From 1997 to 2001 I was working on a project devoted
to the numerical solution of boundary value problems
for ordinary differential equations. This project was funded
by the
Austrian Science Fund
under grant no. P-12507 MAT. The project was continued from 2002 to 2003 under grant
no. P-15072 MAT.
Comprehensive documentation of the activities can be found
on our
project homepage.
From 2003 to 2004, I was working as a group leader in the Special Research Program (SFB)
AURORA
of the Austrian Science Fund, and
from 2004 to 2005 with the
SFB 382 at the Eberhard Karls University
in Tübingen.
Then, from 2005 to 2006, I was employed with the
Institute of Materials Chemistry at Vienna
University of Technology.
From 2007 to 2010, I was funded by the APART scholarship of the
Austrian Academy of Sciences.
From 2010 to 2011, I was employed with the
Austrian Science Fund's
project P21742-N16 at the University of Vienna.
From 2011 to 2014, I was assistant professor at Vienna University of Technology.
From 2015 to 2018, I was employed with my research project MA14-002 funded by the
Vienna Science and Technology Fund at the University of Vienna.
Since 2018, I am employed with my research project P 30819-N32 funded by the
Austrian Science Fund.
So far, my research yielded the following refereed papers,
other publications and talks :
You can view the
abstract of this paper or download the entire text as a
.pdf file.
O. Koch,
P. Kofler,
E. B. Weinmüller,
Initial Value Problems for Systems of Ordinary First and
Second Order Differential Equations with a Singularity of
the First Kind,
Analysis
21(2001), pp. 373-389.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
E. B. Weinmüller,
Iterated Defect Correction for the
Solution of Singular Initial Value Problems,
SIAM J.
Numer. Anal. 38(2001), pp. 1784-1799.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
W. Auzinger,
O. Koch,
E. B. Weinmüller,
Theory and Solution Techniques for Singular
Boundary Value Problems for Ordinary Differential Equations, in:
Parallel Processing and Applied Mathematics (M.P.R. Wyrzykowski,
J. Dongarra, and J. Wasniewsky, eds.),
Springer Lecture
Notes in Computer Science 2328(2002), pp. 851-861.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
E. B. Weinmüller,
The Convergence of Shooting Methods for
Singular Boundary Value Problems,
Math. Comp. 72(2003), pp. 289-305.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
E. B. Weinmüller,
Analytical and Numerical Treatment of a Singular Initial Value
Problem in Avalanche Modeling,
Appl. Math. Comput. 148(2004), pp. 561-570.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
W. Auzinger,
O. Koch,
E. B. Weinmüller,
New Variants of Defect Correction for Boundary Value
Problems in Ordinary Differential
Equations, in Current Trends in Scientific Computing,
Z. Chen, R. Glowinski, K. Li (eds),
Contemp.
Math. 329(2003), pp. 43-50.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
W. Auzinger,
O. Koch,
E. B. Weinmüller,
Collocation Methods for
Boundary Value Problems with an Essential Singularity, in:
Large-Scale Scientific Computing (I. Lirkov, S. Margenov, J.
Wasniewski, and P. Yalamov, eds.),
Springer Lecture Notes in Computer Science 2907, pp. 347-354.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
Discrete Event Simulation of the Transport Logistics of the Austrian Red Cross,
SNE Simulation News Europe, 38/39(2003), pp. 10-15.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
Asymptotically Correct Error Estimation for
Collocation Methods Applied to Singular Boundary Value
Problems,
Numer. Math. 101(2005), pp. 143-164.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
C.J. Budd,
O. Koch,
E. B. Weinmüller,
Computation of Self-Similar Solution Profiles for the Nonlinear
Schrödinger Equation,
Computing 77(2006), pp. 335-346.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
J. Caillat, J. Zanghellini, M. Kitzler, W. Kreuzer, O. Koch,
A. Scrinzi,
Correlated Multielectron Systems in Strong Laser Pulses - An MCTDHF
Approach, Phys. Rev. A 71(2005),
pp. 012712.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
H. Hofstätter, O. Koch,
Analysis of a Defect Correction Method for Geometric Integrators,
Numer. Algorithms 41(2006), pp. 103-126.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch, W. Kreuzer,
A. Scrinzi,
Approximation of the Time-Dependent Electronic Schrödinger Equation by MCTDHF,
Appl. Math. Comput. 173(2006), pp. 960-976.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
