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

Veröffentlichungen

Scientific Journals | Refereed Conference Proceedings | Technical Reports | Dissertation

Scientific Journals

S. Le Borne, Factorization, symmetrization and truncated transformation of RBF-GA stabilized Gaussian radial basis functions to appear in SIAM J. Mat. Anal. Appl. (2019)
S. Le Borne, M. Wende Iterative solution of saddle-point systems from radial basis function (RBF) interpolation submitted (2018)
S. Le Borne, M. Wende Multilevel interpolation of scattered data using H-matrices submitted (2018)
M. Dosta, E.-U. Hartge, R. Ahrens, S. Heinrich, S. Le Borne Investigation of an FFT-based solver applied to dynamic flowsheet simulation of agglomeration processes to appear in Advanced Powder Technology (2018)
S. Le Borne, M. Wende Domain decomposition methods in scattered data interpolation with conditionally positive definite radial basis functions Comput. Math. Appl. 77, 1178-1196 (2019)
R. Ahrens, S. Le Borne FFT-based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids J. Comput. Appl. Math. 338, 280-297 (2018)
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)
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)
R. Kriemann, S. Le Borne H-FAINV: Hierarchically factored approximate inverse preconditioners Comput. Vis. Sci. 17:135-150 (2015)
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