메뉴 건너뛰기




Volumn 36, Issue 2, 2012, Pages 545-560

Calculation of 2D singular and near singular integrals of boundary elements method based on the complex space C

Author keywords

2D potential problems; Boundary elements method (BEM); Dual reciprocity method (DRM); Multiple reciprocity method (MRM); Singular and near singular integrals; The complex space C

Indexed keywords

BOUNDARY ELEMENTS METHOD; COMPLEX SPACE; DUAL RECIPROCITY METHODS; MULTIPLE RECIPROCITY METHOD; NEAR SINGULAR INTEGRALS; POTENTIAL PROBLEMS;

EID: 80052340530     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2011.07.036     Document Type: Article
Times cited : (33)

References (37)
  • 5
    • 78650792867 scopus 로고    scopus 로고
    • Development of circular arc boundary elements method
    • Dehghan M., Hosseinzadeh H. Development of circular arc boundary elements method. Eng. Anal. Bound. Elem. 2011, 35:543-549.
    • (2011) Eng. Anal. Bound. Elem. , vol.35 , pp. 543-549
    • Dehghan, M.1    Hosseinzadeh, H.2
  • 11
    • 59649101812 scopus 로고    scopus 로고
    • A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation
    • Dehghan M., Mirzaei D. A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation. Eng. Anal. Bound. Elem. 2009, 33:522-528.
    • (2009) Eng. Anal. Bound. Elem. , vol.33 , pp. 522-528
    • Dehghan, M.1    Mirzaei, D.2
  • 12
    • 70349970652 scopus 로고    scopus 로고
    • Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method
    • Dehghan M., Ghesmati A. Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method. Eng. Anal. Bound. Elem. 2010, 34:51-59.
    • (2010) Eng. Anal. Bound. Elem. , vol.34 , pp. 51-59
    • Dehghan, M.1    Ghesmati, A.2
  • 13
    • 56249086875 scopus 로고    scopus 로고
    • The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation
    • Dehghan M., Mirzaei D. The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation. Numerical Methods for Partial Differential Eq 2008, 24:1405-1415.
    • (2008) Numerical Methods for Partial Differential Eq , vol.24 , pp. 1405-1415
    • Dehghan, M.1    Mirzaei, D.2
  • 14
    • 77953132937 scopus 로고    scopus 로고
    • Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation
    • Dehghan M., Ghesmati A. Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation. Comput. Phys. Commun. 2010, 181:1410-1418.
    • (2010) Comput. Phys. Commun. , vol.181 , pp. 1410-1418
    • Dehghan, M.1    Ghesmati, A.2
  • 15
    • 42949091441 scopus 로고    scopus 로고
    • Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems
    • Zhou H., Niu Z., Cheng C., Guan Z. Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems. Comput. Struct. 2008, 86:1656-1671.
    • (2008) Comput. Struct. , vol.86 , pp. 1656-1671
    • Zhou, H.1    Niu, Z.2    Cheng, C.3    Guan, Z.4
  • 16
    • 34547452670 scopus 로고    scopus 로고
    • Analytical integral algorithm in the BEM for orthotropic potential problems of thin bodies
    • Zhou H., Niu Z., Cheng C., Guan Z. Analytical integral algorithm in the BEM for orthotropic potential problems of thin bodies. Eng. Anal. Bound. Elem. 2007, 31:739-748.
    • (2007) Eng. Anal. Bound. Elem. , vol.31 , pp. 739-748
    • Zhou, H.1    Niu, Z.2    Cheng, C.3    Guan, Z.4
  • 17
    • 44949125585 scopus 로고    scopus 로고
    • An adaptive element subdivision technique for evaluation of various 2D singular boundary integrals
    • Gao X., Yang K., Wang J. An adaptive element subdivision technique for evaluation of various 2D singular boundary integrals. Eng. Anal. Bound. Elem. 2008, 32:692-696.
    • (2008) Eng. Anal. Bound. Elem. , vol.32 , pp. 692-696
    • Gao, X.1    Yang, K.2    Wang, J.3
  • 18
    • 0016871823 scopus 로고
    • Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics
