2024
. A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity. CRC 1173 Preprint 2024/21, Karlsruhe Institute of Technology, September 2024. [files]
. Überarbeitung der DFG-Denkschrift "Sicherung guter wissenschaftlicher Praxis". WissR, 57(1):13–21, August 2024. URL https://doi.org/10.1628/wissr-2024-0004.
. Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions. CRC 1173 Preprint 2024/16, Karlsruhe Institute of Technology, August 2024.
. Numerische Mathematik. Springer Spektrum Berlin, Heidelberg, July 2024.
. Discrete gradients in short-range molecular dynamics simulations. Numer. Algor., 96(3):1189–1220, July 2024. URL https://doi.org/10.1007/s11075-023-01717-4. [preprint]
. Variational Gaussian approximation for the magnetic Schrödinger equation. J. Phys. A: Math. Theor., 57(29):295202, July 2024. URL https://doi.org/10.1088/1751-8121/ad591e. [preprint]
. Maximum norm error bounds for the full discretization of nonautonomous wave equations. IMA J. Numer. Anal., 44(4):2480–2512, July 2024. URL https://doi.org/10.1093/imanum/drad065. [preprint] [files]
. Error bounds for discrete minimizers of the Ginzburg–Landau energy in the high-$\kappa$ regime. SIAM J. Numer. Anal., 62(3):1313–1343, June 2024. URL https://doi.org/10.1137/23M1560938. [preprint] [files]
. Error analysis of second-order local time integration methods for discontinuous Galerkin discretizations of linear wave equations. Math. Comp., 93(350):2611–2641, April 2024. URL https://doi.org/10.1090/mcom/3952. [preprint] [files]
. Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions. Found. Comput. Math., 48pp., February 2024. URL https://doi.org/10.1007/s10208-024-09639-w. Online first. [preprint] [files]
. Robust fully discrete error bounds for the Kuznetsov equations in the inviscid limit. CRC 1173 Preprint 2024/1, Karlsruhe Institute of Technology, January 2024. [files]
2023
. Time-dependent electromagnetic scattering from dispersive materials. CRC 1173 Preprint 2023/22, Karlsruhe Institute of Technology, November 2023. [files]
. Semi-analytical integration in molecular dynamics. PhD thesis, Karlsruhe Institute of Technology (KIT), September 2023.
. Wellposedness and regularity for linear Maxwell equations with surface current. Z. Angew. Math. Phys., 74(4):131, August 2023. URL https://doi.org/10.1007/s00033-023-02021-w. [preprint]
. On the nonlinear Dirichlet–Neumann method and preconditioner for Newton's method. In S. C. Brenner, A. Klawonn, F. Kwok, J. Xu, and J. Zou, editors, Domain Decomposition Methods in Science and Engineering XXVI, pages 381–389, Cham, March 2023. Springer International Publishing. [preprint]
. Wave Phenomena. Mathematical Analysis and Numerical Approximation, volume 49 of Oberwolfach Seminars. Birkhäuser Cham, March 2023.
. Dynamical low-rank integrators for second-order matrix differential equations. BIT, 63(1):article no. 4, March 2023. URL https://doi.org/10.1007/s10543-023-00941-7. [preprint] [files]
. Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations. BIT, 63(1):article no. 9, March 2023. URL https://doi.org/10.1007/s10543-023-00942-6. [preprint] [files]
. Optimal $W^{1,\infty}$-estimates for an isoparametric finite element discretization of elliptic boundary value problems. Electron. Trans. Numer. Anal., 58:1–21, January 2023. URL https://doi.org/10.1553/etna_vol58s1. [preprint]
2022
. A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions. Numer. Math., 152:907–936, October 2022. URL https://doi.org/10.1007/s00211-022-01326-8. [preprint] [files]
. Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs. SIAM J. Numer. Anal., 60(5):2897–2924, October 2022. URL https://doi.org/10.1137/21M1427255. [preprint] [files]
. Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning. Numer. Algor., 91(1):81–107, September 2022. URL https://doi.org/10.1007/s11075-022-01255-5. [preprint]
. Full discretization error analysis of exponential integrators for semilinear wave equations. Math. Comp., 91(336):1687–1709, July 2022. URL https://doi.org/10.1090/mcom/3736. [preprint]
. Error analysis for space discretizations of quasilinear wave-type equations. IMA J. Numer. Anal., 42(3):1963–1990, July 2022. URL https://doi.org/10.1093/imanum/drab073. [preprint] [files]
. On dynamical low-rank integrators for matrix differential equations. PhD thesis, Karlsruhe Institute of Technology (KIT), July 2022.
