Publications and events
Upcoming Events:
9th NAI Workshop: Numerical Analysis of Evolution Equations (Innsbruck; November 08 - 11, 2016)
Publications:
K. Schratz (joint with A. Ostermann): Derivation of a low regularity exponential-type integrator for semilinear Schrödinger equations with polynomial nonlinearities. To appear in Oberwolfach Reports (2016) DOI 10.4171/OWR/2016/18
M. Caliari, P. Kandolf, A. Ostermann, S. Rainer: The Leja method revisited: backward error analysis for the matrix exponential, SIAM Journal on Scientific Computation, 38 (3), A1639-A1661(2016) (Eprint, arXiv, code) DOI 10.1137/15:1027620
V.T. Luan, A. Ostermann: Parallel exponential Rosenbrock methods. Comput. Math. Appl. 71, 1137-1150 (2016) DOI 10.1016/j.camwa.2016.01.020
A. Ostermann: Exponential integrators. In: Encyclopedia of Applied and Computational Mathematics (B. Engquist, ed.), Springer-Verlag, Berlin Heidelberg (2015), 468-472. ISBN 978-3-540-70528-4 (print); 978-3-540-70529-1 (ebook) DOI 10.1007/978-3-540-70529-1_112
D.A. Hipp, M. Hochbruck, A. Ostermann: An exponential integrator for non-autonomous parabolic problems. Electron. Trans. Numer. Anal. 41, 497-511 (2014)
A. Koskela, A. Ostermann: A moment-matching Arnoldi iteration for linear combinations of φ functions, SIAM J. Matrix Anal. & Appl. 35, 1344-1363 (2014)
DOI 10.1137/130945156
P. Kandolf, A. Ostermann, S. Rainer: A residual based error estimate for Leja interpolation of matrix functions, Linear Algebra and its Applications, 456 (0), 157-173 (2014) (Eprint)
A. Ostermann, Exponential integrators. To appear in: Encyclopedia of Applied and Computational Mathematics, Springer-Verlag, Berlin Heidelberg (2014)
V.T. Luan, A. Ostermann, Stiff order conditions for exponential Runge-Kutta methods of order five. To appear in: Proceedings of the Fifth International Conference on High Performance Scientific Computing, 2012, Hanoi, Vietnam
M. Caliari, P. Kandolf, A. Ostermann, S. Rainer, Comparison of software for computing the action of the matrix exponential. BIT Numer. Math. 54, 113-128 (2014) DOI 10.1007/s10543-013-0446-0
V.T. Luan, A. Ostermann, Explicit exponential Runge-Kutta methods of high order for parabolic problems. J. Comput. Appl. Math. 256, 168-179 (2014) DOI 10.1016/j.cam.2013.07.027 reprinted in: J. Comput. Appl. Math. 262, 361-372 (2014) DOI 10.1016/j.cam.2014.01.001
V.T. Luan, A. Ostermann, Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons. J. Comput. Appl. Math. 255, 417-431 (2014) DOI 10.1016/j.cam.2013.04.041
V.T. Luan, A. Ostermann, Exponential B-series: the stiff case. SIAM J. Numer. Anal. 51, 3431-3445 (2013) DOI 10.1137/130920204
L. Einkemmer, A. Ostermann, Exponential integrators on graphic processing units. In: High Performance Computing and Simulation (HPCS), 2013 International Conference on, IEEE (2013), 490-496. ISBN 978-1-4799-0836-3 (print) DOI 10.1109/HPCSim.2013.6641458
M. Caliari, A. Ostermann, S. Rainer, Meshfree exponential integrators. SIAM J. Sci. Comput. 35, A431-A452 (2013) DOI 10.1137/100818236
M. Caliari, A. Ostermann, S. Rainer, A meshfree splitting method for soliton dynamics in nonlinear Schrödinger equations. In: Meshfree Methods for Partial Differential Equations VI (M. Griebel and M.A. Schweitzer, eds.), Lecture Notes in Computational Science and Engineering 89, Springer, Berlin (2013), 127-139. ISBN 978-3-642-32978-4 DOI 10.1007/978-3-642-32979_8
A. Koskela, A. Ostermann, Exponential Taylor methods: analysis and implementation. Comput. Math. Appl. 65, 487-499 (2013) DOI 10.1016/j.camwa.2012.06.004
D.A. Hipp, M. Hochbruck, A. Ostermann, Exponential integrators for parabolic problems with time dependent coefficients. Oberwolfach Reports 9, 3602-3606 (2012) DOI 10.4171/OWR/2012/60
M. Hochbruck, A. Ostermann, Exponential multistep methods of Adams-type. BIT Numer. Math. 51, 889-908 (2011) DOI 10.1007/s10543-011-0332-6
M. Caliari, A. Ostermann, S. Rainer, Meshfree integrators. Oberwolfach Reports 8, 883-885 (2011) DOI 10.4171/OWR/2011/16
A. Ostermann, Exponential time integration of evolution equations. In: ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010 (T. Simos, G. Psihoyios, C. Tsitouras, eds.), AIP Conf. Proc. 1281 (2010), 11-14, ISBN 978-0-7354-0831-9, DOI 10.1063/1.3497888
M. Hochbruck, A. Ostermann, Exponential integrators. Acta Numerica 19, 209-286 (2010) DOI 10.1017/S0962492910000048
M. Hochbruck, M. Hönig, A. Ostermann, A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems. Inverse Problems 25, 075009 (2009) DOI 10.1088/0266-5611/25/7/075009
M. Hochbruck, M. Hönig, A. Ostermann, Regularization of nonlinear ill-posed problems by exponential integrators. Mathematical Modelling and Numerical Analysis (M2AN) 43, 707-720 (2009) DOI 10.1051/m2an/2009021
M. Hochbruck, A. Ostermann, J. Schweitzer , Exponential Rosenbrock-type methods. SIAM J. Numer. Anal. 47, 786-803 (2009) DOI 10.1137/080717717
M. Caliari, A. Ostermann, Implementation of exponential Rosenbrock-type integrators. Applied Numerical Math. 59, 568-581 (2009) DOI 10.1016/j.apnum.2008.03.021
A. Ostermann, M. Van Daele, Positivity of exponential Runge-Kutta methods. BIT Numer. Math. 47, 419-426 (2007) DOI 10.1007/s10543-007-0124-1
M. Hochbruck, A. Ostermann, Exponential integrators of Rosenbrock-type. Oberwolfach Reports 3, 1107-1110 (2006) DOI 10.4171/OWR/2006/18
A. Ostermann, M. Thalhammer, Positivity of exponential multistep methods. In: Numerical Mathematics and Advanced Applications (A. Bermúdez et al., eds.), Proceedings of Enumath 2005, Springer, Berlin (2006), 564-571. ISBN 978-3540342878
A. Ostermann, M. Thalhammer, W. Wright, A class of explicit exponential general linear methods. BIT Numer. Math. 46, 409-431 (2006) DOI 10.1007/s10543-006-0054-3
C. González, A. Ostermann, M. Thalhammer, A second-order Magnus-type integrator for non-autonomous parabolic problems. J. Comput. Appl. Math. 189, 142-156 (2006) DOI 10.1016/j.cam.2005.04.036
M. Hochbruck, A. Ostermann, Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43, 1069-1090 (2005) DOI 10.1137/040611434
M. Hochbruck, A. Ostermann, Exponential Runge-Kutta methods for parabolic problems. Applied Numerical Math. 53, 323-339 (2005) DOI 10.1016/j.apnum.2004.08.005