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Inhalt des Dokuments

Publications

Books
H. Yserentant,
Regularity and approximability of electronic wave functions,
Lecture Notes in Mathematics, 2000. Springer-Verlag, Berlin, 2010. viii+182 pp.
[Download (PDF, 987,7 KB)]
W. Luther, K. Niederdrenk, F. Reutter, H. Yserentant,
Gewöhnliche Differentialgleichungen. Analytische und numerische Behandlung,
Rechnerorientierte Ingenieurmathematik. Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn. XII, 422 S., 1987.
K. Niederdrenk, H. Yserentant,
Funktionen einer Veränderlichen. Analytische und numerische Behandlung. (Functions of one variable. Analytical and numerical treatment),
Rechnerorientierte Ingenieurmathematik. Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn. XII, 447 S., 1987.
Articles
S. Scholz, H. Yserentant,
On the approximation of electronic wavefunctions by anisotropic Gauss and Gauss-Hermite functions,
Numer. Math. 136 (2017), no. 3, 841–874, doi:10.1007/s00211-016-0856-4.
[DOI] [Download (revised version) (PDF, 210,6 KB)]
R. Kornhuber, H. Yserentant,
Numerical homogenization of elliptic multiscale problems by subspace decomposition,
Multiscale Model. Simul. 14 (2016), no. 3, 1017-1036
[Download (PDF, 301,0 KB)]
R. E. Bank, H. Yserentant,
A note on interpolation, best approximation, and the saturation property,
Numer. Math. 131 (2015), 199-203.
[Download (PDF)]
H. Yserentant,
Regularity, complexity, and approximability of electronic wavefunctions,
in S. Dahlke et al. (eds.), Extraction of Quantifiable Information from Complex Systems, Lecture Notes in Computational Science and Engineering 102 (2014), 413-428.
L. Gauckler, H. Yserentant,
Regularity and approximability of the solutions to the chemical master equation,
ESAIM Math. Model. Numer. Anal. 48 (2014), no. 6, 1757-1775.
[Download (PDF), © EDP Sciences and S.M.A.I., the original publication is available at www.esaim-m2an.org]
R. E. Bank, H. Yserentant,
On the H1-stability of the L2-projection onto finite element spaces,
Numer. Math. 126 (2014), no. 2, 361-381.
[Download (PDF)]
H. Yserentant,
A short theory of the Rayleigh-Ritz method,
Comput. Methods Appl. Math. 13 (2013), no. 4, 495–502.
[Download (PDF)]
H. Yserentant,
Multi-level Decompositions of Electronic Wave Functions,
in R. Bank, M. Holst, O. Widlund, J. Xu (ed.), Domain Decomposition Methods in Science and Engineering XX, 2013, pp 63-72.
J. Gagelman, H. Yserentant,
A spectral method for Schrödinger equations with smooth confinement potentials,
Numer. Math. 122 (2012), no. 2, 383–398.
[Download (PDF, 158,7 KB)]
H.-C. Kreusler, H. Yserentant,
The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces,
Numer. Math. 121 (2012), no. 4, 781-802.
[Download (PDF, 173,5 KB)]
H. Yserentant,
The mixed regularity of electronic wave functions multiplied by explicit correlation factors,
ESAIM Math. Model. Numer. Anal. 45 (2011), no. 5, 803-824.
[Download (PDF, 316,0 KB)]
H. Yserentant,
Remarks on the complexity of the Schrödinger equation,
AIP Conf. Proc. 1281, 35 (2010).
R. E. Bank, H. Yserentant,
Multigrid convergence: a brief trip down memory lane,
Comput. Vis. Sci. 13 (2010), no. 4, 147–152.
R. Kornhuber, H. Yserentant,
Multigrid methods for discrete elliptic problems on triangular surfaces,
Comput. Vis. Sci. 11 (2008), no. 4-6, 251–257.
M. Klingler, P. Leinen, H. Yserentant,
A restart procedure for the finite mass method,
SIAM J. Sci. Comput. 30 (2007/08), no. 1, 117–133.
[Download (PDF, 208,6 KB)]
H. Yserentant,
The hyperbolic cross space approximation of electronic wavefunctions,
Numer. Math. 105 (2007), no. 4, 659–690.
[Download (PDF, 1,1 MB)]
H. Yserentant,
Sparse grids, adaptivity, and symmetry,
Computing 78 (2006), no. 3, 195–209.
[Download (PDF, 113,2 KB)]
S. Gebauer, R. Kornhuber, H. Yserentant,
Hierarchical decomposition of domains with fractures,
Math. Comp. 75 (2006), no. 253, 73–90.
