Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems

Electronic Transactions on Numerical Analysis

Volumn 8, Issue , 1999, Pages 138-153

  Chen, K E ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Boundary elements; Conjugate gradient; Dense linear systems; Fast wavelet transforms; Sparse preconditioners

Indexed keywords

EID: 0001684372     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. S. AMINI, P. J. HARRIS, AND D. T. WILTON, Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem, SPRINGER-VERLAG, 1992.
2. S. AMINI S. AND N. MAINES, Iterative solutions of boundary integral-equations, IN BOUNDARY ELEMENT METHODS 14, C.A. BREBBIA, ED., CM PUBLICATIONS, 1994.
3. _, Qualitative properties of boundary integral operators and their discretizations, MATHEMATICS TECHNICAL REPORT MCS-95-12, UNIVERSITY OF S ALFORD, UK, 1995.
4. _, PRECONDITIONED KRYLOV SUBSPACE METHODS FOR BOUNDARY ELEMENT SOLUTION OF THE HELMHOLTZ EQUATION. TECHNICAL REPORT MCS-95-05, DEPT OF MATHS AND COMP. Sci., UNIVERSITY OF SALFORD, UK, 1995.
5. K. ATKINSON, The Numerical Solution of Integral Equations of the Second Kind, CAMBRIDGE UNIV. PRESS, CAMBRIDGE, 1997.
6. O. AXELSSON AND V. A. BARKER, Finite element solution of boundary values problems: theory and computation. ACADEMIC PRESS, ORLANDO, FLA., 1984.
7. G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms I, COMM. PURE APPL. MATH., 44 (1991), PP. 141-183.
8. D. BOND AND S. VAVASIS, Fast wavelet transforms for matrices arising from boundary element methods, COMPUTER SCIENCE RESEARCH REPORT TR-174, CORNELL UNIVERSITY, 1994.
9. C.A. BREBBIA, J.C.F. TELLES, AND L.C. WROBEL, Boundary Element Techniques: Theory and Applications in Engineering, SPRINGER-VERLAG, BERLIN, 1984.
10. T.F. Chan, W. R Tang, and W.L. Wan, Wavelet Sparse Approximate Inverse Preconditioning, BIT, 37 (1997), PP. 644-660.
11. K. CHEN, Preconditioning boundary element equations, IN BOUNDARY ELEMENTS, IMPLEMENTATION AND ANALYSIS OF ADVANCED ALGORITHMS : PROCEEDINGS OF THE TWELFTH GAMM-SEMINAR, W. Hackbusch and G. Wittum, eds.,Braunschweig/Wiesbaden, Vieweg, 1996, pp. 57-67.
12. K. CHEN, On a class of preconditioning methods for dense linear systems from boundary elements, SIAM J. Sci. Comput., 20 (1998), pp. 684-698.
13. K. CHEN. AND C. H. LAI, PARALLEL SOLUTIONS OF BOUNDARY ELEMENT EQUATIONS BY A FLEXIBLE ELIMINATION PROCESS, Contemp. Math., 218 (1998), pp. 311-317.
14. J. A. CUMINATO, On the uniform convergence of a collocation method for a class of singular integral equations, BIT, 27 (1987), pp. 190-202.
15. F. ERDOGAN AND G. D. GUPTA, On the numerical solution of singular integral equations, Quart. Appl. Math., 30 (1972), pp. 525-534.
16. W., DAHMEN, Wavelet and multiscale methods for operator equations, Acta Numerica, 6, Cambridge Univ. Press, 1997.
17. W. DAHMEN, B. KLEEMANN, S. PROSSDORF, AND R. SCHNEIDER, Multiscale methods for the solution of the Helmholtz and Laplace equations, in Boundary Element Topics, Wolfgang L. Wendland, ed., Springer-Verlag, 1996.
18. G. H. Golub and C. Van Loan, Matrix Computation, 2nd ed, John Hopkins Univ. Press, Baltimore, 1989.
19. I. G. GRAHAM AND G. A. CHANDLER, Higher order methods for linear functional of solutions of second kind integral equations, SIAM J. Numer. Anal, 25 (1988), pp. 1118-1137.
20. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comp. Phys., 73 (1987), pp. 325-348.
21. W. HACKBUSCH, AND Z. P. NOWAK, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
22. A. HARTEN, Multiresolution representation and numerical algorithms: a brief review, CAM report 94-12, Dept of Mathematics, UCLA, USA, 1994.
23. N. I. IOAKIMIDIS AND P. S. THEOCARIS, A comparison between the direct and the classical numerical methods for the solution of Cauchy type singular integral equations, SIAM J. Numer. Anal., 17 (1980), pp. 115-118.
24. C. H. LAI, An extension of Purcell's vector method with applications to panel element equations Comput. Math. Appl., 33 (1997), pp. 101-114.
25. D. MILLER, Wavelet transforms and linear algebra, MSc thesis, Inst. Adv. Sci. Comput., University of Liverpool, UK, 1995.
26. WILLIAM H. PRESS, SAUL A. TEUKOLSKY, WILLIAM T. VETTERLING, AND BRIAN P. FLANNERY, Numerical Recipes in C. The Art of Scientific Computing. 2nd ed., Cambridge Univ. Press, Cambridge, 1992.
27. L. REICHEL, Parallel iterative methods for the solution of Fredholm integral equations of the second kind, in Hypercube Multiprocessors 1987, M. T. Heath, ed. SIAM publications, pp. 520-529, 1987.
28. R. SCHNEIDER, P. L. LEVIN, AND M. SPASOJEVIC, Multiscale compression of BEM equations for electrostatic systems IEEE Trans. Dielectrics Elec. Insulation, 3 (1996), pp. 482-493.
29. G. STRANG AND T. NGUYEN, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1996.
30. W. SWELDENS, The construction and application of wavelets in numerical analysis, PhD. thesis, Catholic University of Leuven, Belgium, 1994.