Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
maximize

Literatur

1
O. Axelsson and P. S. Vassilevski.
Algebraic Multilevel Preconditioning Methods. I.
Numer. Math., 56:157-177, 1989.

2
O. Axelsson and P. S. Vassilevski.
Algebraic Multilevel Preconditioning Methods. II.
SIAM J. Numer. Anal., 27:1569-1590, 1990.

3
S. Balay, K. Buschelman, W. D. Gropp, D. Kaushik, L. C. McInnes and B. F. Smith.
PETSc home page.
http://www.mcs.anl.gov/petsc, 2001.

4
S. Balay, W. D. Gropp, L. C. McInnes and B. F. Smith.
Efficient management of parallelism in object oriented numerical software libraries.
In E. Arge, A. M. Bruaset and H. P. Langtangen, editors, Modern Software Tools in Scientific Computing, pages 163-202. Birkhäuser, 1997.

5
S. Balay, W. D. Gropp, L. C. McInnes and B. F. Smith.
PETSc users manual.
Technical Report ANL-95/11 - Revision 2.1.0, Argonne National Laboratory, 2001.

6
R. E. Bank.
Hierarchical Bases and the Finite Element Method.
Acta Numerica, 5:1-43, 1996.

7
R. E. Bank and S. Gutsch.
Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes.
In P. Bjørstad, M. Espedal and D. Keyes, editors, Ninth International Conference on Domain Decomposition Methods, 1998.

8
R. E. Bank, T. F. Dupont and H. Yserentant.
The Hierarchical Basis Multigrid Method.
Numer. Math., 52:427-458, 1988.

9
G. Beylkin.
On the Representation of Operators in Bases of Compactly Supported Wavelets.
SIAM J. Numer. Anal., 29:1716-1740, 1992.

10
G. Beylkin, R. Coifman and V. Rokhlin.
Fast Wavelet Transforms and Numerical Algorithms. I.
Comm. Pure and Appl. Math., 44:141-183, 1991.

11
J. H. Bramble, J. E. Pasciak and J. Xu.
Parallel Multilevel Preconditioners.
Math. Comp., 55:1-22, 1990.

12
W. L. Briggs, V. E. Henson and S. F. McCormick.
A Multigrid Tutorial.
SIAM, Phiadelphia, 2000.

13
T. F. Chan, W. P. Tang and W. L. Wan.
Wavelet Sparse Approximate Inverse Preconditioners.
BIT, 37:644-660, 1997.

14
A. Cohen and R. Masson.
Wavelet Methods for Second-Order Elliptic Problems, Preconditioning and Adaptivity.
SIAM J. Sci. Comput., 21:1006-1026, 1999.

15
W. Dahmen.
Wavelet and Multiscale Methods for Operator Equations.
Acta Numerica, 6:55-228, 1997.

16
W. Dahmen and A. Kunoth.
Multilevel Preconditioning.
Numer. Math., 63:315-344, 1992.

17
W. Dahmen and R. Schneider.
Wavelets on Manifolds I: Construction and Domain Decomposition.
Technical Report 149, RWTH Aachen, 1999.

18
W. Dahmen, S. Müller and T. Schlinkmann.
On a Robust Adaptive Multigrid Solver for Convection-Dominated Problems.
Technical Report 171, RWTH Aachen, 1999.

19
J. E. Dendy.
Black Box Multigrid for Nonsymmetric Problems.
Appl. Math. Comput., 13:261-283, 1983.

20
M. Floater and E. Quak.
Piecewise Linear Prewavelets on Arbitrary Triangulations.
Numer. Math., 82:221-252, 1999.

21
J. Fuhrmann.
Zur Verwendung von Mehrgitterverfahren bei der numerischen Behandlung elliptischer partieller Differentialgleichungen mit variablen Koeffizienten.
PhD thesis, TU Chemnitz-Zwickau, 1994.

22
D. L. Gines.
Fast Electromagnetic Simulations Using Wavelets.
PhD thesis, University of Colorado at Boulder, 1997.

23
D. L. Gines, G. Beylkin and J. Dunn.
LU Factorization of Non-Standard-Forms and Direct Multiresolution Solvers.
Technical Report 278, Program in Applied Mathematics, University of Colorado at Boulder, 1996.

24
T. Grauschopf, M. Griebel and H. Regler.
Additive Multilevel-Preconditioners Based on Bilinear Interpolation, Matrix Dependent Geometric Coarsening and Algebraic Multigrid Coarsening for Second Order Elliptic PDEs.
Applied Numerical Mathematics, 23:63-96, 1997.
Auch als Techn. Ber. 342/02/96A, Institut für Informatik, TU München, 1996.

25
M. Griebel.
Multilevel Algorithms Considered as Iterative Methods on Semidefinite Systems.
SIAM J. Sci. Comput., 15:547-565, 1994.

26
M. Griebel.
Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen.
B. G. Teubner, Stuttgart, 1994.

27
M. Griebel and P. Oswald.
On The Abstract Theory of Additive and Multiplicative Schwarz Algorithms.
Numer. Math., 70:163-180, 1995.
Auch als Techn. Ber. 342/6/93 A, Institut für Informatik, TU München, 1993.

