Efficient algorithms for the p-version of the boundary element method

Journal of Integral Equations and Applications

Volumn 8, Issue 3, 1996, Pages 337-360

  Heuer, Norbert ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Additive schwarz preconditioner; P version of BEM; Sparse matrices

Indexed keywords

EID: 0041183465     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075956     Document Type: Article

References (20)

1. B. Alpert, G. Beylkin, R. Coifman and V. Rokhlin, Wavelets for the fast solution of second kind integral equations, Tech. Report YALEU/DCS/RR-837, 1990.
2. I. Babuška, A. Craig, J. Mandel and J. Pitkäranta, Efficient preconditioning for the p-version finite element method in two dimensions, SIAM J. Numer. Anal. 28 (1991), 624-661.
3. I. Babuška, M. Griebel and J. Pitkäranta, The problem of selecting the shape functions for a p-type finite element, Internat. J. Numer. Methods Engrg. 28 (1989), 1891-1908.
4. T.F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs and R.G. Voigt, eds., Fifth Conference on Domain Decomposition Methods for Partial Differential Equations, Philadelphia, 1992, SIAM.
5. M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19 (1988), 613-626.
6. V.J. Ervin, N. Heuer and E.P. Stephan, On the h-p version of the boundary element method for Symms integral equation on polygons, Comput. Methods Appl. Mech. Engrg. 110 (1993), 25-38.
7. M. Hahne and E.P. Stephan, Schwarz iterations for the efficient solution of screen problems with boundary elements, Computing, to appear.
8. F.K. Hebeker, On a parallel Schwarz algorithm for symmetric strongly elliptic integral equations, in Domain decomposition methods for partial differential equations (R. Glowinski, Y.A. Kuznetsov, G.A. Meurant, J. Periaux and O.B. Widlund, eds.), SIAM, Philadelphia, 1991.
9. N. Heuer, hp-Versionen der Randelementmethode, Ph.D thesis, Universitat Hannover, 1992.
10. N. Heuer, E.P. Stephan and T. Tran, Multilevel additive Schwarz method for the p- and hp-versions of the boundary element method, Applied Mathematics Report AMR95/37, The University of New South Wales, 1995.
11. U. Lamp, T. Schleicher, E.P. Stephan and W.L. Wendland, Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem, Computing 33 (1984), 269-296.
12. J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications I, Springer, New York, 1972.
13. E.P. Stephan and M. Suri, On the convergence of the p-version of the boundary element method, Math. Comp. 52 (1989), 31-48.
14. E.P. Stephan and M. Suri, The h-p version of the boundary element method on polygonal domains with quasiuniform meshes, Math. Modeling Numer. Anal. 25 (1991), 783-807.
15. E.P. Stephan and T. Tran, Additive Schwarz method for the p-version boundary element method, Applied Mathematics Report AMR95/13, The University of New South Wales, 1995.
16. E.P. Stephan and A. Wathen, Convergence of preconditioned minimum residual iteration for coupled finite element / boundary element computations, SIAM J. Numer. Anal., to appear.
17. E.P. Stephan and W.L. Wendland, Remarks to Galerkin and least squares methods with finite elements for general elliptic problems, Manuscripta Geodaetica 1 (1976), 93-123.
18. T. Tran and E.P. Stephan, Additive Schwarz method for the h-version boundary element method, Applied Mathematics Report AMR95/36, The University of New South Wales, 1995.
19. T. von Petersdorff, Randwertprobleme der Elastizitätstheorie für Polyeder - Singularitdten und Approximation mit Randelementmethoden, Ph.D thesis, Technische Hochschule Darmstadt, Darmstadt, 1989.
20. T. von Petersdorff, C. Schwab, and R. Schneider, Multiwavelets for second kind integral equations, Tech. Report BN-1176, Institute for Physical Science and Technology, University of Maryland, Baltimore, 1994.