Fast wavelet iterative solvers applied to the Neumann problem

Aerospace Science and Technology

Volumn 4, Issue 2, 2000, Pages 135-145

  Choquet, Rémi ^a,c   Perrier, Valérie ^b  

^a ONERA   (France)

^b IMAG Institute   (France)

^c CENTRE D ECOLOGIE FONCTIONNELLE ET EVOLUTIVE   (France)

Author keywords

Compression; FWT; Neumann; Poisson; Preconditioner; Singular linear system

Indexed keywords

EID: 0001261785     PISSN: 12709638     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1270-9638(00)00119-X     Document Type: Article

References (18)

1. Averbuch A., Beylkin G., Coifman R., Fischer P., A wavelet-based constrained preconditioned conjugate gradient for elliptic problems, in: Axelsson O., Neytcheva M., Polman B., Nijmegen (Eds.), Proceedings of PRISM'97, University Press, 1997.
2. Barret R., Berry M., Chan T., Demmel J., Donat J., Dongarra J., Eijkhout V., Pozo R., Romine C., Van der Vorst H., Templates for the solution of linear systems: buiding blocks for iterative methods, SIAM / netlib, 1993.
3. Calvetti D., Reichel L., Zhang Q., New iterative method for the solution of ill posed problem, in: Second SIAM Conference on Sparse Matrices, Idaho, 1996.
4. Choquet R., Erhel J., Amélioration de l'algorithmique pour un code de traitement automatique des relevés geoacoustiques des fonds marins, Technical report, IRISA, 1997.
5. Cohen A., Wavelet methods in numerical analysis, in: Ciarlet P.G., Lions J.L. (Eds.), Handbook of Numerical Analysis, 1999.
6. Cohen A., Masson R., Wavelet adaptive methods for elliptic problems-preconditionning and adaptivity, SIAM J. Sci. Comp. (accepted for publication).
7. Dahmen W., Prössdorf S., Schneider R., Wavelet methods for pseudodifferential equations II: matrix compression and fast solution, Adv. Comp. Math. 1 (1993) 259-335.
8. Daubechies I., Orthonormal bases for compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988) 499-519.
9. Daubechies I., Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
10. Grote M.J., Huckle T., Parallel preconditioning with sparse approximate inverses, SIAM J. Sci. Comput. 18 (3) (1997).
11. Jaffard S., Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal. 29 (1992) 965-986.
12. Juvigny X., Résolution de grands systèmes linéaires sur machines massivement parallèles, Thèse, Paris VI, Janvier 1997.
13. Karki K.C., Patankar S.V., Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations, AIAA J. 27 (9) (1989) 1167-1174.
14. Ko J., Kurdila A., Oswald P., Scaling functions and wavelet preconditioners for second order elliptic problems, in: Kurdila A., Dahmen W., Oswald P. (Eds.), Multi-scale Wavelet Methods for Partial Differential Equations, Wavelet Analysis and its Applications, Vol. 6, Academic Press, 1996, pp. 413-426.
15. Kolotina L.Y., Yeremin L.Yu., Factorized sparse approximate inverse preconditionings I. Theory, SIAM J. Matrix Analysis Applications 14 (1) (1993) 45-58.
16. Lascaux P., Theodor R., Analyse Numérique Matricielle Appliquée à l' Art de l'Ingénieur, Tome 1 et 2, Masson, 1986.
17. Lê T.H., Troff B., Sagaut P., Dang-Tran K., Loc Ta Phuoc, Pégase: a Navier-Stokes solver for direct numerical simulation of incompressible flows, Int. J. Numer. Meth. Fl. 24 (1997) 833-861.
18. Monasse P., Perrier V., Ondelettes sur l'intervalle pour la prise en compte de conditions aux limites, C. R. Acad. Sci. I-Math. 321 (1995).