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Volumn 42, Issue 3, 2008, Pages 457-466

A new transformation technique for evaluating nearly singular integrals

Author keywords

Boundary element method; Nearly singular integrals; Non linear variable transformation; Numerical integration

Indexed keywords

BOUNDARY ELEMENT METHOD; INTEGRAL EQUATIONS; INTEGRATION;

EID: 44449143329     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-008-0262-6     Document Type: Article
Times cited : (31)

References (35)
  • 1
    • 0027149454 scopus 로고
    • A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity
    • Anantharaman N, Mukherjee S (1993) A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity. Comput Mech 12: 19-26
    • (1993) Comput Mech , vol.12 , pp. 19-26
    • Anantharaman, N.1    Mukherjee, S.2
  • 3
    • 0027188099 scopus 로고
    • Non-singular boundary integral equation implementation
    • Cruse TA, Aithal R (1993) Non-singular boundary integral equation implementation. Int J Numer Methods Eng 36: 237-254
    • (1993) Int J Numer Methods Eng , vol.36 , pp. 237-254
    • Cruse, T.A.1    Aithal, R.2
  • 4
    • 0027681565 scopus 로고
    • Efficient evaluation of volume integrals in the boundary element method
    • Dallner R, Gunther K (1993) Efficient evaluation of volume integrals in the boundary element method. Comput Methods Appl Mech Eng 109: 95-109
    • (1993) Comput Methods Appl Mech Eng , vol.109 , pp. 95-109
    • Dallner, R.1    Gunther, K.2
  • 5
    • 0000908836 scopus 로고
    • Quadrature over a pyramid or cube of integrands with a singularity at a vertex
    • 6
    • Duffy MG (1982) Quadrature over a pyramid or cube of integrands with a singularity at a vertex. SIAM J Numer Anal 9(6): 1260-1262
    • (1982) SIAM J Numer Anal , vol.9 , pp. 1260-1262
    • Duffy, M.G.1
  • 6
    • 0002374955 scopus 로고    scopus 로고
    • Sigmoidal transformation and the trapezoidal rule
    • Elliott D (1998) Sigmoidal transformation and the trapezoidal rule. J Aust Math Soc Ser B 40: E77-E137
    • (1998) J Aust Math Soc ser B , vol.40
    • Elliott, D.1
  • 7
    • 33847361409 scopus 로고    scopus 로고
    • Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals
    • Elliott D, Johnston PR (2007) Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals. J Comp Appl Math 203: 103-124
    • (2007) J Comp Appl Math , vol.203 , pp. 103-124
    • Elliott, D.1    Johnston, P.R.2
  • 8
    • 21844511067 scopus 로고
    • An algorithm for the approximate solution of integral equations of Mellin type
    • Elliott D, Prössdorf S (1995) An algorithm for the approximate solution of integral equations of Mellin type. Numerische Mathematik 70: 427-452
    • (1995) Numerische Mathematik , vol.70 , pp. 427-452
    • Elliott, D.1    Prössdorf, S.2
  • 10
    • 0025430991 scopus 로고
    • Hypersingular integrals in boundary element fracture analysis
    • Gray LJ, Martha LF, Ingraffea AR (1990) Hypersingular integrals in boundary element fracture analysis. Int J Numer Methods Eng 29: 1135-1158
    • (1990) Int J Numer Methods Eng , vol.29 , pp. 1135-1158
    • Gray, L.J.1    Martha, L.F.2    Ingraffea, A.R.3
  • 11
    • 0001273497 scopus 로고
    • The evaluation of Cauchy principal value integrals in the boundary element method-a review
    • Guiggiani M (1991) The evaluation of Cauchy principal value integrals in the boundary element method-a review. Math Comput Model 15: 175-184
    • (1991) Math Comput Model , vol.15 , pp. 175-184
    • Guiggiani, M.1
  • 12
    • 0002308925 scopus 로고
    • A robust numerical integration method for three dimensional boundary element analysis
    • Tanaka M, Brebbia CA, Honma T (ed). Computational Mechanics Publication, Southhampton, Springer, Berlin
    • Hayami K (1990) A robust numerical integration method for three dimensional boundary element analysis. In: Tanaka M, Brebbia CA, Honma T (ed) Boundary elements XII., vol 1. Computational Mechanics Publication, Southhampton, Springer, Berlin, pp 33-51
    • (1990) Boundary Elements XII , vol.1 , pp. 33-51
    • Hayami, K.1
  • 13
    • 0008622055 scopus 로고
    • A projection transformation method for nearly singular surface boundary element integrals
