TUHH / Institut für Mathematik / Mitarbeiter / Prof. Dr. Sabine Le Borne / Veröffentlichungen Englische Flagge

Veröffentlichungen

Scientific Journals | Refereed Conference Proceedings | Technical Reports | Dissertation

Scientific Journals

R. Ahrens, S. Le Borne FFT-based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids submitted (2017)
A. Iske, S. Le Borne, M. Wende Hierarchical matrix approximation for kernel-based scattered data interpolation SIAM J. Sci. Comput. 39, p. A2287-A2326 (2017)
H. Eisenschmidt, M. Soumaya, N. Bajcinca, S. Le Borne, K. Sundmacher Estimation of aggregation kernels based on Laurent polynomial approximation Computers & Chemical Engineering 103, 210-217 (2017)
S. Le Borne, L. Shahmuradyan Fast algorithms for hp-discretized univariate population balance aggregation integrals Computers & Chemical Engineering 97:1-12 (2017)
S. Le Borne, L. Shahmuradyan Algorithms for the Haar wavelet based fast evaluation of aggregation integrals in population balance equations Applied Numerical Mathematics 108, 1-20 (2016)
A. Vogt, T. Reuschel, H.-D. Brüns, S. Le Borne, C. Schuster On the Treatment of Arbitrary Boundary Conditions using a Fast Direct H-Matrix Solver in MoM IEEE Transactions on Antennas & Propagation, Vol. 64 No. 08 (2016)
R. Kriemann, S. Le Borne H-FAINV: Hierarchically factored approximate inverse preconditioners Comput. Vis. Sci. 17:135-150 (2015)
S. Le Borne, H. Eisenschmidt, K. Sundmacher Image-based analytical crystal shape computation exemplified for potassium dihydrogen phosphate (KDP) Chemical Engineering Science 139, 61-74 (2016)
S. Le Borne, L. Shahmuradyan, K. Sundmacher Fast evaluation of univariate aggregation integrals on equidistant grids. Computers & Chemical Engineering 74, 115-127 (2015)
S. Le Borne, L. Rebholz Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems. Comput. Vis. Sci. 16:259-269 (2015)
A. Bowers, S. Le Borne, L. Rebholz Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization. CMAME (Computer Methods in Applied Mechanics and Engineering), 275, 1-19 (2014)
B. Cousins, S. Le Borne, A. Linke, Rebholz, Z. Wang Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements. Numerical Methods for Partial Differential Equations 29, 1217 - 1237 (2013)
S. Le Borne, J. Ovall Rapid error reduction for block Gauss-Seidel based on p-hierarchical basis. Numerical Linear Algebra with Applications 20, 743-760 (2013)
S. Boerm, S. Le Borne H-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems. International Journal for Numerical Methods in Fluids 68, 83-98 (2012), doi 10.1002/d.2495
S. Le Borne, C. Ngufor An implicit approximate inverse preconditioner for saddle point problems. Electr. Trans. Num. Anal. 37, 173-188 (2010)
L. Grasedyck, R. Kriemann, S. Le Borne Domain Decomposition Based H-LU Preconditioning. Numerische Mathematik 112, 565-600 (2009), DOI 10.1007/s00211-009-0218-6
S. Le Borne Preconditioned nullspace method for the two-dimensional Oseen problem. SIAM J. Sci. Comp. 31, 2494-2509 (2009)
L. Grasedyck, R. Kriemann, S. Le Borne Parallel blackbox H-LU preconditioning for elliptic boundary value problems. Comput. Vis. Sci. 11, 273-291 (2008)
S. Le Borne Block computation and representation of a sparse nullspace basis of a rectangular matrix. Lin. Alg. Appl. 428, 2455-2467 (2008)
S. Le Borne, S. Oliveira, F. Yang H-matrix preconditioners for symmetric saddle point problems from meshfree discretizations. Numerical Linear Algebra with Applications 15, 911-924 (2008)
S. Le Borne Hierarchical matrix preconditioners for the Oseen equations. Comput. Vis. Sci. 11, 147-157 (2008)
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)
S. Le Borne, S. Oliveira Joint domain-decomposition H-LU preconditioners for saddle point problems. Electr. Trans. Num. Anal. 26, 285-298 (2007)
L. Grasedyck, S. Le Borne H-matrix preconditioners in convection-dominated problems. SIAM J. Sci. Comp. 27, 1172 - 1183 (2006)
S. Le Borne Multilevel hierarchical matrices. SIAM J. Mat. Anal. Appl. 28, 871 - 889 (2006)
W. Hackbusch, L. Grasedyck, S. Le Borne Adaptive Geometrically Balanced Clustering of H-Matrices. Computing 73, 1-23 (2004)
S. Le Borne H-matrices for convection-diffusion problems with constant convection. Computing 70, 261-274 (2003)
S. Le Borne Ordering techniques for two- and three-dimensional convectiondominated elliptic boundary value problems. Computing 64, 123-155 (2000)