28
W. Hackbusch.
Multigrid-Methods and Applications.
Springer, Berlin, Heidelberg, New York, 1985.

29
W. Hackbusch.
Iterative Lösung großer schwachbesetzter Gleichungssysteme.
B. G. Teubner, Stuttgart, 1993.

30
S. Jaffard.
Wavelet Methods for Fast Resolution of Elliptic Problems.
SIAM J. Numer. Anal., 29:965-986, 1992.

31
K. Johannsen.
Robuste Mehrgitterverfahren für die Konvektions-Diffusions Gleichung mit wirbelbehafteter Konvektion.
B. G. Teubner, Stuttgart, 2000.

32
U. Kotyczka and P. Oswald.
Piecewise Linear Prewavelets of Small Support.
In C. Chui and L. Schumaker, editors, Approximation Theory VIII. World Scientific, Singapore, 1995.

33
S. Le Borne.
Multigrid Methods for Convection-Dominated Problems.
PhD thesis, Universität Kiel, 1999.

34
S. Mallat.
Multiresolution Approximation and Wavelet Orthonormal Bases of ${\cal L}^2({\ifmmode{\rm I}\mkern-4mu{\rm R}
\else\leavevmode\hbox{I}\kern-.17em\hbox{R}\fi})$.
Trans. Amer. Math. Soc., 315:69-87, 1989.

35
P. Oswald.
Multilevel Finite Element Approximation.
B. G. Teubner, Stuttgart, 1994.

36
C. Pflaum.
Fast and Robust Multilevel Algorithms.
Habilitation, Universität Würzburg, 1998.

37
C. Pflaum.
Robust Convergence of Multilevel Algorithms for Convection-Diffusion Equations.
SIAM J. Numer. Anal., 37:443-469, 2000.

38
T. Probst.
Mehrgitterverfahren für Konvektionsdiffusionsgleichungen.
PhD thesis, Universität Kiel, 1999.

39
A. Reusken.
On the Approximate Cyclic Reduction Preconditioner.
Technical Report 144, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 1997.

40
A. Reusken.
Approximate Cyclic Reduction Preconditioning.
In W. Hackbusch and G. Wittum, editors, Multigrid Methods V, Lecture Notes in Computational Science and Engineering Vol. 3. Proceedings der Fifth European Multigrid Conference, Springer, Berlin, Heidelberg, New York, 1998.

41
A. Rieder, R. O. Wells and X. Zhou.
A Wavelet Approach to Robust Multilevel Solvers for Anisotropic Elliptic Problems.
Appl. Comput. Harm. Anal., 1:355-367, 1994.

42
J. W. Ruge and K. Stüben.
Algebraic Multigrid.
In S. F. McCormick, editor, Multigrid Methods. SIAM, Phiadelphia, 1987.

43
Y. Saad.
Iterative Methods for Sparse Linear Systems.
PWS Publishing, Boston, 1996.

44
D. Schittko.
Waveletbasierte LU-Faktorisierung für elliptische Probleme.
Master's thesis, Universität Bonn, 2000.

45
R. Stevenson.
Piecewise Linear (Pre-)wavelets on Non-uniform Meshes.
In W. Hackbusch and G. Wittum, editors, Multigrid Methods V, Lecture Notes in Computational Science and Engineering Vol. 3. Proceedings der Fifth European Multigrid Conference, Springer, Berlin, Heidelberg, New York, 1998.

46
R. Stevenson.
Stable Three-Point Wavelet Bases on General Meshes.
Numer. Math., 80:131-158, 1998.

47
K. Stüben.
Algebraic Multigrid (AMG): An Introduction with Applications.
Technical Report 53, GMD-Forschungszentrum Informationstechnik GmbH, St. Augustin, 1999.

48
W. Sweldens.
The Lifting Scheme: A Construction of Second Generation Wavelets.
SIAM J. Math. Anal., 29:511-546, 1997.

49
P. S. Vassilevski.
On Two Ways of Stabilizing the Hierarchical Basis Multilevel Methods.
SIAM Rev., 39:18-53, 1997.

50
P. S. Vassilevski and J. Wang.
Stabilizing the Hierachical Basis by Approximate Wavelets. I: Theory.
Numer. Lin. Algebra Appl., 4:103-126, 1997.

51
P. S. Vassilevski and J. Wang.
Stabilizing the Hierachical Basis by Approximate Wavelets, II: Implementation and Numerical Results.
SIAM J. Sci. Comput., 20:490-514, 1998.

52
G. Wittum.
On the Robustness of ILU Smoothing.
SIAM J. Sci. Comput., 10:699-717, 1989.

53
J. Xu.
Iterative Methods by Space Decomposition and Subspace Correction.
SIAM Rev., 34:581-613, 1992.

54
P. M. de Zeeuw.
Matrix-Dependent Prolongations and Restrictions in a Black-Box Multigrid Solver.
J. Comput. Appl. Math., 33:1-27, 1990.

55
P. M. de Zeeuw.
Acceleration of Iterative Methods by Coarse Grid Corrections.
PhD thesis, University of Amsterdam, 1997.



Frank Kiefer
2001-10-24