고    scopus 로고
    • Conformal mappings and inverse boundary value problems
    • H. Haddar and R. Kress, Conformal mappings and inverse boundary value problems, Inverse Probl. 21 (2005), pp. 935-953.
    • (2005) Inverse Probl , vol.21 , pp. 935-953
    • Haddar, H.1    Kress, R.2
  • 18
    • 0035506004 scopus 로고    scopus 로고
    • Optimal stability for the inverse problem of multiple cavities
    • G. Alessandrini and L. Rondi, Optimal stability for the inverse problem of multiple cavities, J. Diff. Eq. 176 (2001), pp. 356-386.
    • (2001) J. Diff. Eq. , vol.176 , pp. 356-386
    • Alessandrini, G.1    Rondi, L.2
  • 19
    • 0036798099 scopus 로고    scopus 로고
    • Detecting cavities by electrostatic boundary measurements
    • G. Alessandrini, A. Morassi, and E. Rosset, Detecting cavities by electrostatic boundary measurements, Inverse Probl. 18 (2002), pp. 1333-1353.
    • (2002) Inverse Probl , vol.18 , pp. 1333-1353
    • Alessandrini, G.1    Morassi, A.2    Rosset, E.3
  • 20
    • 0032344733 scopus 로고    scopus 로고
    • The method of fundamental solutions for elliptic boundary value problems
    • G. Fairweather and A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math. 9 (1998), pp. 69-95.
    • (1998) Adv. Comput. Math. , vol.9 , pp. 69-95
    • Fairweather, G.1    Karageorghis, A.2
  • 23
    • 0017955679 scopus 로고
    • Numerical properties of integral equations in which the given boundary values and the sought solutions are defined on different curves
    • U. Heise, Numerical properties of integral equations in which the given boundary values and the sought solutions are defined on different curves, Comput. Struct. 8 (1978), pp. 199-205.
    • (1978) Comput. Struct. , vol.8 , pp. 199-205
    • Heise, U.1
  • 24
    • 0042310464 scopus 로고
    • Integral equations for potential problems with the source function not located on the boundary
    • G. de Mey, Integral equations for potential problems with the source function not located on the boundary, Comput. Struct. 8 (1978), pp. 113-115.
    • (1978) Comput. Struct. , vol.8 , pp. 113-115
    • de Mey, G.1
  • 25
    • 0021574589 scopus 로고
    • A comparison of the boundary element and superposition methods
    • G. Burgess and E. Maharejin, A comparison of the boundary element and superposition methods, Comput. Struct. 19 (1984), pp. 697-705.
    • (1984) Comput. Struct. , vol.19 , pp. 697-705
    • Burgess, G.1    Maharejin, E.2
  • 26
    • 0022107918 scopus 로고
    • Fundamental solutions method for elliptic boundary value problems
    • A. Bogomolny, Fundamental solutions method for elliptic boundary value problems, SIAM J. Numer. Anal. 22 (1985), pp. 644-669.
    • (1985) SIAM J Numer. Anal. , vol.22 , pp. 644-669
    • Bogomolny, A.1
  • 27
    • 0001167301 scopus 로고    scopus 로고
    • The collocation points of the fundamental solution method for the potential problem
    • M. Katsurada and H. Okamoto, The collocation points of the fundamental solution method for the potential problem, Comput. Math. Appl. 31 (1996), pp. 123-137.
    • (1996) Comput. Math. Appl. , vol.31 , pp. 123-137
    • Katsurada, M.1    Okamoto, H.2
  • 28
    • 38149144243 scopus 로고
    • Asymptotic stability of the fundamental solution method
    • T. Kitagawa, Asymptotic stability of the fundamental solution method, J. Comput. Appl. Math. 38 (1991), pp. 263-269.
    • (1991) J. Comput. Appl. Math. , vol.38 , pp. 263-269
    • Kitagawa, T.1
  • 29
    • 33748444430 scopus 로고
    • The method of functional equations for the approximate solution of certain boundary value problems, USSR Comput
    • V.D. Kupradze and M.R. Aleksidze, The method of functional equations for the approximate solution of certain boundary value problems, USSR Comput. Maths. Math. Phys. 4 (1964), pp. 82-126.