    • Lachat J., Watson J. Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics. Int. J. Numer. Methods Eng. 1976, 10:991-1005.
    • (1976) Int. J. Numer. Methods Eng. , vol.10 , pp. 991-1005
    • Lachat, J.1    Watson, J.2
  • 19
    • 0039336967 scopus 로고    scopus 로고
    • Optimal transformations of the integration variables in computation of singular integrals in BEM
    • Sladek V., Sladek J., Tanaka M. Optimal transformations of the integration variables in computation of singular integrals in BEM. Int. J. Numer. Methods Eng. 2000, 47:1263-1283.
    • (2000) Int. J. Numer. Methods Eng. , vol.47 , pp. 1263-1283
    • Sladek, V.1    Sladek, J.2    Tanaka, M.3
  • 20
    • 3142749250 scopus 로고    scopus 로고
    • Exact integration for stress evaluation in the boundary element analysis of two-dimensional elastostatics
    • Zhang X., Zhang X. Exact integration for stress evaluation in the boundary element analysis of two-dimensional elastostatics. Eng. Anal. Bound. Elem. 2004, 28:997-1004.
    • (2004) Eng. Anal. Bound. Elem. , vol.28 , pp. 997-1004
    • Zhang, X.1    Zhang, X.2
  • 21
    • 0242489290 scopus 로고    scopus 로고
    • Exact integration in the boundary element method for two-dimensional elastostatic problems
    • Zhang X., Zhang X. Exact integration in the boundary element method for two-dimensional elastostatic problems. Eng. Anal. Bound. Elem. 2003, 27:987-997.
    • (2003) Eng. Anal. Bound. Elem. , vol.27 , pp. 987-997
    • Zhang, X.1    Zhang, X.2
  • 22
    • 3142756439 scopus 로고    scopus 로고
    • Exact integrations of two-dimensional high-order discontinuous boundary elements of elastostatic problems
    • Zhang X., Zhang X. Exact integrations of two-dimensional high-order discontinuous boundary elements of elastostatic problems. Eng. Anal. Bound. Elem. 2004, 28:725-732.
    • (2004) Eng. Anal. Bound. Elem. , vol.28 , pp. 725-732
    • Zhang, X.1    Zhang, X.2
  • 23
    • 38749118959 scopus 로고    scopus 로고
    • Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution
    • Zhena Y., Vainchtein A. Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution. J. Mech. Phys. Solids 2008, 56:496-520.
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 496-520
    • Zhena, Y.1    Vainchtein, A.2
  • 24
    • 1542272602 scopus 로고    scopus 로고
    • Regularization of nearly singular integrals in the BEM of potential problems
    • Zhou H., Niu Z., Wang X. Regularization of nearly singular integrals in the BEM of potential problems. Appl. Math. Mech. 2003, 10:1208-1214.
    • (2003) Appl. Math. Mech. , vol.10 , pp. 1208-1214
    • Zhou, H.1    Niu, Z.2    Wang, X.3
  • 25
    • 12444306328 scopus 로고    scopus 로고
    • A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods
    • Niu Z., Wendland W., Wang X., Zhou H. A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods. Comput. Methods Appl. Mech. Eng. 2005, 194:1057-1074.
    • (2005) Comput. Methods Appl. Mech. Eng. , vol.194 , pp. 1057-1074
    • Niu, Z.1    Wendland, W.2    Wang, X.3    Zhou, H.4
  • 26
    • 29244492336 scopus 로고    scopus 로고
    • Regularization of nearly singular integrals in the boundary element method for 3-D potential problems
    • (in Chinese)
    • Zhou H., Niu Z., Wang X. Regularization of nearly singular integrals in the boundary element method for 3-D potential problems. Chin. J. Comput. Phys. 2005, 6:501-506. (in Chinese).
    • (2005) Chin. J. Comput. Phys. , vol.6 , pp. 501-506
    • Zhou, H.1    Niu, Z.2    Wang, X.3
  • 27
    • 34547451111 scopus 로고    scopus 로고
    • A novel boundary integral equation method for linear elasticitynatural boundary integral equation
    • Niu Z., Wang X., Zhou H., Zhang C. A novel boundary integral equation method for linear elasticitynatural boundary integral equation. Acta. Mech. Sol. Sin. 2001, 2:111-119.
