Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements

Engineering Analysis with Boundary Elements

Volumn 38, Issue , 2014, Pages 83-93

  Rong, Junjie ^a   Wen, Lihua ^a   Xiao, Jinyou ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Acoustics; Boundary element method; Nystr m method; Singular integrals

Indexed keywords

ACOUSTICS; ASPECT RATIO; BOUNDARY INTEGRAL EQUATIONS; CONFORMAL MAPPING; NUMERICAL METHODS; SAILING VESSELS;

CONFORMAL TRANSFORMATION; EFFICIENCY IMPROVEMENT; M METHOD; NUMERICAL INTEGRATIONS; POLAR COORDINATE TRANSFORMATION; SIGMOIDAL TRANSFORMATION; SINGULAR INTEGRAL; TRANSFORMED DOMAIN;

BOUNDARY ELEMENT METHOD;

EID: 84888189158     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2013.10.014     Document Type: Article

References (25)

1. L.F. Canino, J.J. Ottusch, M.A. Stalzer, J.L. Visher, and S.M. Wandzurz Numerical solution of the Helmhotz equation in 2D and 3D using a high-order Nyström discretization J Comput Phys 146 1998 627 633
2. S. Rjasanow, and L. Weggler ACA accelerated high order BEM for Maxwell problems Comput Mech 51 2013 431 441
3. J. Bremer, and Z. Gimbutas A Nyström method for weakly singular integral operators on surfaces J Comput Phys 231 2012 4885 4903
4. X.W. Gao, and T.G. Davies Boundary element programming in mechanics 2002 Cambridge University Press (ISBN: 052177359-8)
5. Willis DJ, Peraire J, White JK. A quadratic basis function, quadratic geometry, high order panel method. In: 44th AIAA aerospace sciences meeting, number AIAA-2006-1253; 2006.
6. H.J. Wu, Y.J. Liu, and W.K. Jiang A low frequency fast multiploe boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems Eng Anal Boundary Elem 37 2013 309 318
7. S.N. Fata Explicit expressions for 3D boundary integrals in potential theory Int J Numer Methods Eng 78 2009 32 47
8. M. Guiggiani, G. Krishnasamy, T.J. Rudolphi, and F.J. Rizzo A general algorithm for the numerical solution of hypersingular boundary integral equations ASME J Appl Mech 59 1992 604 614 (Pubitemid 23590253)
9. S. Järvenpää, M. Taskinen, and P. Ylä-Oijala Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra Int J Numer Methods Eng 58 2003 1149 1165 (Pubitemid 37317279)
10. P. Kolm, and V. Rokhlin Numerical quadratures for singular and hypersingular integrals Comput Math Appl 41 2001 327 352 (Pubitemid 32168348)
11. R.D. Graglia, and G. Lombardi Machine precision evaluation of singular and nearly singular potential integrals by use of Gauss quadrature formulas for rational functions IEEE Trans Antennas Propag 56 2008 981 998 (Pubitemid 351586152)
12. M. Carley Numeriacl quadratures for singular and hypersingular integrals in boundary element methods SIAM J Sci Comput 29 2007 1207 1216 (Pubitemid 351774666)
13. M.A. Khayat, D.R. Wilton, and P.W. Fink An improved transformation and optimized sampling scheme for the numberical evaluation of singular and near-singular potentials IEEE Trans Antennas Propag 7 2008 377 380
14. M.A. Khayat, and D.R. Wilton Numerical evaluation of singular and near-singular potential integrals IEEE Trans Antennas Propag 53 2005 3180 3190 (Pubitemid 41555317)
15. M.G. Duffy Quadrature over a pyramid or cube of integrands with a singularity at a vertex SIAM J Numer Anal 19 6 1982 1260 1262
16. B.M. Johnston, and P.R. Johnston A comparsion of transformation methods for evaluating two-dimensional weakly singular integrals Int J Numer Methods Eng 56 2003 589 607 (Pubitemid 36225453)
17. Q. Huang, and T.A. Cruse Some notes on singular integral techniques in boundary element analysis Int J Numer Methods Eng 36 1993 2643 2659 (Pubitemid 23694789)
18. J.T. Chen, and H.K. Hong Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series ASME Appl Mech Rev 52 1999 17 33
19. X.W. Gao An effective method for numerical evaluation of gneral 2D and 3D high order singular boundary integrals Comput Methods Appl Mech Eng 199 2010 2856 2864
20. L. Scuderi On the compuation of nearly singular integrals in 3D BEM collocation Int J Numer Methods Eng 74 2008 1733 1770
21. K. Hayami Variable transformation for nearly singular integrals in the boundary element method Res Inst Math Sci 41 2005 821 842 Kyoto University (Pubitemid 43331862)
22. B.M. Johnston, P.R. Johnston, and D. Elliott A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method J Comput Appl Math 245 2013 148 161
23. A.J. Burton, and G.F. Miller The application of integral equation methods to the numerical solution of some exterior boundary-value problems Proc R Soc London Ser A 323 1971 201 210
24. P.R. Johnston Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals Int J Numer Methods Eng 45 1999 1333 1348 (Pubitemid 129540465)
25. C. Schwab, and W.L. Wendland Kernel properties and representations of boundary integral operators Math Nachr 156 1992 187 218