    • (1964) Maths. Math. Phys. , vol.4 , pp. 82-126
    • Kupradze, V.D.1    Aleksidze, M.R.2
  • 30
    • 33646719648 scopus 로고    scopus 로고
    • On the convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson equation
    • X. Li, On the convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson equation, Adv. Comput. Math. 23 (2005), pp. 265-277.
    • (2005) Adv. Comput. Math. , vol.23 , pp. 265-277
    • Li, X.1
  • 31
    • 0347601931 scopus 로고    scopus 로고
    • Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed sources
    • P. Mitic and Y.F. Rashed, Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed sources, Eng. Anal. Boundary Elem. 28 (2004), pp. 143-153.
    • (2004) Eng Anal Boundary Elem , vol.28 , pp. 143-153
    • Mitic, P.1    Rashed, Y.F.2
  • 32
    • 0041950033 scopus 로고    scopus 로고
    • Some aspects of the method of fundamental solutions for certain harmonic problems
    • Y.-S. Smyrlis and A. Karageorghis, Some aspects of the method of fundamental solutions for certain harmonic problems, J. Sci. Comput. 16 (2001), pp. 341-371.
    • (2001) J. Sci. Comput. , vol.16 , pp. 341-371
    • Smyrlis, Y.-S.1    Karageorghis, A.2
  • 33
    • 33646230299 scopus 로고    scopus 로고
    • Numerical analysis of the method of fundamental solutions for harmonic problems in annular domains
    • Th. Tsangaris, Y.-S. Smyrlis, and A. Karageorghis, Numerical analysis of the method of fundamental solutions for harmonic problems in annular domains, Numer. Methods Partial Diff. Eq. 22 (2006), pp. 507-539.
    • (2006) Numer Methods Partial Diff Eq , vol.22 , pp. 507-539
    • Tsangaris, T.1    Smyrlis, Y.-S.2    Karageorghis, A.3
  • 34
    • 0005178854 scopus 로고
    • The method of fundamental solutions for the solution of steady-state free boundary problems
    • A. Karageorghis, The method of fundamental solutions for the solution of steady-state free boundary problems, J. Comput. Phys. 98 (1992), pp. 119-128.
    • (1992) J. Comput. Phys. , vol.98 , pp. 119-128
    • Karageorghis, A.1
  • 36
    • 0033115359 scopus 로고    scopus 로고
    • The method of fundamental solutions for axisymmetric potential problems
    • A. Karageorghis and G. Fairweather, The method of fundamental solutions for axisymmetric potential problems, Internat. J. Numer. Methods Eng. 44 (1999), pp. 1653-1669.
    • (1999) Internat J Numer Methods Eng , vol.44 , pp. 1653-1669
    • Karageorghis, A.1    Fairweather, G.2
  • 37
    • 0032384050 scopus 로고    scopus 로고
    • The method of fundamental solutions for Signorini problems
    • A. Poullikkas, A. Karageorghis, and G. Georgiou, The method of fundamental solutions for Signorini problems, IMA J. Numer. Anal. 18 (1998), pp. 273-286.
    • (1998) IMA J Numer Anal , vol.18 , pp. 273-286
    • Poullikkas, A.1    Karageorghis, A.2    Georgiou, G.3
  • 38
    • 0035275662 scopus 로고    scopus 로고
    • The numerical solution of three dimensional Signorini problems with the method of fundamental solutions
    • A. Poullikkas, A. Karageorghis, and G. Georgiou, The numerical solution of three dimensional Signorini problems with the method of fundamental solutions, Eng. Anal. Boundary Elem. 25 (2001), pp. 221-227.
    • (2001) Eng Anal Boundary Elem , vol.25 , pp. 221-227
    • Poullikkas, A.1    Karageorghis, A.2    Georgiou, G.3
  • 39
    • 0000678579 scopus 로고
    • The approximate solution of elliptic boundary-value problems by fundamental solutions
    • R. Mathon and R.L. Johnston, The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM J. Numer. Anal. 14 (1977), pp. 638-650.