. Exponential integrators for quasilinear wave-type equations. SIAM J. Numer. Anal., 60(3):1472–1493, June 2022. URL https://doi.org/10.1137/21M1410579. [preprint] [files]
. Preconditioned implicit time integration schemes for Maxwell's equations on locally refined grids. CRC 1173 Preprint 2022/29, Karlsruhe Institute of Technology, June 2022. [files]
. Error analysis for full discretizations of quasilinear wave-type equations with two variants of the implicit midpoint rule. IMA J. Numer. Anal., drac010, May 2022. URL https://doi.org/10.1093/imanum/drac010. [preprint]
. Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems. Numer. Math., 150(3):893–927, March 2022. URL https://doi.org/10.1007/s00211-021-01262-z. [preprint] [files]
2021
. Erfahrungen bei den Lernbrücken in Karlsruhe 2021. Mitteilungen der Deutschen Mathematiker-Vereinigung, 29(4):234–235, December 2021. URL https://doi.org/10.1515/dmvm-2021-0083.
. Der Kodex „Leitlinien zur Sicherung guter wissenschaftlicher Praxis“ der DFG. Mitteilungen der Deutschen Mathematiker-Vereinigung, 29(4):239–242, December 2021. URL https://doi.org/10.1515/dmvm-2021-0085.
. On leapfrog-Chebyshev schemes for second-order diffferential equations. PhD thesis, Karlsruhe Institute of Technology, December 2021.
. An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions. Numer. Math., 147(4):869–899, April 2021. URL https://doi.org/10.1007/s00211-021-01184-w. [preprint] [files]
. On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. SN Partial Differ. Equ. Appl., 2(2):23, 27pp., March 2021. URL https://doi.org/10.1007/s42985-020-00045-9. [preprint] [files]
. Error analysis of exponential integrators for nonlinear wave-type equations. PhD thesis, Karlsruhe Institute of Technology (KIT), February 2021.
. A unified error analysis for the numerical solution of nonlinear wave-type equations with application to kinetic boundary conditions. PhD thesis, Karlsruhe Institute of Technology (KIT), February 2021.
2020
. Error analysis of discontinuous Galerkin discretizations of a class of linear wave-type problems. In W. Dörfler, M. Hochbruck, D. Hundertmark, W. Reichel, A. Rieder, R. Schnaubelt, and B. Schörkhuber, editors, Mathematics of Wave Phenomena, Trends in Mathematics, pages 197–218, October 2020. Birkhäuser Basel.
W. Dörfler, M. Hochbruck, D. Hundertmark, W. Reichel, A. Rieder, R. Schnaubelt, and B. Schörkhuber, editors. Mathematics of Wave Phenomena, Trends in Mathematics, October 2020. Birkhäuser Basel.
. On leapfrog-Chebyshev schemes. SIAM J. Numer. Anal., 58(4):2404–2433, August 2020. URL https://doi.org/10.1137/18M1209453. [preprint]
. Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions. Electron. Trans. Numer. Anal., 53:522–540, August 2020. URL https://doi.org/10.1553/etna_vol53s522. [preprint]
. On the convergence of Lawson methods for semilinear stiff problems. Numer. Math., 145(3):553–580, July 2020. URL https://doi.org/10.1007/s00211-020-01120-4. [preprint]
. Error analysis for space and time discretizations of quasilinear wave-type equations. Dissertation, Karlsruhe Institute of Technology (KIT), May 2020.