G. Kitzhofer, O. Koch,
P. Lima,
E. B. Weinmüller,
Efficient Numerical Solution of the Density Profile
Equation in Hydrodynamics,
J. Sci. Comput.
32(2007), pp. 411-424.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
C. Lubich,
Regularity of the Multi-Configuration Time-Dependent
Hartree Approximation in Quantum Molecular Dynamics,
M2AN Math. Model. Numer. Anal. 41(2007), pp. 315-331.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
G. Kitzhofer, O. Koch,
E. B. Weinmüller,
Pathfollowing for Essentially Singular Boundary Value
Problems with Application to the Complex Ginzburg-Landau
Equation,
BIT 49(2009), pp. 141-160.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
Efficient Computation of the MCTDHF Approximation to the
Time-Dependent Schrödinger Equation,
Opuscula Math.
26(2006), pp. 473-487.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
W. Auzinger, E. Karner,
O. Koch,
E. B. Weinmüller,
Collocation Methods for the Solution of Eigenvalue Problems for Singular
Ordinary Differential Equations,
Opuscula Math. 26(2006), pp. 29-41.
You can view the
abstract of this
paper or download the entire text as a
.pdf file.
O. Koch,
R. März,
D. Praetorius,
E. B. Weinmüller,
Collocation Methods for Index-1 DAES with a Critical Point,
Oberwolfach Report No. 18, ID 06016(2006), pp. 81-84.
I. Rachunkova,
O. Koch, G. Pulverer,
E. B. Weinmüller,
On a Singular Problem Arising in the Theory of Shallow Membrane Caps,
J. Math. Anal. Appl. 332(2007), pp. 523-541.
O. Koch, The Variational Splitting Method for the Multi-Configuration
Time-Dependent Hartree-Fock Equations for Atoms,
JNAIAM J. Numer. Anal. Indust. Appl. Math. 7(2012), pp. 1-13.
O. Koch,
C. Neuhauser,
M. Thalhammer,
Error Analysis of High-order Splitting Methods for Nonlinear Evolutionary
Schrödinger Equations and Application to the MCTDHF Equations in Electron Dynamics,
M2AN Math. Model. Numer. Anal.
47(2013), pp. 1265-1286.
R. Hammerling, O. Koch, Ch. Simon, and
E. B. Weinmüller,
Numerical Solution of Singular ODE Eigenvalue Problems in Electronic
Structure Computations,
J. Comput. Phys. 181 (2010),
pp. 1557-1561.
N. Happenhofer, O. Koch,
F. Kupka, and
F. Zaussinger,
Total variation diminishing implicit Runge--Kutta methods
for dissipative advection-diffusion problems in astrophysics,
PAMM, Proc. Appl. Math. Mech. 2011, pp. 777-778.
F. Kupka,
N. Happenhofer,
I. Higueras,
and O. Koch,
Total-Variation-Diminishing Implicit-Explicit Runge-Kutta Methods
for the Simulation of Double-Diffusive Convection in Astrophysics,
J. Comput. Phys. 231(2012), pp. 3561-3586.
A. Dick, O. Koch, R. März, and
E. B. Weinmüller,
Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point,
Math. Comp.
82 (2013), pp. 893-918.
You can download a preprint of this article as a
.pdf file.
H. Hofstätter, O. Koch, and M. Thalhammer,
Convergence of split-step generalized-Laguerre-Fourier-Hermite methods for Gross-Pitaevskii equations with rotation term,
Numer. Math. 127(2014), pp. 315-364.
H. Hofstätter and O. Koch,
An Approximate Eigensolver for Self-Consistent Field Calculations,
Numer. Algorithms 66(2014), pp. 609-641.
You can download a preprint of this article as a
.pdf file.
