Numerical methods for ordinary differential equations
and partial differential equations and in particular: geometric
numerical integration.
Krylov subspace and preconditioning methods for the
numerical solution of large linear systems. Methods for the
approximation of the matrix exponential.
Waveform Relaxation methods and Krylov subspace
methods for
linear systems of ODEs.
Numerical optimization on maniflods: gradient and
descent methods.
List of publications:
Reports
(with B. Owren and Y. Sun), The minimal stage, energy-preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged vector Fiels method. arXiv:1203.3252v1.
(with F. Grimm, R.I. McLachlan, D.I. McLaren, D.R.J. O'Neale,
B. Owren, G.R.W. Quispel)
Preserving energy resp. dissipation in numerical PDEs, using the
"average vector field" method.
NTNU reports, Numerics No 7/09. Submitted.
(with B. Kometa) Order conditions for the semi-Lagrangian
exponential integrators. NTNU reports,
Numerics No.4/09.
Articles in Journals
SL E. Celledoni and B. K. Kometa Semi-Lagrangian multistep methods for
index 2 differential algebraic systems. NTNU reports,
Numerics No 3/10. J. of Comp. Phys. 230, pp 3413-3429 (2011).
EP (with RI McLachlan, B Owren, GWR Quispel )
On conjugate B-series and their geometric structure
NTNU reports, Numerics No 2/10. JNAIAM, vol 5, pp 85-94, (2010).
GPDE (with N. Säfström)
Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions.
CMAME, 199(45-48), pp. 2813-2819, article.
EP (with R. McLachlan, B. Owren, R. Quispel)
Energy-preserving integrators and the structure of B-series.
J. of FoCM, vol 10, pp 673-693.
Online.
RB (with A. Zanna) FRB-FORTRAN routines for the exact
computation of free rigid body motions, ACM ToMS, vol 37 nr. 2
(2010). See also
NTNU reports,
Numerics No.7/08.
SL (with B. K. Kometa)
Semi-Lagrangian exponential integrators for convection dominated problems.
Journal of Scientific Computing, vol. 41, issue
1, 139-164, (2009). See also
NTNU report nr 9 (2008).
EP (with R. McLachlan, D. McLaren, B. Owren, R. Quispel and
W. Wright)
Energy-preserving Runge-Kutta methods.
M2AN (Mathematical Modelling and Numerical Analysis), vol 43 (4),
645-649, (2009). See also
NTNU reports,
Numerics No.6/08.
P (with T. Kvamsdal) Parallelization in time for
thermo-viscoplastic problems in extrusion of aluminium,
Journal of Numerical Methods in Engineering, vol. 79, 576-598, (2009).
Revised version, (January 2009).
RB (with F. Fassó, N. Säfsröm and A. Zanna) The exact
computation of the free rigid body motion and its use in splitting methods,
SIAM J. Sci. Comp. vol 30 issue 4, pp. 2084-2112, (2008).
LGM (with S. Fiori) Descent methods for optimization on
homogenous manifolds, J. of Mathematics and Computers in
Simulation, 79 pp. 1298-1323, (2008).
GPDE (with D. Cohen and B. Owren) Symmetric exponential integrators
for the cubic Schrödinger equation,
J. of FoCM 8, n 3, 303--317, (2008).
RB (with N. Säfström) Efficient time-symmetric simulation of
torqued rigid bodies using Jacobi elliptic functions, Journal
of Physics A, 39,pp.5463-5478, (2006).
RB (with N. Säfström) A symmetric splitting method for rigid
body dynamics, Journal of Modeling Identification and Control
(A Norwegian Research bulletin), 27, no. 2, 95--108, (2006).
SL Eulerian and Semi-Lagrangian schemes based on commutator free
exponential integrators, CRM Proceedings and Lecture notes, ISSN: 1065-8580, Vol. 39, (2005).
LGM (with S. Fiori) Neural Learning by Geometric Integration of
Reduced 'Rigid Body' Equations in J. CAM vol 172,
247-269, (2004).
LGM (with B. Owren) On the implementation of Lie group methods on the
Stiefel manifold,
Numerical Algorithms, vol. 32, no. 2-4, pp 163-183, (2003).
LGM (with A. Marthinsen and B. Owren) Commutator-free Lie gorup
methods, Future Generation Computer Systems, Volume/Issue: vol
19/3, pp 341 - 352, (2003).
LGM (with B. Owren) Lie group methods for rigid body dynamics and
time integration on manifolds, Comput.
meth. in Appl. Mech. and Eng., Vol 19, n. 3-4, pp 421-438, (2003).