. A conjugate-gradient-type rational Krylov subspace method for ill-posed problems. Inverse Problems, 36(1):015008, 19, January 2020. URL https://doi.org/10.1088/1361-6420/ab5819. [preprint]
2019
. Heterogeneous multiscale method for Maxwell's equations. Multiscale Model. Simul., 17(4):1147–1171, October 2019. URL https://doi.org/10.1137/18M1234072. [preprint]
. Unified error analysis for nonconforming space discretizations of wave-type equations. IMA J. Numer. Anal., 39(3):1206–1245, July 2019. URL https://doi.org/10.1093/imanum/dry036. [preprint]
. Upwind discontinuous Galerkin space discretization and locally implicit time integration for linear Maxwell's equations. Math. Comp., 88(317):1121–1153, May 2019. URL https://doi.org/10.1090/mcom/3365. [preprint]
. Analytical and numerical analysis of linear and nonlinear properties of an rf-SQUID based metasurface. Phys. Rev. B, 99(7):075401, February 2019. URL https://doi.org/10.1103/PhysRevB.99.075401. [preprint]
. On the efficiency of the Peaceman–Rachford ADI-dG method for wave-type problems. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, and I. S. Pop, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017, volume 126 of Lecture Notes in Computational Science and Engineering, pages 135–144, January 2019. Springer International Publishing. [preprint]
2018
. Fehleranalyse von auf trigonometrischen Integratoren basierenden Splittingverfahren für hochoszillatorische, semilineare Probleme. Dissertation, Karlsruhe Institute of Technology (KIT), November 2018.
. The Peaceman–Rachford ADI-dG method for linear wave-type problems. Dissertation, Karlsruhe Institute of Technology (KIT), September 2018.
. Error analysis of implicit Runge–Kutta methods for quasilinear hyperbolic evolution equations. Numer. Math., 138(3):557–579, March 2018. URL https://doi.org/10.1007/s00211-017-0914-6. [preprint]
. Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations. IMA J. Numer. Anal., 38(1):57–74, January 2018. URL https://doi.org/10.1093/imanum/drx007. [preprint]
2017
. Finite element heterogeneous multiscale method for time-dependent Maxwell's equations. In M. L. Bittencourt, N. A. Dumont, and J. S. Hesthaven, editors, Spectral and high order methods for partial differential equations—ICOSAHOM 2016, volume 119 of Lect. Notes Comput. Sci. Eng., pages 269–281. Springer, Cham, November 2017. [preprint]
. Discrete gradient methods for solving variational image regularisation models. J. Phys. A, 50(29):295201, 21, June 2017. URL https://doi.org/10.1088/1751-8121/aa747c. [preprint]
. Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $C_0$-semigroups. SIAM J. Numer. Anal., 55(3):1483–1504, June 2017. URL https://doi.org/10.1137/15M104880X. [preprint]
. A unified error analysis for spatial discretizations of wave-type equations with applications to dynamic boundary conditions. Dissertation, Karlsruhe Institute of Technology (KIT), June 2017.
. Acceleration of contour integration techniques by rational Krylov subspace methods. J. Comput. Appl. Math., 316:133–142, May 2017. URL https://doi.org/10.1016/j.cam.2016.08.040. [preprint]
. On the approximation of electromagnetic fields by edge finite elements. Part 2: A heterogeneous multiscale method for Maxwell's equations. Comput. Math. Appl., 73(9):1900–1919, May 2017. URL https://doi.org/10.1016/j.camwa.2017.02.043. [preprint]
. Locally implicit time integration for linear Maxwell's equations. Dissertation, Karlsruhe Institute of Technology (KIT), April 2017.
. A fast mollified impulse method for biomolecular atomistic simulations. J. Comput. Phys., 333:180–198, March 2017. URL https://doi.org/10.1016/j.jcp.2016.12.024. [preprint]
. Implementation of discrete gradient methods for dissipative PDEs in image processing on GPUs. In G. R. W. Quispel, P. Bader, D. I. McLaren, and D. Tagami, editors, Geometric Numerical Integration and its Applications, IMI-La Trobe Joint Conference 2016, volume 74 of MI Lecture Notes, pages 69–71, March 2017. IMI, Kyushu University, Japan.