W. Auzinger,
O. Koch,
M. Thalhammer,
Defect-Based Local Error Estimators for Splitting Methods
with Application to Schrödinger Equations, Part I. The Linear Case.J. Comput. Appl. Math. 236(2012), pp. 2643-2659.
W. Auzinger,
O. Koch,
M. Thalhammer,
Defect-Based Local Error Estimators for Splitting Methods
with Application to Schrödinger Equations, Part II. Higher-Order Methods for Linear Problems,
J. Comput. Appl. Math.
255(2014), pp. 384-403.
W. Auzinger,
A. S. Bagherzadeh, and O. Koch.
Error Estimation Based on Locally Weighted
Defect for Boundary Value Problems in Second
Order Ordinary Differential Equations,
BIT Numer. Math. 54(2014), pp. 873-900.
You can download a preprint of this paper as a
.pdf file.
W. Auzinger,
O. Koch,
M. Thalhammer,
Defect-Based Local Error Estimators for High-Order Splitting Methods Involving
Three Linear Operators,
Numer. Algorithms 70(2015),
pp. 61-91.
W. Auzinger,
Th. Kassebacher, O. Koch,
M. Thalhammer,
Adaptive Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Regime,
Numer. Algorithms 72(2016), pp. 1-35.
You can download a preprint of this paper as a
.pdf file.
W. Auzinger,
W. Herfort, O. Koch, and
M. Thalhammer,
The BCH-Formula and Order Conditions for Splitting Methods,
in: Lie Groups, Differential Equations, and Geometry, G. Falcone (ed.),
UNIPA Springer Series, Vol. XIV(2017), pp. 71-84.
W. Auzinger,
H. Hofstätter, and O. Koch,
Symbolic Manipulation of Flows of Nonlinear
Evolution Equations, with Application in the
Analysis of Split-Step Time Integrators, Springer LNCS 9890(2016), pp. 43-57.
W. Auzinger,
I. Brezinova,
H. Hofstätter, O. Koch, and M. Quell,
Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations.
Part II: Comparisons of Local Error Estimation and Step-Selection Strategies,
Comput. Phys. Commun.
234(2019), pp. 55-71.
S. Donsa,
H. Hofstätter, O. Koch,
J. Burgdörfer, and I. Brezinova,
Long-time expansion of a Bose-Einstein condensate: Observability of Anderson localization,
Phys. Rev. A 96, 043630 (2017).
H. Hofstätter and O. Koch,
Non-satisfiability of a positivity condition for commutator-free exponential integrators of order higher than four,
Numer. Math. 141(2019), pp. 681-691.
You can download a reprint of this paper as a
.pdf file.
The original publication is available at
www.esaim-m2an.org, the copyright is owned by
EDP Sciences.
You can download an extended preprint of this paper as a
.pdf file.
W. Auzinger and O. Koch,
An improved local error estimator for symmetric time-stepping schemes,
Appl. Math. Lett.
82(2018), pp.106-110.
W. Auzinger,
I. Brezinova,
H. Hofstätter, O. Koch, and T. Sato,
Efficient adaptive exponential time integrators for nonlinear Schrödinger equations with nonlocal potential, in preparation.
W. Auzinger,
T. Jawecki, and O. Koch,
Computable strict upper bounds for Krylov approximations to a class of matrix exponentials and φ-functions, submitted.
P. Amodio,
C.J. Budd,
O. Koch,
V. Rottschäfer,
G. Settanni,
E. B. Weinmüller,
Near critical, self-similar, blow-up solutions
of the generalised Korteweg-de Vries equation: asymptotics and computations, submitted.
W. Auzinger,
H. Hofstätter, and O. Koch,
An algorithm for computing coefficients of
words in expressions involving exponentials
and its application to the construction of
exponential integrators, submitted.
O. Koch,
Approximation Methods in Multi-Particle Quantum Dynamics,
poster presentation at Stipendiatenwochenende of the Austrian
Academy of Sciences, March 31^{st} 2006.
You can view the
abstract
of this talk I gave on June 29^{th} 1999.
