The construction of some efficient preconditioners in the boundary element method (original) (raw)
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. ArticleMATHMathSciNet Google Scholar
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. ArticleMATHMathSciNet Google Scholar
H. Bückner, Die Praktische Behandlung von Integralgleichungen(Springer, Berlin, 1952). Google Scholar
C. Carstensen, M. Kuhn and U. Langer, Fast parallel solvers for symmetric boundary element domain decomposition equations, Numer. Math., to appear.
M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19(6) (1988) 613-626. ArticleMATHMathSciNet Google Scholar
W. Hackbusch, Iterative Lösung Großer Schwachbesetzter Linearer Gleichungssysteme(Teubner, 1993).
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. ArticleMATHMathSciNet Google Scholar
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. ArticleMATHMathSciNet Google Scholar
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. ArticleMATHMathSciNet Google Scholar
G.C. Hsiao and W.L. Wendland, The Aubin-Nitsche lemma for integral equations, J. Integral Equations 3 (1981) 299-315. MATHMathSciNet Google Scholar
B.N. Khoromskij and W.L. Wendland, Spectrally equivalent preconditioners in substructuring techniques, East-West J. Numer. Math. 1 (1992) 1-25. MathSciNet Google Scholar
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. ArticleMATHMathSciNet Google Scholar
W. McLean and T. Tran, A preconditioning strategy for boundary element Galerkin methods, Numer. Methods Partial Differential Equations 13 (1997) 283-301. ArticleMATHMathSciNet Google Scholar
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. MathSciNet Google Scholar
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. ArticleMATHMathSciNet Google Scholar
E.S. Nikolaev and A.A. Samarskij, Numerical Methods for Grid Equations(Birkhäuser, Basel, 1989). Google Scholar
J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables(Academic Press, New York, 1970). Google Scholar
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. ArticleMATHMathSciNet Google Scholar
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.
S. Sirtori, General stress analysis method by means of integral equations and boundary elements, Meccanica 14 (1979) 210-218. ArticleMATH Google Scholar
O. Steinbach, Gebietszerlegungsmethoden mit Randintegralgleichungen und effiziente numerische Lösungsverfahren für gemischte Randwertprobleme, Doctoral thesis, University of Stuttgart (1996).
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.
O. Steinbach, A-posteriori L 2-error estimators in direct adaptive boundary element methods, in preparation.
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. Google Scholar
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).
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. Google Scholar
E.P. Stephan and T. Tran, Additive Schwarz method for the _h_-version boundary element method, Appl. Anal. 60 (1996) 63-84. MATHMathSciNet Google Scholar
J. Xu and S. Zhang, Preconditioning the Poincaré-Steklov operator by using Green's function, Math. Comp. 66(217) (1997) 125-138. ArticleMATHMathSciNet Google Scholar
Y. Yan, Sparse preconditioned iterative methods for dense linear systems, SIAM J. Sci. Comput. 15(5) (1994) 1190-1200. ArticleMATHMathSciNet Google Scholar