Numerical evaluation of two-dimensional singular boundary integrals - Theory and Fortran code

Journal of Computational and Applied Mathematics

Volumn 188, Issue 1, 2006, Pages 44-64

  Gao, Xiao Wei ^a,b  

^a SOUTHEAST UNIVERSITY   (China)

^b ZONA TECHNOLOGY INC   (United States)

Author keywords

Boundary element; Boundary integral; Fortran subroutine; Gaussian quadrature; Singular integrals

Indexed keywords

BOUNDARY CONDITIONS; CODES (SYMBOLS); FORTRAN (PROGRAMMING LANGUAGE); INTEGRATION; NUMERICAL ANALYSIS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

BOUNDARY ELEMENTS; BOUNDARY INTEGRALS; FORTRAN SUBROUTINE; GAUSSIAN QUADRATURE; SINGULAR INTEGRALS;

INTEGRAL EQUATIONS;

EID: 28044469086     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.03.051     Document Type: Article

References (21)

1. M.H. Aliabadi, and D. Martin Boundary element hyper-singular formulation for elastoplastic contact problems Int. J. Numer. Methods Eng. 48 2000 995 1014
2. P.K. Banerjee The Boundary Element Methods in Engineering 1994 McGraw-Hill London
3. C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel Boundary Element Techniques 1984 Springer Berlin
4. X.W. Gao The radial integration method for evaluation of domain integrals with boundary-only discretization Eng. Anal. Boundary Elements 26 2002 905 916
5. X.W. Gao Boundary element analysis in thermoelasticity with and without internal cells Int. J. Numer. Methods Eng. 57 2003 975 990
6. X.W. Gao Evaluation of regular and singular domain integrals with boundary-only discetization - theory and Fortran code J. Comput. Appl. Math. 175 2005 265 290
7. X.W. Gao, and T.G. Davies An effective boundary element algorithm for 2D and 3D elastoplastic problems Int. J. Solids Struct. 37 2000 4987 5008
8. X.W. Gao, and T.G. Davies Boundary Element Programming in Mechanics 2002 Cambridge University Press Cambridge
9. L.J. Gray, L.F. Martha, and A.R. Ingraffea Hypersingular integrals in boundary element fracture analysis Int. J. Numer. Methods Eng. 29 1990 1135 1158
10. M. Guiggiani, and P. Casalini Direct computation of Cauchy principal value integrals in advanced boundary elements Int. J. Numer. Methods Eng. 24 1987 1711 1720
11. M. Guiggiani, G. Krishnasamy, T.J. Rudolphi, and F.J. Rizzo General algorithm for the numerical solution of hyper-singular boundary integral equations (ASME) J. Appl. Mech. 59 1992 604 614
12. O. Huber, A. Lang, and G. Kuhn Evaluation of the stress tensor in 3D elastostatics by direct solving of hypersingular integrals Comput. Mech. 12 1993 39 50
13. G. Karami, and D. Derakhshan An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis Eng. Anal. Boundary Elements 23 1999 317 326
14. G. Krishnasamy, L.W. Schmerr, T.J. Rudolphi, and F.J. Rizzo Hypersingular boundary integral equations some applications in acoustic and elastic wave scattering ASME J. Appl. Mech. 57 1990 404 414
15. H. Ma, and N. Kamiya A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity Comput. Mech. 29 2002 277 288
16. H. Ma, and N. Kamiya Nearly singular approximations of CPV integrals with end- and corner-singularities for the numerical solution of hypersingular boundary integral equations Eng. Anal. Boundary Elements 27 2003 625 637
17. S. Mukherjee CPV and HFP integrals and their applications in the boundary element methods Int. J. Solids Struct. 37 2000 6623 6634
18. J.D. Richardson, and T.A. Cruse Weakly singular stress-BEM for 2D elastostatics Int. J. Numer. Methods Eng. 45 1999 13 35
19. V. Sladek, and J. Sladek Regularization of hypersingular integrals in BEM formulations using various kinds of continuous elements Eng. Anal. Boundary Elements 17 1996 5 18
20. V. Sladek, and J. Sladek Singular Integrals in Boundary Element Methods 1998 WIT Press Southampton
21. M. Tanaka, V. Sladek, and J. Sladek Regularization techniques applied to boundary element methods Appl. Mech. Rev. 47 1994 457 499