. On multiscale algorithms for selected applications in molecular mechanics. Dissertation, Karlsruhe Institute of Technology (KIT), March 2017.
. Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations. Numer. Math., 135(2):547–569, February 2017. URL https://doi.org/10.1007/s00211-016-0810-5. [preprint]
2016
. Error analysis of a second-order locally implicit method for linear Maxwell's equations. SIAM J. Numer. Anal., 54(5):3167–3191, October 2016. URL https://doi.org/10.1137/15M1038037. [preprint]
. On the blunting method in verified integration of ODEs. Reliab. Comput., 23:15–34, July 2016. URL http://interval.louisiana.edu/reliable-computing-journal/volume-23/reliable-computing-23-pp-015-034.pdf.
. A finite element heterogeneous multiscale method with improved control over the modeling error. Commun. Math. Sci., 14(2):463–487, March 2016. URL https://doi.org/10.4310/CMS.2016.v14.n2.a7. [preprint]
. Convergence of viscoelastic constraints to nonholonomic idealization. Eur. J. Mech. A Solids, 58:140–147, jul-aug 2016. URL https://doi.org/10.1016/j.euromechsol.2016.01.003.
2015
. A convergence analysis for the shift-and-invert Krylov subspace method. Technical Report, Karlsruhe Institute of Technology, December 2015.
. A short course on exponential integrators. In Matrix Functions and Matrix Equations, volume 19 of Series in Contemporary Applied Mathematics CAM, pages 28–49. Higher Ed. Press, Beijing, November 2015.
. Das CAS Maple als Werkzeug zur Modellierung und Visualisierung in Schule und Studium. Technical Report, Karlsruhe Institute of Technology, September 2015.
. Finite element heterogeneous multiscale method for Maxwell's equations in frequency domain. In Proceedings of the 12th International Conference on the Mathematical and Numerical Aspects of Waves, pages 192–193, July 2015.
. Efficient time integration for discontinuous Galerkin approximations of linear wave equations [Plenary lecture presented at the 83rd Annual GAMM Conference, Darmstadt, 26th–30th March, 2012]. ZAMM Z. Angew. Math. Mech., 95(3):237–259, March 2015. URL https://doi.org/10.1002/zamm.201300306. [preprint]
. Convergence of an ADI splitting for Maxwell's equations. Numer. Math., 129(3):535–561, March 2015. URL https://doi.org/10.1007/s00211-014-0642-0. [preprint]
. Efficient multiple time-stepping algorithms of higher order. J. Comput. Phys., 285:133–148, March 2015. URL https://doi.org/10.1016/j.jcp.2015.01.018. [preprint]
. The exponential Rosenbrock–Euler method for nonsmooth initial data. Technical Report, Karlsruhe Institute of Technology, March 2015.
. Implicit Runge–Kutta methods and discontinuous Galerkin discretizations for linear Maxwell's equations. SIAM J. Numer. Anal., 53(1):485–507, February 2015. URL https://doi.org/10.1137/130944114. [preprint]
. High order numerical methods for highly oscillatory problems. ESAIM Math. Model. Numer. Anal., 49(3):695–711, may-june 2015. URL https://doi.org/10.1051/m2an/2014056. [preprint]
2014
. Uniform approximation of $\varphi$-functions in exponential integrators by a rational Krylov subspace method with simple poles. SIAM J. Matrix Anal. Appl., 35(4):1467–1489, December 2014. URL https://doi.org/10.1137/140964655. [preprint]
. An exponential integrator for non-autonomous parabolic problems. Electron. Trans. Numer. Anal., 41:497–511 (electronic only), December 2014. URL http://etna.mcs.kent.edu/volumes/2011-2020/vol41/abstract.php?vol=41&pages=497-511.
. Finite-element heterogeneous multiscale method for the Helmholtz equation. C. R. Math. Acad. Sci. Paris, 352(9):755–760, September 2014. URL https://doi.org/10.1016/j.crma.2014.07.006. [preprint]
. Finite element heterogeneous multiscale method for the wave equation: long-time effects. Multiscale Model. Simul., 12(3):1230–1257, September 2014. URL https://doi.org/10.1137/13094195X. [preprint]
. Rational Krylov Subspace Methods for phi-Functions in Exponential Integrators. Dissertation, Karlsruhe Institute of Technology (KIT), July 2014.