    • Springer Berlin
    • Hayami K (1992) A projection transformation method for nearly singular surface boundary element integrals. In: Breddia CA, Orszag SA(eds) Lecture Notes in Engineering, vol 73. Springer, Berlin
    • (1992) Lecture Notes in Engineering, Vol 73
    • Hayami, K.1    Breddia, C.A.2    Orszag, S.A.3
  • 14
    • 33644670348 scopus 로고    scopus 로고
    • Variable transformations for nearly singular integrals in the boundary element method
    • Hayami K (2005) Variable transformations for nearly singular integrals in the boundary element method. Publ RIMS, Kyoto Univ 41: 821-842
    • (2005) Publ RIMS, Kyoto Univ , vol.41 , pp. 821-842
    • Hayami, K.1
  • 15
    • 0039313234 scopus 로고
    • Quadrature methods for singular and nearly singular integrals in 3-D boundary element method
    • Brebbia CA (ed), Southhampton, Springer, Berlin
    • Hayami K, Brebbia CA (1988) Quadrature methods for singular and nearly singular integrals in 3-D boundary element method. In: Brebbia CA (ed) Boundary elements X., vol 1, Southhampton, Springer, Berlin, pp 237-264
    • (1988) Boundary Elements X , vol.1 , pp. 237-264
    • Hayami, K.1    Brebbia, C.A.2
  • 16
    • 0027990126 scopus 로고
    • A numerical quadrature for nearly singular boundary element integrals
    • Hayami K, Matsumoto H (1994) A numerical quadrature for nearly singular boundary element integrals. Eng Anal Bound Elem 13: 143-154
    • (1994) Eng Anal Bound Elem , vol.13 , pp. 143-154
    • Hayami, K.1    Matsumoto, H.2
  • 17
    • 0027641784 scopus 로고
    • Some notes on singular integral techniques in boundary element analysis
    • Huang Q, Cruse TA (1993) Some notes on singular integral techniques in boundary element analysis. Int J Numer Methods Eng 36: 2643-2659
    • (1993) Int J Numer Methods Eng , vol.36 , pp. 2643-2659
    • Huang, Q.1    Cruse, T.A.2
  • 18
    • 0000736808 scopus 로고    scopus 로고
    • Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals
    • Johnston PR (1999) Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals. Int J Numer Methods Eng 45: 1333-1348
    • (1999) Int J Numer Methods Eng , vol.45 , pp. 1333-1348
    • Johnston, P.R.1
  • 19
    • 0033900686 scopus 로고    scopus 로고
    • Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals
    • Johnston PR (2000) Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals. Int J Numer Methods Eng 47: 1709-1730
    • (2000) Int J Numer Methods Eng , vol.47 , pp. 1709-1730
    • Johnston, P.R.1
  • 20
    • 0037469363 scopus 로고    scopus 로고
    • A comparison of transformation methods for evaluating two-dimensional weakly singular integrals
    • Johnston BM, Johnston PR (2003) A comparison of transformation methods for evaluating two-dimensional weakly singular integrals. Int J Numer Methods Eng 56: 589-607
    • (2003) Int J Numer Methods Eng , vol.56 , pp. 589-607
    • Johnston, B.M.1    Johnston, P.R.2
  • 21
    • 33846848073 scopus 로고    scopus 로고
    • A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals
    • Johnston BM, Johnston PR, Elliott D (2007) A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals. Int J Numer Methods Eng 69: 1460-1479
    • (2007) Int J Numer Methods Eng , vol.69 , pp. 1460-1479
    • Johnston, B.M.1    Johnston, P.R.2    Elliott, D.3
  • 22
    • 0035360320 scopus 로고    scopus 로고
    • A generalization of Telles' method for evaluating weakly singular boundary element integrals
    • Johnston PR, Elliott D (2001) A generalization of Telles' method for evaluating weakly singular boundary element integrals. J Comp Appl Math 131: 223-241
    • (2001) J Comp Appl Math , vol.131 , pp. 223-241
    • Johnston, P.R.1    Elliott, D.2
  • 23
    • 0037106232 scopus 로고    scopus 로고
    • Transformations for evaluating singular boundary element integrals
    • Johnston PR, Elliott D (2002) Transformations for evaluating singular boundary element integrals. J Comp Appl Math 146: 231-251
    • (2002) J Comp Appl Math , vol.146 , pp. 231-251
    • Johnston, P.R.1    Elliott, D.2
  • 24
    • 0016871823 scopus 로고
    • Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics
    • Lachat JC, Watson JO (1976) Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics. Int J Numer Methods Eng 10: 991-1005
