Semi-analytic treatment of nearly-singular Galerkin surface integrals

Applied Numerical Mathematics

Volumn 60, Issue 10, 2010, Pages 974-993

  Fata, S Nintcheu ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Boundary element method; Galerkin approximation; Hyper singular integrals; Nearly singular integrals; Potential theory; Singular integrals

Indexed keywords

GALERKIN APPROXIMATIONS; NEARLY-SINGULAR INTEGRALS; POTENTIAL THEORY; SINGULAR INTEGRAL; SINGULAR INTEGRALS;

COMPUTATIONAL EFFICIENCY; DRUG PRODUCTS PLANTS; GALERKIN METHODS; MECHANICS; PIECEWISE LINEAR TECHNIQUES;

BOUNDARY ELEMENT METHOD;

EID: 77955557747     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.06.003     Document Type: Article

References (21)

1. A. Aimi, and M. Diligenti Numerical integration in 3D Galerkin BEM solution of HBIEs Comput. Mech. 28 2002 233 249
2. F.C. Araújo, and L.J. Gray Analysis of thin-walled structural elements via 3D standard BEM with generic substructuring Comput. Mech. 41 5 2008 633 645
3. M.G. Duffy Quadrature over a pyramid or cube of integrands with singularity at a vertex SIAM J. Numer. Anal. 19 6 1982 1260 1262
4. S. Erichsen, and S.A. Sauter Efficient automatic quadrature in 3-d Galerkin BEM Comput. Meth. Appl. Mech. Eng. 157 3-4 1998 215 224
5. C. Ericson Real-Time Collision Detection 2005 Morgan Kaufmann San Francisco, CA
6. L.J. Gray, A. Salvadori, A.-V. Phan, and V. Mantič Direct evaluation of hypersingular Galerkin surface integrals II Electron. J. Boundary Elem. 4 3 2006 105 130
7. W. Hackbusch, and S.A. Sauter On numerical cubatures of nearly singular surface integrals arising in BEM collocation Computing 52 2 1994 139 159
8. K. Hayami, and H. Matsumoto A numerical quadrature for nearly singular boundary element integrals Eng. Anal. Boundary Elem. 13 1994 143 154
9. B.M. Johnston, P.R. Johnston, and D. Elliott A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals Int. J. Numer. Meth. Eng. 69 7 2007 1460 1479 (Pubitemid 46210527)
10. P.R. Johnston, and D. Elliott A sinh transformation for evaluating nearly singular boundary element integrals Int. J. Numer. Meth. Eng. 62 4 2005 564 578
11. D.E. Medina, and J.A. Liggett Exact integrals for three-dimensional boundary element potential problems Commun. in Appl. Num. Methods 5 1989 555 561
12. S. Nintcheu Fata Fast Galerkin BEM for 3D-potential theory Comput. Mech. 42 3 2008 417 429
13. S. Nintcheu Fata Explicit expressions for 3D boundary integrals in potential theory Int. J. Numer. Meth. Eng. 78 1 2009 32 47
14. S. Nintcheu Fata, and L.J. Gray Semi-analytic integration of hypersingular Galerkin BIEs for three-dimensional potential problems J. Comput. Appl. Math. 231 2 2009 561 576
15. S. Nintcheu Fata, and L.J. Gray On the implementation of 3D Galerkin boundary integral equations Eng. Anal. Boundary Elem. 34 1 2010 60 65
16. S.A. Sauter, and C. Schwab Quadrature for hp-Galerkin BEM in R 3 Numer. Math. 78 2 1997 211 258
17. C. Schwab Variable order composite quadrature for singular and nearly singular integrals Computing 53 2 1994 173 194
18. L. Scuderi On the computation of nearly singular integrals in 3D BEM collocation Int. J. Numer. Meth. Eng. 74 11 2008 1733 1770
19. L. Scuderi A new smoothing strategy for computing nearly singular integrals in 3D Galerkin BEM J. Comput. Appl. Math. 225 2 2009 406 427
20. G.L.G. Sleijpen, and D.R. Fokkema BiCGSTAB (l) for linear equations involving unsymmetric matrices with complex spectrum ETNA 1 1993 11 32
21. Y. Wenjing A new transformation technique for evaluating nearly singular integrals Comput. Mech. 42 3 2008 457 466