. Conditional space-time stability of collocation Runge–Kutta for parabolic evolution equations. Electron. Trans. Numer. Anal., 41:62–80 (electronic only), May 2014. URL http://etna.mcs.kent.edu/volumes/2011-2020/vol41/abstract.php?vol=41&pages=62-80.
. Eine flexible Klasse von local time stepping Verfahren. Dissertation, Karlsruhe Institute of Technology (KIT), April 2014.
. A preconditioned Krylov method for an exponential integrator for non-autonomous parabolic systems. Oberwolfach Rep., 11(1):822–824, March 2014. URL https://doi.org/10.4171/OWR/2014/14.
2013
. Error analysis of implicit and exponential time integration of linear Maxwell's equations. Dissertation, Karlsruhe Institute of Technology (KIT), December 2013.
. Convergence analysis of an extended Krylov subspace method for the approximation of operator functions in exponential integrators. SIAM J. Numer. Anal., 51(4):2189–2213, July 2013. URL https://doi.org/10.1137/12089226X. [preprint]
. Positivity Preservation in the Simulation of Relativistic Laser-Plasma Interaction. Dissertation, Karlsruhe Institute of Technology (KIT), July 2013.
. Finite Element Heterogeneous Multiscale Methods for the Wave Equation. Dissertation, University of Basel, July 2013.
. FE heterogeneous multiscale method for long-time wave propagation. C. R. Math. Acad. Sci. Paris, 351(11-12):495–499, June 2013. URL https://doi.org/10.1016/j.crma.2013.06.002. [preprint]
. Finite element heterogeneous multiscale method for the wave equation: long-time effects. In Proceedings of the 11th International Conference on the Mathematical and Numerical Aspects of Waves, pages 233–234, June 2013.
. Residual, restarting, and Richardson iteration for the matrix exponential. SIAM J. Sci. Comput., 35(3):A1376–A1397, May 2013. URL https://doi.org/10.1137/110820191. [preprint]
2012
. Exponential integrators for parabolic problems with time dependent coefficients. Oberwolfach Rep., 9(4):3602–3606, December 2012. URL https://doi.org/10.4171/OWR/2012/60.
. Resolvent Krylov subspace approximation to operator functions. BIT, 52(3):639–659, September 2012. URL https://doi.org/10.1007/s10543-011-0367-8.
. Preserving energy resp. dissipation in numerical PDEs using the "average vector field" method. J. Comput. Phys., 231(20):6770–6789, August 2012. URL https://doi.org/10.1016/j.jcp.2012.06.022. [preprint]
. Methoden zur Lösungsverifikation und Einschließungsverfahren für gemischte Komplementaritätsprobleme. Dissertation, Karlsruhe Institute of Technology (KIT), July 2012.
2011
. Exponential multistep methods of Adams-type. BIT, 51(4):889–908, December 2011. URL https://doi.org/10.1007/s10543-011-0332-6. [preprint]
. Finite element heterogeneous multiscale method for transient wave propagation. In Proceedings of the 10th International Conference on the Mathematical and Numerical Aspects of Waves, pages 45–48, July 2011.
. Optimal boundary control of the wave equation with pointwise control constraints. Comput. Optim. Appl., 49(1):123–147, May 2011. URL https://doi.org/10.1007/s10589-009-9289-7.