    • (1976) Int J Numer Methods Eng , vol.10 , pp. 991-1005
    • Lachat, J.C.1    Watson, J.O.2
  • 25
    • 0022160123 scopus 로고
    • A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method
    • Li HB, Han GM, Mang HA (1985) A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method. Int J Numer Methods Eng 21: 2071-2098
    • (1985) Int J Numer Methods Eng , vol.21 , pp. 2071-2098
    • Li, H.B.1    Han, G.M.2    Mang, H.A.3
  • 26
    • 0026869795 scopus 로고
    • Some improvements of accuracy and efficiency in three dimensional direct boundary element method
    • Li Y, Obata T, Koguchi H, Yada T (1992) Some improvements of accuracy and efficiency in three dimensional direct boundary element method. Int J Numer Methods Eng 33: 1451-1464
    • (1992) Int J Numer Methods Eng , vol.33 , pp. 1451-1464
    • Li, Y.1    Obata, T.2    Koguchi, H.3    Yada, T.4
  • 27
    • 0031997408 scopus 로고    scopus 로고
    • Analysis of shell-like structures by the boundary element method based on 3-D elasticity: Formulation and verification
    • Liu Y (1998) Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. Int J Numer Methods Eng 41: 541-558
    • (1998) Int J Numer Methods Eng , vol.41 , pp. 541-558
    • Liu, Y.1
  • 28
    • 33847420572 scopus 로고    scopus 로고
    • Evaluation of supersingular integrals: Second-order boundary derivatives
    • Moore MN, Gray LJ, Kaplan T (2007) Evaluation of supersingular integrals: Second-order boundary derivatives. Int J Numer Methods Eng 69: 1930-1947
    • (2007) Int J Numer Methods Eng , vol.69 , pp. 1930-1947
    • Moore, M.N.1    Gray, L.J.2    Kaplan, T.3
  • 29
    • 0034557410 scopus 로고    scopus 로고
    • Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity
    • Mukherjee S, Chati MK, Shi X (2000) Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity. Int J Solids Struct 37: 7633-7654
    • (2000) Int J Solids Struct , vol.37 , pp. 7633-7654
    • Mukherjee, S.1    Chati, M.K.2    Shi, X.3
  • 30
    • 0000046873 scopus 로고
    • A new variable transformation for numerical integration
    • Birkhäuser Basel
    • Sidi A (1993) A new variable transformation for numerical integration. In: Brass H, Hämmerlin G(eds) Numerical integration IV. Birkhäuser, Basel, pp 359-373
    • (1993) Numerical Integration IV , pp. 359-373
    • Sidi, A.1    Brass, H.2    Hämmerlin, G.3
  • 31
    • 0023349184 scopus 로고
    • A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals
    • Telles JCF (1987) A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Int J Numer Methods Eng 24: 959-973
    • (1987) Int J Numer Methods Eng , vol.24 , pp. 959-973
    • Telles, J.C.F.1
  • 32
    • 0027929668 scopus 로고
    • Third degree polynomial transformation for boundary element integrals: Further improvements
    • Telles JCF, Oliveira RF (1994) Third degree polynomial transformation for boundary element integrals: further improvements. Eng Anal Bound Elem 13: 135-141
    • (1994) Eng Anal Bound Elem , vol.13 , pp. 135-141
    • Telles, J.C.F.1    Oliveira, R.F.2
  • 33
    • 84989432303 scopus 로고
    • On the evaluation of nearly singular kernel integrals in boundary element analysis
    • Wu S (1995) On the evaluation of nearly singular kernel integrals in boundary element analysis. Numer Method Eng 11: 331-337
    • (1995) Numer Method Eng , vol.11 , pp. 331-337
    • Wu, S.1
  • 34
    • 0039351165 scopus 로고    scopus 로고
    • On the evaluation of nearly singular kernel integrals in boundary element analysis-some improved formulations
    • Wu S, Lu P-A (1996) On the evaluation of nearly singular kernel integrals in boundary element analysis-some improved formulations. Comm Numer Method Eng 12: 85-93
    • (1996) Comm Numer Method Eng , vol.12 , pp. 85-93
    • Wu, S.1    Lu, P.-A.2
  • 35
    • 33645309365 scopus 로고    scopus 로고
    • A generalized non-linear transformation for evaluating singular integrals
    • Yun BI (2006) A generalized non-linear transformation for evaluating singular integrals. Int J Numer Methods Eng 65: 1947-1969
    • (2006) Int J Numer Methods Eng , vol.65 , pp. 1947-1969
    • Yun, B.I.1


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