메뉴 건너뛰기




Volumn 42, Issue 2, 2009, Pages 151-175

Generalized extrapolation for computation of hypersingular integrals in boundary element methods

Author keywords

Asymptotic error expansion; Extrapolation algorithm; Hypersingular integrals; Trapezoidal rule

Indexed keywords

ASYMPTOTIC ERROR EXPANSION; ASYMPTOTIC EXPANSION; CONVERGENCE RATES; ERROR FUNCTION; FINITE PART INTEGRALS; HADAMARD; HYPERSINGULAR INTEGRAL; HYPERSINGULAR INTEGRALS; NUMERICAL RESULTS; SINGULAR POINTS; THEORETIC ANALYSIS; TRAPEZOIDAL RULE; TRAPEZOIDAL RULES;

EID: 67649787320     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (34)

References (33)
  • 1
    • 49749086511 scopus 로고    scopus 로고
    • A boundary element formulation for boundary only analysis of thin shallow shells
    • Albuquerque, E. L.; Aliabadi, M. H. (2008):A boundary element formulation for boundary only analysis of thin shallow shells. CMES:Computer Modeling in Engineering & Sciences, vol. 29, no. 2, pp. 63-73.
    • (2008) CMES:Computer Modeling in Engineering & Sciences , vol.29 , Issue.2 , pp. 63-73
    • Albuquerque, E.L.1    Aliabadi, M.H.2
  • 4
    • 4544244895 scopus 로고    scopus 로고
    • Improvement of the asymptotic behaviour of the Euler-Maclaurin formula for Cauchy principal value and Hadamard finite-part integrals
    • Choi, U.J.; Kim, S.W.; Yun, B.I.(2004): Improvement of the asymptotic behaviour of the Euler-Maclaurin formula for Cauchy principal value and Hadamard finite-part integrals Int. J. Numer. Methods., vol.61, pp. 496-513.
    • (2004) Int. J. Numer. Methods , vol.61 , pp. 496-513
    • Choi, U.J.1    Kim, S.W.2    Yun, B.I.3
  • 5
    • 0035839287 scopus 로고    scopus 로고
    • Evaluations of certain hypersingular integrals on interval
    • Du, Q.K. (2001): Evaluations of certain hypersingular integrals on interval. Int. J. Numer. Methods., vol. 512, pp. 1195-1210.
    • (2001) Int. J. Numer. Methods , vol.512 , pp. 1195-1210
    • Du, Q.K.1
  • 6
    • 0031498864 scopus 로고    scopus 로고
    • Sigmoidal transformations and the Euler- Maclaurin expansion for evaluating certain Hadamard finite-part integrals
    • Elliott, D.; Venturino, E. (1997): Sigmoidal transformations and the Euler- Maclaurin expansion for evaluating certain Hadamard finite-part integrals. Numer. Math., vol. 77, pp. 453-465.
    • (1997) Numer. Math , vol.77 , pp. 453-465
    • Elliott, D.1    Venturino, E.2
  • 8
    • 1642521646 scopus 로고    scopus 로고
    • Uniform approximations to finite Hilbert transform and its derivative
    • Hasegawa, T. (2004): Uniform approximations to finite Hilbert transform and its derivative. J. Comput. Appl. Math., vol. 163, pp. 127-138.
    • (2004) J. Comput. Appl. Math , vol.163 , pp. 127-138
    • Hasegawa, T.1
  • 9
    • 0032803628 scopus 로고    scopus 로고
    • Evaluations of hypersingular integrals using Gaussian quadrature
    • Hui, C.Y.; Shia, D.(1999): Evaluations of hypersingular integrals using Gaussian quadrature. Int. J. Numer. Methods., vol. 44, pp. 205-214.
    • (1999) Int. J. Numer. Methods , vol.44 , pp. 205-214
    • Hui, C.Y.1    Shia, D.2
  • 10
    • 84966222583 scopus 로고
    • On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives
    • Ioakimidis, N.I.(1985): On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives. Math. Comp., vol 44, pp. 191-198.
    • (1985) Math. Comp , vol.44 , pp. 191-198
    • Ioakimidis, N.I.1
  • 11
    • 0037457820 scopus 로고    scopus 로고
    • Two trigonometric quadrature formulae for evaluating hypersingular integrals
    • Kim, P.; Jin, U.C. (2003): Two trigonometric quadrature formulae for evaluating hypersingular integrals. Inter. J. Numer. Methods., vol. 56, pp. 469-486.
    • (2003) Inter. J. Numer. Methods , vol.56 , pp. 469-486