2010
. Approximation of semigroups and related operator functions by resolvent series. SIAM J. Numer. Anal., 48(5):1826–1845, October 2010. URL https://doi.org/10.1137/090768084. [preprint]
. A multilevel Jacobi–Davidson method for polynomial PDE eigenvalue problems arising in plasma physics. SIAM J. Sci. Comput., 32(6):3151–3169, October 2010. URL https://doi.org/10.1137/090774604. [preprint]
. Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator. IEEE Plasma Sci., 38(9):2383–2389, September 2010. URL https://doi.org/10.1109/TPS.2010.2056706. [preprint]
. Exponential integrators. Acta Numer., 19:209–286, May 2010. URL https://doi.org/10.1017/S0962492910000048. [preprint]
. On the convergence of a regularizing Levenberg–Marquardt scheme for nonlinear ill-posed problems. Numer. Math., 115(1):71–79, March 2010. URL https://doi.org/10.1007/s00211-009-0268-9. [preprint]
2009
. Perturbation results for exponential Rosenbrock-type methods. AIP Conf. Proc., 1168(1):1196–1199, September 2009. URL https://doi.org/10.1063/1.3241278. [preprint]
. Regularization of nonlinear ill-posed problems by exponential integrators. M2AN Math. Model. Numer. Anal., 43(4):709–720, July 2009. URL https://doi.org/10.1051/m2an/2009021. [preprint]
. A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems. Inverse Problems, 25(7):075009, 18, June 2009. URL https://doi.org/10.1088/0266-5611/25/7/075009. [preprint]
. Effect of poloidal inhomogeneity in plasma parameters on edge anomalous transport. Phys. Plasmas, 16(2):4, April 2009. URL https://doi.org/10.1063/1.3121222. [preprint]
. Numerical Methods for Eigenvalue Problems in the Description of Drift Instabilities in the Plasma Edge. Dissertation, Heinrich-Heine Universität Düsseldorf, March 2009. [preprint]
. Exponential Rosenbrock-type methods. SIAM J. Numer. Anal., 47(1):786–803, February 2009. URL https://doi.org/10.1137/080717717. [preprint]
2008
. Approximation of matrix operators applied to multiple vectors. Math. Comput. Simulation, 79(4):1270–1283, December 2008. URL https://doi.org/10.1016/j.matcom.2008.03.016. [preprint]
. One-dimensional electromagnetic relativistic PIC-hydrodynamic hybrid simulation code H-VLPL (hybrid virtual laser plasma lab). Comput. Phys. Comm., 179(6):371–379, September 2008. URL https://doi.org/10.1016/j.cpc.2008.03.008. [preprint]
. Geometric integration methods that unconditionally contract volume. Appl. Numer. Math., 58(8):1103–1112, August 2008. URL https://doi.org/10.1016/j.apnum.2007.04.018. [preprint]
. A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems. J. Comput. Phys., 227(16):7701–7719, August 2008. URL https://doi.org/10.1016/j.jcp.2008.04.024. [preprint]
. Numerical Simulation of Relativistic Laser-Plasma Interaction. Dissertation, Heinrich-Heine Universität Düsseldorf, July 2008. [preprint]
. Rational approximation to trigonometric operators. BIT, 48(2):215–229, June 2008. URL https://doi.org/10.1007/s10543-008-0185-9. [preprint]
2007
. A note on a sum associated with the generalized hypergeometric function. Appl. Math. Comput., 187(2):1527–1534, April 2007. URL https://doi.org/10.1016/j.amc.2006.09.073.
. Verified integration of linear $n$th order ODEs using large steps. Appl. Math. Comput., 186(1):879–890, March 2007. URL https://doi.org/10.1016/j.amc.2006.08.033.
. On Taylor model based integration of ODEs. SIAM J. Numer. Anal., 45(1):236–262, January 2007. URL https://doi.org/10.1137/050638448.
2006
. On the use of the Gautschi-type exponential integrator for wave equations. In A. B. de Castro, D. Gómez, P. Quintela, and P. Salgado, editors, Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2005, pages 557–563, September 2006. Springer, Berlin, Heidelberg. [preprint]
. Numerical solution of nonlinear wave equations in stratified dispersive media. J. Comput. Phys., 216(1):138–152, July 2006. URL https://doi.org/10.1016/j.jcp.2005.11.024. [preprint]
. A higher-order PDE-based image registration approach. Numer. Linear Algebra Appl., 13(5):399–417, June 2006. URL https://doi.org/10.1002/nla.467.