H. Yserentant,
Sparse grid spaces for the numerical solution of the electronic Schrödinger equation,
Numer. Math. 101 (2005), no. 2, 381–389.
[Download (PDF, 131,9 KB)]
T. Bubeck, R. Hiptmair, H. Yserentant,
The finite mass mesh method,
Comput. Vis. Sci. 8 (2005), no. 2, 49–68.
M. Klingler, P. Markus, H. Yserentant,
The finite mass method on domains with boundary,
SIAM J. Sci. Comput. 26 (2005), no. 5, 1744–175.
[Download (PDF, 1,7 MB)]
H. Yserentant,
On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives,
Numer. Math. 98 (2004), no. 4, 731–759.
[Download (PDF, 236,8 KB)]
H. Yserentant,
The finite mass method, a new approach to the solution of flow problems,
in M. Breuer, F. Durst, C. Zenger, editors, High-Perfomance Scientific and Engineering Computing. Springer, 2002.
H. Yserentant,
The convergence of the finite mass method for flows in given force and velocity fields,
Meshfree methods for partial differential equations (Bonn, 2001), 419–440, Lect. Notes Comput. Sci. Eng., 26, Springer, Berlin, 2003.
[Download (PS, 756,3 KB)]
H. Yserentant,
The propagation of sound in particle models of compressible fluids,
Numer. Math. 88 (2001), no. 3, 581–601.
C. Gauger, P. Leinen, H. Yserentant,
The finite mass method,
SIAM J. Numer. Anal. 37 (2000), no. 6, 1768–179.
[Download (PDF, 830,3 KB)]
M. Hipp, S. Hüttemann, M. Konold, M. Klingler, P. Leinen, M. Ritt, W. Rosenstiel, H. Ruder, R. Speith, H. Yserentant,
A parallel object-oriented framework for particle methods,
in E. Krause, W. Jäger (ed.), High Performance Computing in Science and Engineering ’99, pages 483–495.
H. Yserentant,
Coarse grid spaces for domains with a complicated boundary,
Numer. Algorithms 21 (1999), no. 1-4, 387–392.
H. Yserentant,
The particle model of compressible fluids,
in Fey, Michael (ed.) et al., Hyperbolic problems: Theory, numerics, applications. Proceedings of the 7th international conference, Zürich, Switzerland, February 1998. Vol. II. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 130, 993-998 . Birkhäuser, 1999.
H. Yserentant,
Entropy generation and shock resolution in the particle model of compressible fluids,
Numer. Math. 82 (1999), no. 1, 161–177.
H. Yserentant,
Particles of variable size,
Numer. Math. 82 (1999), no. 1, 143–159.
H. Yserentant,
A particle model of compressible fluids,
Numer. Math. 76 (1997), no. 1, 111–142.
H. Yserentant,
A new class of particle methods,
Numer. Math. 76 (1997), no. 1, 87–109.
R. Kornhuber, H. Yserentant,
Multilevel methods for elliptic problems on domains not resolved by the coarse grid,
Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993), 49–60, Contemp. Math., 180, Amer. Math. Soc., Providence, RI, 1994.
H. Yserentant,
Old and new convergence proofs for multigrid methods,
Acta numerica, 1993, 285–326, Acta Numer., Cambridge Univ. Press, Cambridge, 1993.
F. Bornemann, H. Yserentant,
A basic norm equivalence for the theory of multilevel methods,
Numer. Math. 64 (1993), no. 4, 455–476.
H. Yserentant,
Hierarchical bases,
ICIAM 91 (Washington, DC, 1991), 256–276, SIAM, Philadelphia, PA, 1992.
P. Leinen, H. Yserentant,
Two fast solvers based on the multi-level splitting of finite element spaces,
Multigrid methods, III (Bonn, 1990), 83–90, Internat. Ser. Numer. Math., 98, Birkhäuser, Basel, 1991.
H. Yserentant,
Two multi-level methods for nonuniformly refined grids,
in E. Spedicato, editor, Computer algorithms for solving linear algebraic equations. The state of the art, NATO ASI Ser., Ser. F 77, 161-167, Springer, 1991.
H. Yserentant,
Two preconditioners based on the multi-level splitting of finite element spaces,
Numer. Math. 58 (1990), no. 2, 163–184.
R. E. Bank, B. D. Welfert, H. Yserentant,
A class of iterative methods for solving saddle point problems,
Numer. Math. 56 (1990), no. 7, 645–666.