    • Kim, P.1    Jin, U.C.2
  • 12
    • 84869281549 scopus 로고    scopus 로고
    • Liem, C.B.; &lü, T.; Shih, T.M. (1995): The Splitting Extrapolation Method. World Scientific, Singapore.
    • Liem, C.B.; &lü, T.; Shih, T.M. (1995): The Splitting Extrapolation Method. World Scientific, Singapore.
  • 13
    • 0022197247 scopus 로고
    • On the approximate computation of certain strongly singular integrals
    • Linz, P. (1985): On the approximate computation of certain strongly singular integrals. Computing., vol. 352, pp. 345-353.
    • (1985) Computing , vol.352 , pp. 345-353
    • Linz, P.1
  • 14
    • 62449249877 scopus 로고    scopus 로고
    • The coupling method of natural boundary element and mixed finite element for stationary Navier-Stokes equation in unbounded domains
    • Liu, D.J; Yu, D. H.(2008): The coupling method of natural boundary element and mixed finite element for stationary Navier-Stokes equation in unbounded domains. CMES:Computer Modeling in Engineering & Sciences, vol. 37, no. 3, pp. 305-330.
    • (2008) CMES:Computer Modeling in Engineering & Sciences , vol.37 , Issue.3 , pp. 305-330
    • Liu, D.J.1    Yu, D.H.2
  • 15
    • 34547764810 scopus 로고    scopus 로고
    • A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain
    • Liu, C.S.(2007): A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain. CMES:Computer Modeling in Engineering & Sciences, vol. 20, No. 2, pp. 111-122.
    • (2007) CMES:Computer Modeling in Engineering & Sciences , vol.20 , Issue.2 , pp. 111-122
    • Liu, C.S.1
  • 16
    • 33748904596 scopus 로고    scopus 로고
    • &lü, T.; Huang, Y. (2006): Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind. J. Math. Anal. Appl, 324, pp. 223-237.
    • &lü, T.; Huang, Y. (2006): Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind. J. Math. Anal. Appl, vol. 324, pp. 223-237.
  • 17
    • 0038687918 scopus 로고    scopus 로고
    • &lü, T.; Huang, Y. (2003): A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind. J. Math. Anal. Appl, 282, pp. 56-62.
    • &lü, T.; Huang, Y. (2003): A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind. J. Math. Anal. Appl, vol.282, pp. 56-62.
  • 18
    • 0028422932 scopus 로고
    • Numerical evaluation of hypersingular integrals
    • Monegato, G.(1994): Numerical evaluation of hypersingular integrals. J. Comput. Appl. Math., vol.50, pp. 9-31.
    • (1994) J. Comput. Appl. Math , vol.50 , pp. 9-31
    • Monegato, G.1
  • 19
    • 55349129209 scopus 로고    scopus 로고
    • A cell-less BEM formulation for 2D and 3D elastoplastic problems using particular integrals
    • Owatsiriwong, A.; Phansri, B.; Park, K.H.(2008): A cell-less BEM formulation for 2D and 3D elastoplastic problems using particular integrals. CMES:Computer Modeling in Engineering & Sciences, vol.31, no.l, pp. 37-59.
    • (2008) CMES:Computer Modeling in Engineering & Sciences , vol.31 , Issue.L , pp. 37-59
    • Owatsiriwong, A.1    Phansri, B.2    Park, K.H.3
  • 20
    • 34247160330 scopus 로고    scopus 로고
    • Hypersingular BEM for piezoelectric solids: Formulation and applications for fracture mechanics
    • Sanz, J.A.;Solis, M.; Dominguez, J.(2007): Hypersingular BEM for piezoelectric solids: formulation and applications for fracture mechanics. CMES:Computer Modeling in Engineering & Sciences, vol.17, no.3, pp. 215-229.
    • (2007) CMES:Computer Modeling in Engineering & Sciences , vol.17 , Issue.3 , pp. 215-229
    • Sanz, J.A.1    Solis, M.2    Dominguez, J.3
  • 22
    • 43049179400 scopus 로고    scopus 로고
    • The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
    • Wu, J.M.; Sun, W.W. (2008): The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval. Numer. Math., vol. 109, pp. 143-165.
    • (2008) Numer. Math , vol.109 , pp. 143-165
