Overall Objectives
Scientific Foundations
Application Domains
New Results
Other Grants and Activities


Major publications by the team in recent years

G. Andreoiu, E. Faou.
Complete asymptotics for shallow shells, in: Asymptotic analysis, 2001, vol. 25, p. 239-270.
A. Aubry, P. Chartier.
On improving the convergence of Radau IIA methods when applied to index-2 DAEs, in: SIAM Journal on Numerical Analysis, 1998, vol. 35, no 4, p. 1347-1367.
A. Aubry, P. Chartier.
Pseudo-symplectic Runge-Kutta methods, in: BIT, 1998, vol. 38, p. 439–461.
F. Castella.
From the von Neumann equation to the Quantum Boltzmann equation in a deterministic framework, in: J. Stat. Phys., 2001, vol. 104–1/2, p. 387–447.
F. Castella.
Propagation of space moments in the Vlasov-Poisson Equation and further results, in: Ann. I.H.P., Anal. NonLin., 1999, vol. 16–4, p. 503–533.
R. Chan, P. Chartier, A. Murua.
Post-projected Runge-Kutta methods for index-2 differential-algebraic equations, in: Applied Numerical Mathematics, 2002, vol. 42, no 1-3, p. 77-94.
M. Dauge, I. Djurdjevic, E. Faou, A. Roessle.
Eigenmode asymptotics in thin elastic plates, in: J. Math. Pures Appl., 1999, vol. 78, p. 925-954.
E. Faou.
Elasticity on a thin shell: Formal series solution, in: Asymptotic analysis, 2002, vol. 31, p. 317-361.

Publications of the year

Articles in International Peer-Reviewed Journal

N. B. Abdallah, F. Castella, F. Fendt, F. Méhats.
The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire, in: SIAM Journal on Applied Mathematics, 2009, vol. 69, no 4, p. 1162–1173.
F. Castella, P. Chartier, S. Descombes, G. Vilmart.
Splitting methods with complex times for parabolic equations, in: BIT Numerical Mathematics, 2009, vol. 49.
F. Castella, P. Chartier, E. Faou.
An averaging technique for highly-oscillatory Hamiltonian problems, in: SIAM J. Numer. Anal., 2009, vol. 47, p. 2808-2837.
F. Castella, G. Dujardin.
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation, in: Math. Mod. An. Num., 2009, vol. 43, no 4, p. 651–676.
F. Castella, G. Dujardin, B. Sericola.
Moments analysis in Markov reward models, in: Methodology and Computing in Applied Probability, 2009.
P. Chartier, E. Darrigrand, E. Faou.
A Fast Multipole Method for Geometric Numerical Integrations of Hamiltonian Systems, in: BIT Numerical Analysis, 2009, Under minor revision for BIT Numerical Analysis.
P. Chartier, E. Hairer, G. Vilmart.
Algebraic structures of B-series, in: Foundations of Computational Mathematics, 2009, Under minor revision for FOCM.
P. Chartier, A. Murua.
An algebraic theory of order, in: M2AN Math. Model. Numer. Anal., 2009, vol. 43.
P. Chartier, J.-M. Sanz-Serna, A. Murua.
Higher-order averaging, formal series and numerical integration I: B-series, in: Foundations of Computational Mathematics, 2009, submitted.
A. Crudu, A. Debussche, O. Radulescu.
Hybrid stochastic simplifications for multiscale gene networks, in: BMC Systems Biology, 2009, vol. 89, no 3.
A. de Bouard, A. Debussche.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise, in: Elec. Journal Proba., 2009, vol. 31, no 58.
A. Debussche.
Weak approximation of stochastic partial differential equations: the nonlinear case, in: Math. Comp., 2009, to appear.
A. Debussche, E. Faou.
Modified energy for split-step methods applied to the linear Schrödinger equation., in: SIAM J. Numer. Anal., 2009, vol. 47, p. 3705–3719.
A. Debussche, J. Printems.
Weak order for the discretization of the stochastic heat equation, in: Math. Comp., 2009, vol. 266, no 78, p. 845-863.
A. Debussche, J. Vovelle.
Long-time behavior in scalar conservation laws, in: Diff. Int. Eq., 2009, vol. 22, no 3-4, p. 225-238.
E. Faou.
Analysis of splitting methods for reaction-diffusion problems using stochastic calculus., in: Math. Comp., 2009, vol. 78, p. 1467–1483.
E. Faou, B. Grébert, E. Paturel.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization, in: Numer. Math., 2009, to appear.
E. Faou, B. Grébert, E. Paturel.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part II: Abstract splitting, in: Numer. Math., 2009, to appear.
E. Faou, V. Gradinaru, C. Lubich.
Computing semi-classical quantum dynamics with Hagedorn wavepackets, in: SIAM J. Sci. Comp., 2009, vol. 31, p. 3027–3041.
E. Faou, T. Lelièvre.
Conservative stochastic differential equations: Mathematical and numerical analysis, in: Math. Comp., 2009, vol. 78, p. 2047–2074.

Other Publications

N. Champagnat, C. Chipot, E. Faou.
A probabilistic approach of high-dimensional least-squares approximations, 2009, Preprint.
E. Faou, B. Grébert.
Quasi invariant modified Sobolev norms for semi linear reversible PDEs., 2009, Preprint.
E. Faou, B. Grébert.
Resonances in long time integration of semi linear Hamiltonian PDEs., 2009, Preprint.

References in notes

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On the necessity of negative coefficients for operator splitting schemes of order higher than two, in: Appl. Num. Math., 2005, vol. 54, p. 23–37.
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J. C. Butcher.
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Two Hopf algebras of trees interacting, 2008
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Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, p. 996–1007.
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A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, p. 355–368.
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On variational approximations in quantum molecular dynamics, in: Math.   Comp., 2009, to appear.
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