R. E. Bank, H. Yserentant,
Some remarks on the hierarchical basis multigrid method,
Domain decomposition methods (Los Angeles, CA, 1988), 140–146, SIAM, Philadelphia, PA, 1989.
P. Deuflhard, P. Leinen, H. Yserentant,
Concepts of an adaptive hierarchical finite element code,
IMPACT Comput. Sci. Eng. 1 (1989), no. 1, 3-35.
H. Yserentant,
Preconditioning indefinite discretization matrices,
Numer. Math. 54 (1989), no. 6, 719–734.
R. E. Bank, T. F. Dupont, H. Yserentant,
The hierarchical basis multigrid method,
Numer. Math. 52 (1988), no. 4, 427–458.
H. Yserentant,
Hierarchical bases in the numerical solution of parabolic problems,
Large scale scientific computing (Oberwolfach, 1985), 22–36, Progr. Sci. Comput., 7, Birkhäuser Boston, Boston, MA, 1987.
H. Yserentant,
Erratum: "On the multilevel splitting of finite element spaces'',
Numer. Math. 50 (1986), no. 1, 123.
H. Yserentant,
The convergence of multilevel methods for solving finite-element equations in the presence of singularities,
Math. Comp. 47 (1986), no. 176, 399–409.
H. Yserentant,
On the multilevel splitting of finite element spaces,
Numer. Math. 49 (1986), no. 4, 379–412.
H. Yserentant,
Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence,
Appl. Math. Comput. 19 (1986), no. 1-4, 347–358.
H. Yserentant,
On the multilevel splitting of finite element spaces for indefinite elliptic boundary value problems,
SIAM J. Numer. Anal. 23 (1986), no. 3, 581–595.
H. Yserentant,
Über die Maximumnormkonvergenz der Methode der finiten Elemente bei geringsten Regularitätsvoraussetzungen,
Z. Angew. Math. Mech. 65 (1985), no. 2, 91–100.
H. Yserentant,
Hierarchical bases of finite-element spaces in the discretizaton of nonsymmetric elliptic boundary value problems,
Computing 35 (1985), no. 1, 39–49.
H. Yserentant,
Über die Konvergenz von Mehrgitterverfahren für nichtuniform verfeinerte Familien von Gittern,
Z. Angew. Math. Mech. 64 (1984), no. 5, 324–326.
K. Niederdrenk, H. Yserentant,
Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme,
Numer. Math. 41 (1983), no. 2, 223–253.
H. Yserentant,
Eine einfache und robuste Maximumnormabschätzung für die Methode der finiten Elemente,
Z. Angew. Math. Mech. 63 (1983), no. 5, T394–T395.
H. Yserentant,
Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art,
Numer. Math. 42 (1983), no. 1, 119–123.
H. Yserentant,
A remark on the numerical computation of improper integrals,
Computing 30 (1983), no. 2, 179–183.
H. Yserentant,
On the convergence of multilevel methods for strongly nonuniform families of grids and any number of smoothing steps per level,
Computing 30 (1983), no. 4, 305–313.
H. Yserentant,
Die Mehrstellenformeln für den Laplaceoperator,
Numer. Math. 34 (1980), no. 2, 171–187.
Technical reports and manuscripts
H. Yserentant,
A Note on Approximate Inverse Iteration,
Technical report, 2016, arXiv:1611.04141
[arXiv:1611.04141]
H. Yserentant,
On the complexity of the electronic Schrödinger equation,
Technical report, DFG-Schwerpunktprogramm 1324, Preprint 50, 2010.
[Download (PDF, 520,8 KB)]
H. Yserentant,
Regularity properties of wavefunctions and the complexity of the quantum-mechanical N-body problem,
Unpublished manuscript, November 2007.
[Download (PDF, 449,0 KB)]
H. Yserentant,
On the electronic schrödinger equation,
Technical report, Universität Tübingen, 2003.
[Download (PS, 414,7 KB)]
Theses
H. Yserentant,
Über die Aufspaltung von Finite-Element-Räumen in Teilräume verschiedener Verfeinerungsstufen. (On the splitting of finite-element spaces in subspaces of different refinement levels),
Habilitation thesis, Mathematisch-Naturwissenschaftliche Fakultät der Rheinisch- Westfälischen Technischen Hochschule Aachen. 81 S., 1984.
H. Yserentant,
Außenraumprobleme und finite Elemente,
PhD thesis, Mathematisch-Naturwissenschaftliche Fakultät der Rheinisch-Westfälischen Technischen Hochschule Aachen. 251 S., 1981.

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