The construction of some efficient preconditioners in the boundary element method

Advances in Computational Mathematics

Volumn 9, Issue 1-2, 1998, Pages 191-216

  Steinbach, O ^a   Wendland, W L ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Boundary element methods; Preconditioning techniques

Indexed keywords

EID: 0032359242     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018937506719     Document Type: Article

References (30)

1. K.E. Atkinson and I.G. Graham, Iterative solution of linear systems arising from the boundary element method, SIAM J. Sci. Statist. Comput. 13(3) (1992) 694-722.
2. J.H. Bramble, Z. Leyk and J.E. Pasciak, The analysis of multigrid algorithms for pseudodifferential operators of order minus one, Math. Comp. 63(208) (1994) 461-478.
3. H. Bückner, Die Praktische Behandlung von Integralgleichungen (Springer, Berlin, 1952).
4. C. Carstensen, M. Kuhn and U. Langer, Fast parallel solvers for symmetric boundary element domain decomposition equations, Numer. Math., to appear.
5. M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19(6) (1988) 613-626.
6. W. Hackbusch, Iterative Lösung Großer Schwachbesetzter Linearer Gleichungssysteme (Teubner, 1993).
7. W. Hackbusch and Z.P. Nowak, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math. 54 (1989) 463-491.
8. B. Heise and M. Kuhn, Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE formulations, Comput. 56 (1996) 237-258.
9. G.C. Hsiao and W.L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977) 449-481.
10. G.C. Hsiao and W.L. Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3 (1981) 299-315.
11. B.N. Khoromskij and W.L. Wendland, Spectrally equivalent preconditioners in substructuring techniques, East-West J. Numer. Math. 1 (1992) 1-25.
12. F.T. Korsmeyer, F.T. Leighton, K. Nabors and J. White, Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first kind integral equations of potential theory, SIAM J. Sci. Comput. 15(3) (1994) 713-735.
13. W. McLean and T. Tran, A preconditioning strategy for boundary element Galerkin methods, Numer. Methods Partial Differential Equations 13 (1997) 283-301.
14. M. Maischak, E.P. Stephan and T. Tran, Domain decomposition for integral equations of the first kind: Numerical results, Appl. Anal. 63 (1997) 111-132.
15. A. Meyer and S. Rjasanow, An effective direct solution method for certain boundary element equations in 3D, Math. Methods Appl. Sci. 13 (1990) 43-53.
16. E.S. Nikolaev and A.A. Samarskij, Numerical Methods for Grid Equations (Birkhäuser, Basel, 1989).
17. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).
18. T. von Petersdorff and E.P. Stephan, On the convergence of the multigrid method for a hypersingular integral equation of the first kind, Numer. Math. 57 (1990) 379-391.
19. S. Rjasanow, Effective iterative solution methods for boundary element equations, in: Boundary Elements XIII, eds. C.A. Brebbia and G.S. Gipson (CMP, 1991) pp. 889-899.
20. S. Sirtori, General stress analysis method by means of integral equations and boundary elements, Meccanica 14 (1979) 210-218.
21. O. Steinbach, Gebietszerlegungsmethoden mit Randintegralgleichungen und effiziente numerische Lösungsverfahren für gemischte Randwertprobleme, Doctoral thesis, University of Stuttgart (1996).
22. O. Steinbach, Fast solvers for the symmetric boundary element method, in: Boundary Elements: Implementation and Analysis of Advanced Algorithms, eds. W. Hackbusch and G. Wittum (Vieweg, 1996) pp. 232-242.
23. 2-error estimators in direct adaptive boundary element methods, in preparation.
24. O. Steinbach and W.L. Wendland, Efficient preconditioners for boundary element methods and their use in domain decomposition methods, in: Domain Decomposition Methods in Sciences and Engineering: 8th International Conference, Bejing, China, 1995, eds. R. Glowinski, J. Periaux, Z.C. Shi and O. Widlund (Wiley, New York, 1997) pp. 3-18.
25. O. Steinbach and W.L. Wendland, Hierarchical boundary element preconditioners in domain decomposition methods, in: Proceedings of the 9th Int. Conf. on Domain Decomposition Methods, Bergen, 1996, eds. P. Bjørstad, M. Espedal and D. Keyes (Wiley, New York, to appear).
26. E.P. Stephan, Additive Schwarz methods for integral equations of the first kind, in: MAFELAP 96, ed. J. Whiteman (Wiley, New York, 1997) pp. 123-144.
27. E.P. Stephan and T. Tran, Additive Schwarz method for the h-version boundary element method, Appl. Anal. 60 (1996) 63-84.
28. S. Vavasis, Preconditioning for boundary integral equations, SIAM J. Matrix Anal. Appl. 13 (1992) 905-925.
29. J. Xu and S. Zhang, Preconditioning the Poincaré-Steklov operator by using Green's function, Math. Comp. 66(217) (1997) 125-138.
30. Y. Yan, Sparse preconditioned iterative methods for dense linear systems, SIAM J. Sci. Comput. 15(5) (1994) 1190-1200.