Publications

1. S. Le Borne
   Preconditioned nullspace method for the Oseen problem.
   SIAM J. Sci. Comp. 31, 2494-2509 (2009)
2. L. Grasedyck, S. Le Borne, R. Kriemann
   Parallel blackbox H-LU preconditioning for elliptic boundary value problems.
   Comput. Vis. Sci. 11, 273-291 (2008)
3. S. Le Borne
   Block computation and representation of a sparse nullspace basis of a rectangular matrix.
   Lin. Alg. Appl. 428, 2455-2467 (2008)
4. S. Le Borne, S. Oliveira
   Joint domain-decomposition H-LU preconditioners for saddle point problems.
   Electr. Trans. Num. Anal. 26, 285-298 (2007)
5. S. Le Borne, D.W. Cook II
   Construction of a discrete divergence-free basis through orthogonal factorization in H-arithmetic.
   Computing 81, 215-238 (2007)
6. S. Le Borne, S. Oliveira, F. Yang
   H-matrix preconditioners for symmetric saddle point problems for meshfree discretizations.
   Num. Lin. Alg. Appl. 15, 911-924 (2008)
7. L. Grasedyck, R. Kriemann, S. Le Borne.
   Domain Decomposition Based H-LU Preconditioning.
   Numerische Mathematik 112, 565-600 (2009)
8. S. Le Borne
   Hierarchical matrix preconditioners for the Oseen equations.
   Comput. Vis. Sci. 11, 147-157 (2008)
9. S. Le Borne
   Multilevel hierarchical matrices.
   SIAM J. Matrix Anal. Appl. 28, 871-889 (2006)
10. S. Le Borne, L. Grasedyck
    H-matrix preconditioners in convection-dominated problems.
    SIAM J. Matrix Anal. Appl., Vol. 27, No. 4, pp. 1172 - 1183 (2006)
11. L. Grasedyck, W. Hackbusch and S. Le Borne
    Adaptive Geometrically Balanced Clustering of H-Matrices.
    Computing 73, 1-23 (2004)
12. S. Le Borne
    H-matrices for convection-diffusion problems with constant convection.
    Computing 70, 261-274 (2003)
13. S. Le Borne
    Ordering techniques for two- and three-dimensional convection-dominated elliptic boundary value problems.
    Computing 64, 123-155 (2000)

Refereed conference proceedings

1. S. Le Borne.
   Block and joint H-matrix preconditioners for the Oseen equations.
   PAMM - Proc. Appl. Math. Mech. 6, 747-748 (2006)
2. S. Le Borne.
   Hierarchical matrix preconditioners for the Stokes equations.
   Proceedings of the 8th European Multigrid Conference on Multigrid, Multilevel and Multiscale Methods, (eds. P. Wesseling, C.W. Oosterlee and P.W. Hemker) 27-30 September 2005, Scheveningen 2005, CD-ROM.
3. S. Le Borne, L. Grasedyck, R. Kriemann
   Domain-decomposition based H-matrix preconditioners.
   LNCSE Vol. 55, 661-668 (2006) (online available at ddm.org)
4. S. Le Borne
   Hierarchical Matrices for Convection-Dominated Problems.
   LNCSE Vol. 40, 631-638 (2004) (online available at ddm.org)
5. S. Le Borne
   Modified H-matrices for convection dominated problems.
   PAMM - Proc. Appl. Math. Mech. 3, 537-538 (2003)
6. S. Le Borne
   H-matrices for the convection-diffusion equation.
   PAMM - Proc. Appl. Math. Mech. 2, 21-24 (2003)
7. W. Hackbusch, R. Kriemann, S. Le Borne, J.-F. Maitre
   CD2D3D - a package to solve convection dominated problems employing ordering techniques.
   Notes on Numerical Fluid Mechanics Vol. 75 (Springer), Numerical Flow Simulation II, CNRS-DFG Collaborative Research Programme, Results 1998-2000, 34-48 (2001)
8. S. Le Borne
   Ordering techniques for convection-dominated problems on unstructured three-dimensional grids.
   11th International Symposium on Domain Decomposition Methods for Partial Differential Equations (C. Lai, P. Bjorstad, M. Cross, O. Widlund, eds), DDM.org, 529-536 (1999)
9. S. Gutsch
   Cyclic and feedback vertex set ordering for convection-dominated problems.
   ZAMM 79, Supplement 3 (1998), 897-898
10. W. Hackbusch, S. Gutsch, J.-F. Maitre, F. Musy
    The appropriate numbering for the multigrid solution of convection dominated problems.
    in Notes on Numerical Fluid Mechanics, Vieweg (1998), Numerical Flow Simulation I, CNRS-DFG Collaborative Research Programme, Results 1996-1998, 75 - 88
11. R. Bank, S. Gutsch
    An algebraic approach to the HBMG method for unstructured grids.
    ZAMM 78, Supplement 3 (1998), 863-864
12. R. Bank, S. Gutsch
    The generalized hierarchical basis two-level method for the convection-diffusion equation on a regular grid.
    Multigrid methods V, Springer, Lecture Notes in Computational Science and Engineering 3 (1998), 1 - 20
13. R. Bank, S. Gutsch
    Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes.
    Ninth International Symposium on Domain Decomposition Methods for Partial Differential Equations, (P. Bjorstad, M. Espedal, D. Keyes, eds.) DDM.org, 251 - 265 (1998)

Technical reports

1. W. Hackbusch, L. Grasedyck, S. Le Borne
   H-matrix preconditioners in convection-dominated problems..
   Preprint 62/2004, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2004), available online at http://www.mis.mpg.de/preprints/2004/prepr2004_62.html
2. W. Hackbusch, L. Grasedyck, S. Le Borne
   Adaptive geometrically balanced clustering of H-matrices.
   Preprint 19/2004, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2004), available online at http://www.mis.mpg.de/preprints/2004/prepr2004_19.html
3. W. Hackbusch, L. Grasedyck, S. Le Borne
   Adaptive refinement and clustering of H-matrices.
   Preprint 106/2001, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2001), available online at http://www.mis.mpg.de/preprints/2001/prepr10601-abstr.html
4. S. Gutsch, T. Probst
   Cyclic and feedback vertex set ordering for the 2D convection-diffusion equation.
   Technical Report 97-22, University Kiel (1997)