On the computation of nearly singular integrals in 3D BEM collocation

International Journal for Numerical Methods in Engineering

Volumn 74, Issue 11, 2008, Pages 1733-1770

  Scuderi, Letizia ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Boundary element method; Numerical quadrature; Singular integrals

Indexed keywords

NEARLY-SINGULAR INTEGRALS;

INTEGRAL EQUATIONS;

EID: 47249151036     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2229     Document Type: Article

References (15)

1. Hackbusch W. Integral Equations. Theory and Numerical Treatment, vol. 120. ISNM Birkhäuser Verlag: Basel, Boston, Berlin, 1995.
2. Davis PJ, Rabinowitz P. Methods of Numerical Integration (2nd edn). Academic Press: New York, 1984.
3. 3 using Gauss quadrature. Engineering Analysis 1995; 2:119-123.
4. Lachat JC, Watson JO. Effective numerical treatment of boundary integral equations: a formulation for three dimensional elastostatics. International Journal for Numerical Methods in Engineering 1976; 10:273-289.
5. Telles JCF. A self-adaptive co-ordinates transformation for efficient numerical evaluation of general boundary element integrals. International Journal for Numerical Methods in Engineering 1987; 24:959-973.
6. Fink PW, Wilton DR, Khayat MA. Issues and methods concerning the evaluation of hypersingular and near hypersingular integrals in BEM formulations. Proceedings of Joint 9th International Conference on Electromagnetics in Advanced Applications ICEEA '05 and 11th European Electromagnetic Structures Conference, Torino, Italy, 2005; 861-864.
7. Hackbusch W, Sauter SA. On numerical cubatures of nearly singular surface integrals arising in BEM collocation. Computing 1994; 52:139-159.
8. Hayami K. Variable transformations for nearly singular integrals in the boundary element method. Publications of the Research Institute for Mathematical Sciences 2005; 41:821-842.
9. Hayami K, Brebbia CA. A new coordinate transformation method for singular and nearly singular integrals over general curved boundary elements. In Boundary Elements IX, Proceedings of the 9th International Conference on Boundary Elements, Stuttgart, Brebbia CA, Wendland WL, Kuhn G (eds), vol. 1. A Computational Mechanics Publications with Springer-Verlag: Berlin, 1987; 375-399.
10. Hayami K, Brebbia CA. Quadrature methods for singular and nearly singular in 3-D boundary element method. In Boundary Elements X, Proceedings of the 10th International Conference on Boundary Elements, Southampton, Brebbia CA (ed.), vol. 1. Computational Mechanics Publications with Springer-Verlag: Berlin, 1988; 237-264.
11. Khayat MA, Wilton DR. Numerical evaluation of singular and near singular potential integrals. IEEE Transactions on Antennas and Propagation 2005; 53:3180-3190.
12. Monegato G, Scuderi L. Numerical integration of functions with endpoint singularities and/or complex poles in 3D Galerkin boundary element methods. Publications of the Research Institute for Mathematical Sciences 2005; 41:869-895.
13. Monegato G, Scuderi L. Numerical integration of functions with boundary singularities. Journal of Computation and Applied Mathematics 1999; 112:201-214.
14. Johnston BM, Johnston PR, Elliott D. A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals. International Journal for Numerical Methods in Engineering 2007; 69:1460-1479.
15. Johnston PR, Elliott D. A sinh transformation for evaluating nearly singular boundary element integrals. International Journal for Numerical Methods in Engineering 2005; 62:959-973.