    • (2001) Acta. Mech. Sol. Sin. , vol.2 , pp. 111-119
    • Niu, Z.1    Wang, X.2    Zhou, H.3    Zhang, C.4
  • 28
    • 0346094019 scopus 로고    scopus 로고
    • The natural boundary integral equation in potential problems and regularization of the hypersingular integral
    • Niu Z., Zhou H. The natural boundary integral equation in potential problems and regularization of the hypersingular integral. Comput. Struct. 2004, 82:315-323.
    • (2004) Comput. Struct. , vol.82 , pp. 315-323
    • Niu, Z.1    Zhou, H.2
  • 29
    • 26844444286 scopus 로고    scopus 로고
    • Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems
    • Tang W., Fenner R. Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems. Appl. Math. Model. 2005, 29:1073-1099.
    • (2005) Appl. Math. Model. , vol.29 , pp. 1073-1099
    • Tang, W.1    Fenner, R.2
  • 30
    • 74449084050 scopus 로고    scopus 로고
    • Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method
    • Tomioka S., Nishiyama S. Analytical regularization of hypersingular integral for Helmholtz equation in boundary element method. Eng. Anal. Bound. Elem. 2010, 34:393-404.
    • (2010) Eng. Anal. Bound. Elem. , vol.34 , pp. 393-404
    • Tomioka, S.1    Nishiyama, S.2
  • 31
    • 77953700178 scopus 로고    scopus 로고
    • Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives
    • Xu Y., Dong F., Tan C. Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives. Eng. Anal. Bound. Elem. 2010, 34:876-883.
    • (2010) Eng. Anal. Bound. Elem. , vol.34 , pp. 876-883
    • Xu, Y.1    Dong, F.2    Tan, C.3
  • 32
    • 44449143329 scopus 로고    scopus 로고
    • A new transformation technique for evaluating nearly singular integrals
    • Wenjing Y. A new transformation technique for evaluating nearly singular integrals. Comput. Mech. 2008, 42:457-466.
    • (2008) Comput. Mech. , vol.42 , pp. 457-466
    • Wenjing, Y.1
  • 33
    • 0033736992 scopus 로고    scopus 로고
    • Exact boundary element integrations for two-dimensional Laplace equation
    • Fratantonio M., Rencis J. Exact boundary element integrations for two-dimensional Laplace equation. Eng. Anal. Bound. Elem. 2000, 24:325-342.
    • (2000) Eng. Anal. Bound. Elem. , vol.24 , pp. 325-342
    • Fratantonio, M.1    Rencis, J.2
  • 34
    • 77955427817 scopus 로고    scopus 로고
    • Solution of Poissons equation by analytical boundary element integration
    • Ghadimi P., Dashtimanesh A., Hosseinzadeh H. Solution of Poissons equation by analytical boundary element integration. Appl. Math. Comput. 2010, 217:152-163.
    • (2010) Appl. Math. Comput. , vol.217 , pp. 152-163
    • Ghadimi, P.1    Dashtimanesh, A.2    Hosseinzadeh, H.3
  • 35
    • 0034475272 scopus 로고    scopus 로고
    • A complex variable boundary element method for elliptic partial differential equations in a multiplyconnected region
    • Ang W.T., Kang I. A complex variable boundary element method for elliptic partial differential equations in a multiplyconnected region. Int. J. Comput. Math. 2000, 75:515-525.
    • (2000) Int. J. Comput. Math. , vol.75 , pp. 515-525
    • Ang, W.T.1    Kang, I.2
  • 36
    • 80053576223 scopus 로고    scopus 로고
    • A complex variable boundary element method for an exterior boundary value problem governed by an elliptic partial differential equation
    • Ang W.T., Park Y.S. A complex variable boundary element method for an exterior boundary value problem governed by an elliptic partial differential equation. Southeast Asian Bull. Math. 1999, 23:541-549.
    • (1999) Southeast Asian Bull. Math. , vol.23 , pp. 541-549
    • Ang, W.T.1    Park, Y.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.