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Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals. (English) Zbl 0966.65093

The author introduces and studies a new method for evaluating weakly singular integrals based on semi-sigmoidal transformations, which cluster integration nodes only near the singular point. Comparison of this new method with existing coordinate transformation techniques shows that more accurate evaluation of weakly singular integrals can be obtained.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
35J25 Boundary value problems for second-order elliptic equations
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[1] Gaussian Quadrature Formulas. Prentice-Hall: Englewood Cliffs, NJ, 1966.
[2] Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1994.
[3] Introduction to Finite and Boundary Element Methods for Engineers. Wiley: Chichester, England, 1992. · Zbl 0809.73001
[4] Telles, International Journal for Numerical Methods in Engineering 24 pp 959– (1987) · Zbl 0622.65014 · doi:10.1002/nme.1620240509
[5] Cerrolaza, International Journal for Numerical Methods in Engineering 28 pp 987– (1989) · Zbl 0679.73040 · doi:10.1002/nme.1620280502
[6] Doblar?, International Journal for Numerical Methods in Engineering 40 pp 3325– (1997) · Zbl 1049.74789 · doi:10.1002/(SICI)1097-0207(19970930)40:18<3325::AID-NME215>3.0.CO;2-Q
[7] Johnston, International Journal for Numerical Methods in Engineering 45 pp 1333– (1999) · Zbl 0935.65130 · doi:10.1002/(SICI)1097-0207(19990810)45:10<1333::AID-NME632>3.0.CO;2-Q
[8] Elliott, Journal of Australian Mathematical Society Series B 40 pp e77– (1998)
[9] The spline collocation method for Mellin convolution equations. Technical Report 96/04, Universit?t Stuttgart, 1996.
[10] Elliott, Numerical Mathematics 70 pp 427– (1995) · Zbl 0828.65143 · doi:10.1007/s002110050127
[11] On an integral equation of the first kind arising from a cruciform crack problem. In Integral Equations and Inverse Problems, (eds). Longman: Coventry, 1991; 210-219. · Zbl 0753.65098
[12] A new variable transformation for numerical integration. In Numerical Integration IV, (eds). Birkhauser: Basel, 1993; 359-373. · doi:10.1007/978-3-0348-6338-4_27
[13] Boundary Element Techniques. Springer: Berlin, 1984. · doi:10.1007/978-3-642-48860-3
[14] Boundary Elements An Introductory Course (2nd edn). Computational Mechanics Publications: Southampton, 1992. · Zbl 0780.73002
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