LGM (with B. Owren) A class of intrinsic schemes
for orthogonal integration SIAM
J. Num. Anal. Vol. 40, n. 6, pp. 2069-2084, (2002).
LGM (with A. Iserles and S. P. Nørsett and B. Orel)
Complexity theory for Lie-group solvers, Journal of Complexity, Vol 18, n. 1, (2002).
ME (with A. Iserles) Methods for the approximation of the matrix
exponential in a Lie-algebraic setting, IMA Journal of
Numerical Analysis, Vol. 21, pp. 463-488, (2001).
GPDE A note on the numerical integration of the KdV equation via
isospectral deformations, Journal of Physics A:
Mathematical and General 34, 2205-2214, (2001).
ME (with A.
Iserles) Approximating the matrix exponential from a Lie
algebra to a Lie group, Math. Comp. 69, 1457-1480, (2000).
ME Discrete QMR and BCG in the numerical solution of
linear systems of ODEs, J. CAM 91 (1), (April 1998).
ME (with I. Moret) A Krylov projection method for systems of ODEs,
Appl. Num. Math. 24: 365-378, (August 1997).
ME: matrix exponential, GPDE: geometic PDEs, LGM:
Lie group methods, SL:semi-Lagrangian methods,
RB:rigid body dynamics, P: parallel methods,
EP: energy-preservation in numerical integrators.
Articles in Conference Proceedings
(with Owren and Sun) The minimal stage, energy-preserving Runge-Kutta method for polynomial Hamiltonian systems is the avereged vector field method, Oberwolfach reports 2011.
(with N. Saefstroem) An elastic rod model and its
Hamiltonian structure, AIP Conference Proceedings 2009;
vol. 1168, s. 1005-1008.
(with R.I. McLachlan, B. Owren and G.W.R. Quispel)
Structure of B-series for some classes of Geometric Integrators,
AIP Conference Proceedings 2009;
vol. 1168, s. 739-742.
(with R. McLachlan, D. McLaren, B. Owren, R. Quispel and
W. Wright)
Energy-preserving methods and B-series.
pdf
in 21st Nordic seminar in
Computational Mechanics, NSCM-21, T. Kvamsdal, K.M. Mathisen and B. Pettersen (Eds.), published by CIMNE, october 2008. ISBN: 978-84-96736-56-6
Semi-Lagrangian methods and new integrators for convection dominated problems Oberwolfach Reports march 2006
Exponential integrators for convection dominated problems Oberwolfach Reports april 2006
(with N. Saefstroem) A symmetric splitting method for rigid body dynamics, Proceedings of the SIMS 2005 Conference, Trondheim, October 13th-14th, 2005.
(with T. Kvamsdal) Parallel time solver for the transient Stokes problem In NSCM 17: Proceedings of the 17th Nordic Seminar in Computational Mechanics, Stockholm, Sweden, 15th-16th October 2004.
(with T. Kvamsdal) Parallelism in time for the solution of the time dependent Stokes problem In Proceedings of the International Conference on Parallel CFD, Gran Canary, Carary Island, Spain 24th-27th May 2004.
(with G. Johannessen and T. Kvamsdal
) Parallelization of a CFD code: the use of Aztec library in the
parallel numerical simulation of Extrusion of Aluminium in
Proceedings of the
Parallel CFD Conference (May 22-25, 2000),
Jenssen et al. editors, North - Holland, pp. 291--298.
Reports for the Norwegian Research Council
G. Gisler, E. Celledoni, T.U. Helgaker, T. Iversen, K.S. Jakobsen, C. Jones, A. Lipniacka, A. Lundervold, N.R.B. Olsen, K. De Smedt, J. Koster, G. Høst, 2010, The scientific case for eInfrastructure in Norway, published by the Norwegian Research Council, ISBN 978-82-12-02831-9.
G. Gisler, D. Bjørge, E. Celledoni, T.U. Helgaker, C. Jones, A. Lipniacka, A. Lundervold, S. Oepen, N.R.B. Olsen, with the assistance of J. Koster and G. Høst, 2011, Roadmap for the Norwegian eInfrastructure, published by the Norwegian Research Council, ISBN 978-82-12-03055-8.
Technical reports and other manuscripts
with K. Markova and B. Owren, Citti-Sarti model of perceptual
completion in roto-translational space. Numerical algorithm
development. NTNU report nr. 12, 2009.
Sulla risoluzione numerica delle equazioni di Navier-Stokes
tramite metodi di Krylov, Quad. Mat. n . 314, Dip. Sci. Mat. Università di Trieste (December 1993).
A comparison of Krylov subspace methods for systems
of ODEs, Quad. Mat. n. 317, Dip. Sci. Mat. Università di
Trieste. (January 1994)