. Error analysis of exponential integrators for oscillatory second-order differential equations. J. Phys. A, 39(19):5495–5507, April 2006. URL https://doi.org/10.1088/0305-4470/39/19/S10. [preprint]
. Explicit integrators of Rosenbrock-type. Oberwolfach Rep., 3(2):1107–1110, April 2006. URL https://doi.org/10.4171/OWR/2006/18. [preprint]
. Exponential integrators for highly oscillatory differential equations. Oberwolfach Rep., 3(1):868–869, March 2006. URL https://doi.org/10.4171/OWR/2006/14.
. Preconditioning Lanczos approximations to the matrix exponential. SIAM J. Sci. Comput., 27(4):1438–1457, January 2006. URL https://doi.org/10.1137/040605461. [preprint]
2005
. Geometric integration methods that preserve Lyapunov functions. BIT, 45(4):709–723, December 2005. URL https://doi.org/10.1007/s10543-005-0034-z. [preprint]
. A note on the Gautschi-type method for oscillatory second-order differential equations. Numer. Math., 102(1):61–66, November 2005. URL https://doi.org/10.1007/s00211-005-0639-9. [preprint]
. Explicit exponential Runge–Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal., 43(3):1069–1090, September 2005. URL https://doi.org/10.1137/040611434. [preprint]
. Subspace extraction for matrix functions. Technical Report, Case Western Reserve University, September 2005.
. Exponential Runge–Kutta methods for parabolic problems. Appl. Numer. Math., 53(2-4):323–339, May 2005. URL https://doi.org/10.1016/j.apnum.2004.08.005. [preprint]
. On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations. Numer. Math., 100(1):71–89, March 2005. URL https://doi.org/10.1007/s00211-005-0583-8. [preprint]
2004
. A complex mean value form for curves. Numer. Algorithms, 37(1-4):337–343, December 2004. URL https://doi.org/10.1023/B:NUMA.0000049479.71077.08.
2003
. ACETAF: a software package for computing validated bounds for Taylor coefficients of analytic functions. ACM Trans. Math. Software, 29(3):263–286, September 2003. URL https://doi.org/10.1145/838250.838252.
. On Magnus integrators for time-dependent Schrödinger equations. SIAM J. Numer. Anal., 41(3):945–963, June 2003. URL https://doi.org/10.1137/S0036142902403875. [preprint]
. A generalized $W$-transformation for constructing symplectic partitioned Runge–Kutta methods. BIT, 43(1):57–66, March 2003. URL https://doi.org/10.1023/A:1023676219630. [preprint]
2002
. Exponentielle Integratoren als Lange-Zeitschritt-Verfahren für oszillatorische Differentialgleichungen zweiter Ordnung. Dissertation, Heinrich-Heine Universität Düsseldorf, July 2002. [preprint]
. Mathematik fürs Leben am Beispiel der Computertomographie. Math. Semesterber., 49(1):95–113, June 2002. URL https://doi.org/10.1007/s005910200042. [preprint]
2001
. The mean value form for complex analytic functions. Computing, 67(3):255–268, October 2001. URL https://doi.org/10.1007/s006070170008.
. Validated bounds for Taylor coefficients of analytic functions. Reliab. Comput., 7(4):307–319, August 2001. URL https://doi.org/10.1023/A:1011411307404.
. Geometric series bounds for the local errors of Taylor methods for linear $n$-th order ODEs. In G. Alefeld, J. Rohn, S. Rump, and T. Yamamoto, editors, Symbolic Algebraic Methods and Verification Methods (Dagstuhl, 1999), pages 183–193. Springer, Vienna, March 2001.
1999
. Exponential integrators for quantum-classical molecular dynamics. BIT, 39(4):620–645, December 1999. URL https://doi.org/10.1023/A:1022335122807. [preprint]
. A Gautschi-type method for oscillatory second-order differential equations. Numer. Math., 83(3):403–426, September 1999. URL https://doi.org/10.1007/s002110050456. [preprint]
. An enclosure method for the solution of linear ODEs with polynomial coefficients. Numer. Funct. Anal. Optim., 20(7-8):779–803, September 1999. URL https://doi.org/10.1080/01630569908816923.
