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Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals. (English) Zbl 0935.65130
This paper presents a clear contribution to the ever important subject of efficiently computing numerical integrals over boundary elements. Here, a coordinate transformation technique, based on sigmoidal transformations, is implemented to compute weakly singular and nonsingular integrals. The complete approach is presented in a practical and well-written manner and the promissing technique is compared with existing alternative procedures.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
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[1] Gaussian Quadrature Formulas. Prentice-Hall: Englewood Cliffs, NJ, 1966.
[2] Boundary Element Techniques. Springer: Berlin, 1984. · doi:10.1007/978-3-642-48860-3
[3] Boundary Elements An Introductory Course (2nd edn). Computational Mechanics Publications: Southampton, 1992. · Zbl 0780.73002
[4] Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1994.
[5] Telles, International Journal for Numerical Methods in Engineering 24 pp 959– (1987)
[6] Sigmoidal transformations and the trapezoidal rule. Technical Report 270, University of Tasmania, Department of Mathematics, December 1996.
[7] The spline collocation method for Mellin convolution equations. Technical Report 96/04, Universität Stuttgart, 1996.
[8] Elliott, Numerical Mathematics 70 pp 427– (1995)
[9] 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
[10] 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
[11] Mathematical Handbook of Formulas and Tables, Schaum’s Outline Series. McGraw-Hill: New York, 1990.
[12] Handbook of Mathematical Functions. Dover: New York, 1965.
[13] Cerrolaza, International Journal for Numerical Methods in Engineering 28 pp 987– (1989)
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