Calculation of strongly singular and hypersingular surface integrals

Journal of Geodesy

Volumn 72, Issue 9, 1998, Pages 530-546

  Klees, R ^a   Lehmann, R ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Technical University of Freiberg   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; MATHEMATICAL METHOD;

EID: 0032426112     PISSN: 09497714     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001900050192     Document Type: Article

References (33)

1. Andrä H (1996) A Galerkin-type boundary element implementation for 3D elasticity problems by using a computer algebra system. In: Hackbusch W, Wittum G (eds) Boundary elements: implementation and analysis of advanced algorithms, vol 54 of Notes on numerical fluid mechanics. Vieweg, Wiesbaden, pp 45-56
2. Bian S, Sun H (1994) The expression of common singular integrals in physical geodesy. Manuscr Geod 19: 62-69
3. Bosch W (1977) Geschlossene Integration von Potentialkernen beim Modell der einfachen Schicht mit stückweise ebenem Rand. Mitteilungen aus dem Institut für theoretische Geodäsie 49, Universität Bonn
4. Guiggiani M (1991) The evaluation of Cauchy principal value integrals in the boundary element method - a review. Math Comput Modelling 15: 175-184
5. Guiggiani M, Krishnasamy G, Rudolphi T, Rizzo F (1992) A general algorithm for the numerical solution of hypersingular boundary integral equations. Trans ASME 59: 604-614
6. Hadamard J (1923) Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven
7. Hayami K, Brebbia C (1987) A new coordinate transformation method for singular and nearly singular integrals over general curved boundary elements. In: Brebbia C, Wendland W, Kuhn G (eds) Boundary elements IX, vol 1, 9th Int Conf, Stuttgard, pp 376-399
8. Kieser R (1991) Über einseitige Sprungrelationen und hypersinguläre Operatoren in der Methode der Randelemente. PhD Thesis, Univ Stuttgart, Stuttgart
9. Kieser R, Schwab C, Wendland W (1992) Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation. Computing 49: 279-301
10. Klees R (1992) Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode. PhD Thesis, Deutasche Geodätische Kommission, Reihe C, No 382, München
11. Klees R (1995) Boundary value problems and approximation of integral equations by finite elements. Manuscr Geod 20: 345-361
12. Klees R (1996) Numerical calculation of weakly singular surface integrals. J Geod 70: 781-797
13. Krishnasamy G, Rizzo F, Rudolphi T (1992) Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. In: Banerjee & Kubayashi S (eds) Advanced dynamic analysis by boundary element methods, vol 7. Development in boundary element methods. Elsevier, Oxford, pp 207-252
14. Kupradze V, Gegelia T, Basheleishvili M, Burchuladze T (1979) Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. North-Holland, Amsterdam
15. Kutt H (1975) The numerical evaluation of principal value integrals by finite part integration. Numer Math 24: 205-210
16. Lehmann R (1997) Studies on the use of boundary element method in physical geodesy. Deutsche Geodätische Kommission, Reihe A 113
17. Li H-B, Han G-M, Mang H (1985) A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method. Int J Numer Meth Engng 21: 2071-2096
18. Mantic V (1994) On computing boundary limiting values of boundary integrals with strongly singular and hypersingular kernels in 3D BEM for elastostatics. Engng Anal Bound Elem 13: 115-134
19. Maue A (1949) Zur Formulierung eines all gemeinen Beugungs-problems durch eine Integralgleichung. Z Phys 126: 601-618
20. Nedelec JC (1982) Integral equations with non integrable kernels. J Integ Eq 5: 563-572
21. Petersdorff T von, Schwab C (1995) Fully discrete multiscale Galerkin BEM. Preprint, Seminar für Angewandte Mathematik, ETH Zürich
22. Ramm A, van der Sluis A (1990) Calculating singular integrals as an ill-posed problem. Numer Math 57: 139-145
23. Sauter S (1992) Über die effiziente Verwendung des Galerkinverfahrens zur Lösung Fredholmscher Integralgleichungen. PhD Thesis, Lehrstuhl Prakt Math, Univ Kiel, Kiel
24. Sauter S (1996) Cubature techniques for 3-D Galerkin BEM. In: Hackbusch W, Wittum G (eds) Boundary elements: implementation and analysis of advanced algorithms, vol 54. Notes on numerical fluid mechanics. Vieweg, Wiesbaden, pp 29-44
25. Schneider R (1995) Multiskalen- und Wavelet-Matrix Kompression: Analysis basierte Methoden zur effizienten Lösung großer vollbesetrter Gleichungssysteme. PhD Thesis, Tech Univ Darmstadt, Darmstadt
26. Schwab C, Wendland W (1992a) Kernel properties and representations of boundary integral operators. Math Nachr 156: 187-218
27. Schwab C, Wendland W (1992b) On numerical cubatures of singular surface integrals in boundary element methods. Numer Math 62: 343-369
28. Schwab C, Wendland W (1992c) Numerical integration of singular and hypersingular integrals in boundary element methods. In: Espelid T, Genz A (eds) Numerical integration. Kluwer Academic, Dordrecht, pp 203-218
29. Shaofeng B, Xurong D (1991) On the singular integration in physical geodesy. Manuscr Geod 16: 283-287
30. Stroud A (1972) Approximate calculation of multiple integrals. Prentice-Hall, Englewood Cliffs
31. Svensson S (1983) Pseudodifferential operators. Manuscr Geod 8: 1-40
32. Tanaka M, Sladek V, Sladek J (1994) Regularization techniques applied to boundary element methods. Appl Mech Rev 47: 457-499
33. Vijayakumar S, Cormack D (1988) An invariant imbedding method for singular integral evaluation of finite domains. SIAM J Appl Math 48: 1335-1349