. A bunch of time integrators for quantum/classical molecular dynamics. In P. Deuflhard, J. Hermans, B. Leimkuhler, A. E. Mark, S. Reich, and R. D. Skeel, editors, Computational Molecular Dynamics: Challenges, Methods, Ideas (Proceedings of the 2nd International Symposium on Algorithms for Macromolecular Modelling, Berlin, 1997), volume 4 of Lecture Notes in Computational Science and Engineering, pages 421–432, January 1999. Springer, Berlin. [preprint]
1998
. A numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems. In P. Arbenz, M. Paprzycki, A. Sameh, and V. Sarin, editors, High Performance Algorithms for Structured Matrix Problems, volume 2 of Advances in the Theory of Computation and Computational Mathematics, pages 127–148. Nova Sci. Publ., Commack, NY, December 1998. [preprint]
. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput., 19(5):1552–1574, September 1998. URL https://doi.org/10.1137/S1064827595295337. [preprint]
. Error analysis of Krylov methods in a nutshell. SIAM J. Sci. Comput., 19(2):695–701, March 1998. URL https://doi.org/10.1137/S1064827595290450. [preprint]
. Enclosing solutions of an inverse Sturm–Liouville problem for an impedance. J.UCS, 4(2):178–192, February 1998. SCAN-97 (Lyon).
1997
. Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations. J. Comput. Appl. Math., 86(1):219–236, November 1997. URL https://doi.org/10.1016/S0377-0427(97)00157-X. Special issue dedicated to William B. Gragg (Monterey, CA, 1996). [preprint]
. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal., 34(5):1911–1925, October 1997. URL https://doi.org/10.1137/S0036142995280572. [preprint]
1996
. A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems. Numer. Algorithms, 11(1-4):181–187, December 1996. URL https://doi.org/10.1007/BF02142495. Orthogonal polynomials and numerical analysis (Luminy, 1994).
. Optimized look-ahead recurrences for adjacent rows in the Padé table. BIT, 36(2):264–285, June 1996. URL https://doi.org/10.1007/BF01731983.
1995
. The stability of inversion formulas for Toeplitz matrices. Linear Algebra Appl., 223/224:307–324, July 1995. URL https://doi.org/10.1016/0024-3795(94)00218-3. Special issue honoring Miroslav Fiedler and Vlastimil Pták.
. Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems. Numer. Math., 70(2):181–227, March 1995. URL https://doi.org/10.1007/s002110050116.
. Preconditioned Krylov subspace methods for Lyapunov matrix equations. SIAM J. Matrix Anal. Appl., 16(1):156–171, January 1995. URL https://doi.org/10.1137/S0895479892239238.
1994
. Enclosing solutions of an inverse Sturm–Liouville problem with finite data. Computing, 53(3-4):379–395, September 1994. URL https://doi.org/10.1007/BF02307388. International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993).
. Look-ahead Levinson- and Schur-type recurrences in the Padé table. Electron. Trans. Numer. Anal., 2:104–129 (electronic only), September 1994. URL http://etna.mcs.kent.edu/vol.2.1994/pp104-129.dir/pp104-129.pdf.
. On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Numer. Linear Algebra Appl., 1(4):403–420, July 1994. URL https://doi.org/10.1002/nla.1680010406.
1993
. Experiments with Krylov subspace methods on a massively parallel computer. Appl. Math., 38(6):440–451, 1993.
. A Chebyshev-like semi-iteration for inconsistent linear systems. Electron. Trans. Numer. Anal., 1(Dec.):89–103 (electronic only), December 1993. URL http://etna.mcs.kent.edu/vol.1.1993/pp89-103.dir/pp89-103.pdf.
. Ein Einschließungsverfahren für das inverse Dirichletproblem. Dissertation, Universität Karlsruhe, June 1993.
1992
. Inclusion of eigenvalues and eigenfunctions of the Sturm–Liouville problem. In L. Atanassova and J. Herzberger, editors, Computer Arithmetic and Enclosure Methods, pages 401–408. North-Holland, Amsterdam, November 1992.