O. Koch,
Acceleration Techniques for Singular Initial Value Problems,
4^{th} World Multi-Conference on Circuits, Systems,
Communication and Computers,
Athens,
Greece,
July 2000.
Joint with
E. B. Weinmüller.
You can view the
abstract
of this invited talk I gave on July 11^{th} 2000.
O. Koch,
Theory and Computation of the MCTDHF Approximation for the
Time-Dependent Schrödinger Equation,
3rd Austrian
NA Day, Vienna, Austria, April 2007.
O. Koch,
Numerical Solution of Singular Boundary Value Problems
in Ordinary Differential Equations,
1st Austrian-Mongolian Mathematics Day,
Vienna University of Technology, Vienna,
Austria, October 2007. Joint with
W. Auzinger
and E. B. Weinmüller.
O. Koch,
Variational Approximations in Linear Algebra and Quantum Dynamics,
79th Annual GAMM Conference, Bremen,
Germany, April 2008.
Joint with
C. Lubich.
O. Koch,
Time Integration of the
Multi-Configuration Time-Dependent Hartree-Fock Equations,
4th Austrian
NA Day, Linz, Austria, April 2008.
Joint with
C. Lubich.
O. Koch,
The Variational Splitting Method for the
Multi-Configuration Time-Dependent Hartree-Fock Equations,
Splitting
Methods in Time Integration, Innsbruck, Austria, October 2008.
Joint with C. Lubich.
O. Koch,
Variational Approximations in Quantum Dynamics and Multilinear Algebra,
ÖMG Congress/ DMV Conference 2009,
Graz, Austria, September 2009.
Joint with C. Lubich.
O. Koch,
Total Variation Diminishing Implicit Runge-Kutta Methods
for Dissipative Advection-Diffusion Problems in Astrophysics,
82^{nd} GAMM Conference,
Graz, Austria, April 2011.
Joint with F. Kupka,
A. Mayerhofer, and
F. Zaussinger,
O. Koch,
Total-Variation Diminishing Runge-Kutta Methods for
Advection-Diffusion Equations in Astrophysics,
1^{st} International Workshop on Small Scale Solar Magnetic Fields,
Bairisch-Kölldorf, Austria, April 2011.
Joint with N. Happenhofer,
F. Kupka,
A. Mayerhofer, and
F. Zaussinger.
O. Koch,
Total Variation Diminishing Runge-Kutta Time Integrators
for Dissipative Flow Problems in Astrophysics,
ICNAAM 2011,
Halkidiki, Greece, September 2011.
Joint with N. Happenhofer,
F. Kupka, and
F. Zaussinger.
O. Koch,
Adaptive exponential splitting and Lawson methods for Schrödinger equations,
SciCADE 2017, Bath, U.K., September 2017.
Joint with W. Auzinger, I. Brezinova,
H. Hofstätter,
and M. Thalhammer.
O. Koch, Adaptive Magnus-type integrators for the simulation of solar cells,
ICNAAM 2018, Rhodes, Greece.
Joint with W. Auzinger, H. Hofstätter, M. Quell, and M. Thalhammer.
O. Koch,
Numerische Lösung von singulären Differentialgleichungen,
University of Tübingen,
Germany, June 2004.
O. Koch,
The Time-Dependent Multi-Particle
Schrödinger Equation and Dynamical Low Rank Approximation,
Humboldt University Berlin, Germany,
November 2005.
O. Koch,
MCTDHF: A Model Reduction Technique for Computational Quantum Dynamics,
Vienna University of Technology, Austria,
March 2006.
O. Koch,
Model Reduction Techniques for the Simulation of High-
Dimensional Quantum Dynamics,
Universität Stuttgart, Germany, May 2011.
O. Koch,
Adaptive Simulation of High-Dimensional Quantum Dynamics,
Freie Universität Berlin, Germany, October 2011.
O. Koch,
Adaptive Split-Step Time Integrators for Quantum Dynamics,
Technische Universität Chemnitz, Germany, February 2012.
O. Koch,
Adaptive Solution of Nonlinear Evolution Equations,
Universität Osnabrück, Germany, April 2012.