Refereed Conference Proceedings

S. Le Borne Hierarchical preconditioners for high-order FEM. LNCSE 104, Domain Decomposition Methods in Science and Engineering XXII, Dickopf, Gander, Halpern, Krause, Pavarino (eds.), 559-566 (2016)
S. Le Borne, R. Kriemann The nullspace method for the three-dimensional Stokes problem. PAMM · Proc. Appl. Math. Mech. 7, 1101101-1101102 (2007)
S. Le Borne Block and joint H-matrix preconditioners for the Oseen equations. PAMM · Proc. Appl. Math. Mech. 6, 747-748 (2006)
S. Le Borne Hierarchical matrix preconditioners for the Stokes equations. Proceedings of the 2005 European Multigrid Conference, (eds. P. Wesseling et. al.), Scheveningen 2005, CD-ROM
S. Le Borne, L. Grasedyck, R. Kriemann Domain-decomposition based H-LU preconditioners. LNCSE, Vol. 55, 661-668, online available at DDM.org (2006)
S. Le Borne Hierarchical matrices for Convection-Dominated Problems. LNCSE, Vol. 40, 631-638, online available at DDM.org (2004)
S. Le Borne Modified H-matrices for convection dominated problems. PAMM · Proc. Appl. Math. Mech., Vol. 3, 537 - 538 (2003)
S. Le Borne H-matrices for the convection-diffusion equation. PAMM · Proc. Appl. Math. Mech., Vol. 2, 21-24 (2003)
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)
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. Bjørstad, M. Cross, O. Widlund, eds), DDM.org, 529-536 (1999)
S. Gutsch Cyclic and feedback vertex set ordering for convection-dominated problems. ZAMM 79, Supplement 3, 897-898 (1998)
W. Hackbusch, S. Gutsch, J.-F. Maitre, F. Musy The appropriate numbering for the multigrid solution of convection dominated problems. Notes on Numerical Fluid Mechanics 66 (Vieweg), Numerical Flow Simulation I, CNRS-DFG Collaborative Research Programme, Results 1996-1998, 75 - 88
R. Bank, S. Gutsch An algebraic approach to the HBMG method for unstructured grids ZAMM 78, Supplement 3, 863-864 (1998)
R. Bank, S. Gutsch The generalized hierarchical basis two-level method for the convection-diffusion equation on a regular grid. Multigrid Methods V, Lecture Notes in Computational Science and Engineering 3, Springer, 1-20 (1998)
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. Bjørstad, M. Espedal, D. Keyes, eds), DDM.org, 251-265 (1998)

Technical Reports

Le Borne, J. Ovall Rapid error reduction for block Gauss-Seidel based on p-hierarchical basis. Max-Planck-Institute Technical Report, number 33/2011
S. Le Borne, J. Ovall One-step hierarchical preconditioners for higher-order FEM. Oberwolfach Report No. 28/2011
S. Le Borne Preconditioned nullspace method for the Oseen problem. Oberwolfach Report No. 23/2008, 27-29 (2008)
L. Grasedyck, R. Kriemann, S. Le Borne Domain Decomposition Based H-LU Preconditioning. Technical Report No. 115, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2005)
L. Grasedyck, S. Le Borne H-matrix preconditioners in convection-dominated problems. Technical Report No. 62, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2004)
L. Grasedyck, S. Le Borne Adaptive Geometrically Balanced Clustering of H-Matrices. Technical Report No. 19, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2004)
L. Grasedyck, S. Le Borne Adaptive refinement and clustering of H-matrices. Technical Report No. 106, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany (2001)

Dissertation

S. Le Borne Multigrid methods for convection-dominated problems. Dissertation, Verlag dissertation.de, No. 54, ISBN 3-933342-56-2 (1999