    • (1977) SIAM J Numer Anal , vol.14 , pp. 638-650
    • Mathon, R.1    Johnston, R.L.2
  • 40
    • 36048958473 scopus 로고    scopus 로고
    • Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods
    • P. Gorzelańczyk and J.A. Kolodziej, Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods, Eng. Anal. Boundary Elem. 32 (2008), pp. 64-75.
    • (2008) Eng Anal Boundary Elem , vol.32 , pp. 64-75
    • Gorzelańczyk, P.1    Kolodziej, J.A.2
  • 41
    • 0033996710 scopus 로고    scopus 로고
    • The method of fundamental solutions for linear diffusion-reaction equations
    • K. Balakrishnan and P.A. Ramachandran, The method of fundamental solutions for linear diffusion-reaction equations, Math. Comput. Model. 31 (2000), pp. 221-237.
    • (2000) Math. Comput. Model. , vol.31 , pp. 221-237
    • Balakrishnan, K.1    Ramachandran, P.A.2
  • 42
    • 0041623678 scopus 로고
    • A geometrical inverse problem
    • A.G. Ramm, A geometrical inverse problem, Inverse Probl. 2 (1986), pp. L19-L21.
    • (1986) Inverse Probl , vol.2
    • Ramm, A.G.1
  • 43
    • 34248149996 scopus 로고    scopus 로고
    • On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations
    • J.T. Chen, C.S. Wu, Y.T. Lee, and K.H. Chen, On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations, Comput. Math. Appl. 53 (2007), pp. 851-879.
    • (2007) Comput. Math. Appl. , vol.53 , pp. 851-879
    • Chen, J.T.1    Wu, C.S.2    Lee, Y.T.3    Chen, K.H.4
  • 44
    • 20344402529 scopus 로고    scopus 로고
    • Novel meshless method for solving the potential problems with arbitrary domain
    • D.L. Young, K.H. Chen, and C.W. Lee, Novel meshless method for solving the potential problems with arbitrary domain, J. Comput. Phys. 209 (2005), pp. 290-321.
    • (2005) J. Comput. Phys. , vol.209 , pp. 290-321
    • Young, D.L.1    Chen, K.H.2    Lee, C.W.3
  • 45
    • 33748450782 scopus 로고    scopus 로고
    • Regularized meshless method for multiply-connected-domain Laplace problems
    • K.H. Chen, J.H. Kao, J.T. Chen, D.L. Young, and M.C. Lu, Regularized meshless method for multiply-connected-domain Laplace problems, Eng. Anal. Boundary Elem. 30 (2006), pp. 882-896.
    • (2006) Eng Anal Boundary Elem , vol.30 , pp. 882-896
    • Chen, K.H.1    Kao, J.H.2    Chen, J.T.3    Young, D.L.4    Lu, M.C.5
  • 47
    • 0026472833 scopus 로고
    • Determination of the boundary of an object inserted into a water-filled cylinder
    • Y.Z. Ider, B. Nakiboglu, M. Kuzuoglu, and N.G. Gençer, Determination of the boundary of an object inserted into a water-filled cylinder, Clin. Phys. Physiol. Meas. 13 (1992), pp. 151-154.
    • (1992) Clin. Phys. Physiol. Meas. , vol.13 , pp. 151-154
    • Ider, Y.Z.1    Nakiboglu, B.2    Kuzuoglu, M.3    Gençer, N.G.4
  • 48
    • 70349749801 scopus 로고    scopus 로고
    • NAG(UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK
    • Numerical Algorithms Group Library Mark 21, NAG(UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK, 2007.
    • (2007) Numerical Algorithms Group Library Mark 21
  • 51
    • 0036684726 scopus 로고    scopus 로고
    • Efficient determination of multiple regularization parameters in a generalized L-curve framework
    • M. Belge, M.E. Kilmer, and E.L. Miller, Efficient determination of multiple regularization parameters in a generalized L-curve framework, Inverse Probl. 18 (2002), pp. 1161-1183.
    • (2002) Inverse Probl , vol.18 , pp. 1161-1183
    • Belge, M.1    Kilmer, M.E.2    Miller, E.L.3
  • 52
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 7 (1966), pp. 414-417.
    • (1966) Soviet Math Dokl , vol.7 , pp. 414-417
    • Morozov, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.