O. Koch,
Approximation of High-Dimensional Quantum Dynamics,
Universität Salzburg, Austria, November 2012.
O. Koch,
Adaptive Full Discretization of Nonlinear Schrödinger Equations,
Universität Köln, Germany, December 2012.
O. Koch,
Adaptive Full Discretization of Nonlinear Schrödinger Equations,
Leibniz Universität Hannover, Germany, December 2012.
O. Koch,
Adaptive Discretization Methods for Nonlinear Evolution Equations
with Application to Rotating Bose-Einstein Condensates,
Karl von Ossietzky Universität Oldenburg, Germany, January 2013.
O. Koch,
Adaptive Numerical Methods for Quantum Propagation,
Universität Heidelberg, Germany, October 2013.
O. Koch,
Partitioned Time Integrators for Nonlinear Evolution Equations,
Universität Bayreuth, Germany, April 2014.
O. Koch,
Adaptive numerische Verfahren für die Quantendynamik,
Universität Paderborn, Germany, June 2014.
W. Auzinger,
Transformed Companion Matrices as a Theoretical Tool
in the Numerical Analysis of Differential Equations,
CBC Workshop, Györ,
Hungary, October 2004.
Joint with O. Koch,
G. Schranz-Kirlinger.
You can view the abstract of this invited talk
here.
A. S. Bagherzadeh,
A posteriori Error Estimation for Second Order ODEs via Defect Correction,
5^{th} Austrian NA Day,
Innsbruck, Austria, May 2009. Joint with
W. Auzinger and O. Koch.
W. Auzinger,
Exact FD Schemes and Defect-Based Error Estimation for Second Order ODEs,
Colloquium,
Györ University,
Györ, Hungary, May 2009.
Joint with A. S. Bagherzadeh, and O. Koch.
A. S. Bagherzadeh,
Robust and Highly Accurate Error Estimators for Second Order ODEs,
6^{th} Austrian NA Day,
Salzburg, Austria, May 2010. Joint with
W. Auzinger and O. Koch.
E. B. Weinmüller,
Collocation for Nonlinear Index 1 DAEs with Singular Point,
ICIAM 2011,
Vancouver, Canada, July 2011. Joint with A. Dick, O. Koch, and
R. März.
W. Auzinger,
Local Error Estimation for Exponential Splitting Schemes,
Conference on Simulation and Optimization, Györ, Hungary, June 2011.
Joint with O. Koch and M. Thalhammer.
H. Hofstätter,
A Perl Program for the Symbolic Manipulation of Flows of Differential Equations and Its Application to
the Analysis of Defect-Based Error Estimators for Splitting Methods,
9th Austrian NA Day, Graz, April 2013.
Joint with W. Auzinger,
O. Koch, and M. Thalhammer.
W. Auzinger,
Representation and estimation of the local error of higher-order exponential splitting schemes involving two or three sub-operators,
Mathematical Seminar, University of Tartu, Estonia, September 2014.
Joint with O. Koch and M. Thalhammer.
H. Hofstätter,
Time propagation for Schrödinger-type equations with expensive nonlinearity,
University of Innsbruck,
Innsbruck, July 2017.
Joint with O. Koch.
S. Donsa,
Anderson localization of a one-dimensional Bose-Einstein condensate after long-time expansion,
Vienna young Scientists Symposium, Vienna, June 2016.
Joint with H. Hofstätter, O. Koch,
J. Burgdörfer,
and I. Brezinova.
I. Brezinova (invited talk),
Expansion of Bose-Einstein condensates in disorder: Anderson localization and wave chaos,
International Workshop on Quantum-Classical Transition in Many-Body Systems, Dresden, Germany, February 2017.
Joint with S. Donsa,
H. Hofstätter, O. Koch, and
J. Burgdörfer.
T. Jawecki, A computable strict upper bound for Krylov subspace approximations to the
exponential of skew-Hermitian matrices,
14th Austrian Numerical Analysis Day 2018,
Klagenfurt, May 2018. Joint with W. Auzinger
and O. Koch.