    • Wu, J.M.1    Sun, W.W.2
  • 23
    • 24644432501 scopus 로고    scopus 로고
    • Newton-Cotes formulae for the numerical evaluation of certain hypersingular integral
    • Wu, J.M.; Sun, W.W. (2005): Newton-Cotes formulae for the numerical evaluation of certain hypersingular integral. Computing., vol.75, pp. 297-309.
    • (2005) Computing , vol.75 , pp. 297-309
    • Wu, J.M.1    Sun, W.W.2
  • 24
    • 29144477751 scopus 로고    scopus 로고
    • The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals
    • Wu, J.M.; Sun, W.W. (2005): The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals., Numer. Math., vol. 102, pp. 343-363.
    • (2005) Numer. Math , vol.102 , pp. 343-363
    • Wu, J.M.1    Sun, W.W.2
  • 25
    • 25844514748 scopus 로고    scopus 로고
    • A superconvergence result for the second order Newton-Cotes formula for certain finite part integrals
    • Wu, J.M.; Lü,Y. (2005): A superconvergence result for the second order Newton-Cotes formula for certain finite part integrals. IMA Journal of Numerical Analy- sis.,vol.25 pp. 253-263.
    • (2005) IMA Journal of Numerical Analy- sis , vol.25 , pp. 253-263
    • Wu, J.M.1    Lü, Y.2
  • 26
    • 24644460480 scopus 로고    scopus 로고
    • The approximate computation of hypersingular integrals on interval
    • Wu, J.M.; Yu,D.H.(1999): The approximate computation of hypersingular integrals on interval., Chinese J. Numer. Math. Appl, vol.21 pp. 25-33.
    • (1999) Chinese J. Numer. Math. Appl , vol.21 , pp. 25-33
    • Wu, J.M.1    Yu, D.H.2
  • 27
    • 58149526315 scopus 로고    scopus 로고
    • The artificial boundary method for a nonlinear interface problem on unbounded domain
    • Yu, D. H.; Huang,H.Y.(2008): The artificial boundary method for a nonlinear interface problem on unbounded domain. CMES:Computer Modeling in Engineering & Sciences, vol.35, no.3, pp. 227-252.
    • (2008) CMES:Computer Modeling in Engineering & Sciences , vol.35 , Issue.3 , pp. 227-252
    • Yu, D.H.1    Huang, H.Y.2
  • 30
    • 0004581086 scopus 로고
    • The approximate computation of hypersingular integrals on interval
    • Yu,D.H.(1992): The approximate computation of hypersingular integrals on interval., Numer. Math. J. Chinese Univ.,vol.l, pp. 114-127.
    • (1992) Numer. Math. J. Chinese Univ , vol.50 , pp. 114-127
    • Yu, D.H.1
  • 31
    • 0000637292 scopus 로고
    • Approximation of boundary conditions at infinity for a harmonic equation
    • Yu,D.H.(1985): Approximation of boundary conditions at infinity for a harmonic equation., J. Comp. Math.,vol. 3, no. 3, pp. 219-227.
    • (1985) J. Comp. Math , vol.3 , Issue.3 , pp. 219-227
    • Yu, D.H.1
  • 32
    • 34250213281 scopus 로고    scopus 로고
    • Young, D.L.;Chen, K.H.; ChenJ.T.;Kao, J.H. (2007): A modified method of fundamental solutions with source on the boundary for solving laplace equations with circular and arbitrary domains. CMES:Computer Modeling in Engineering & Sciences, 19, no.3, pp.197-221.
    • Young, D.L.;Chen, K.H.; ChenJ.T.;Kao, J.H. (2007): A modified method of fundamental solutions with source on the boundary for solving laplace equations with circular and arbitrary domains. CMES:Computer Modeling in Engineering & Sciences, vol.19, no.3, pp.197-221.
  • 33
    • 58149518438 scopus 로고    scopus 로고
    • Integral method for contact problem of bonded plane material with arbitrary cracks
    • Zhou, Y.T.; Li,X.; Yu, D. H.(2008): Integral method for contact problem of bonded plane material with arbitrary cracks., CMES:Computer Modeling in Engineering & Sciences, vol. 36, no.2, pp. 147-172.
    • (2008) CMES:Computer Modeling in Engineering & Sciences , vol.36 , Issue.2 , pp. 147-172
    • Zhou, Y.T.1    Li, X.2    Yu, D.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.