8 papers
Post-processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds
Adrien Busnot Laurent, Sébastien Macé
In this work, we propose a novel intrinsic approach to the approximation of ergodic SDEs on Riemannian manifolds, which include Riemannian Langevin dynamics. In opposition to the s…
The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods
Adrien Busnot Laurent, Hans Munthe-Kaas, Venkatesh G. S
Aromatic Butcher series were successfully introduced for the study and design of numerical integrators that preserve volume while solving differential equations in Euclidean spaces…
Aromatic and clumped multi-indices: algebraic structure and Hopf embeddings
Zhicheng Zhu, Adrien Busnot Laurent
Butcher forests extend naturally into aromatic and clumped forests and play a fundamental role in the numerical analysis of volume-preserving methods. The design of general volume-…
Derivation of optimal stochastic Runge-Kutta methods with exotic and decorated Butcher series for the weak integration of stochastic dynamics
Adrien Busnot Laurent, Kristian Debrabant, Anne Kværnø
The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The ori…
Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs
Charles-Edouard Bréhier, Adrien Busnot Laurent, Arnaud Debussche +1
For a class of ergodic parabolic semilinear stochastic partial differential equations (SPDEs) with gradient structure, we introduce a preconditioning technique and design high-orde…
High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods
Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet
We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In o…
Butcher series for Hamiltonian Poisson integrators through symplectic groupoids
Adrien Busnot Laurent, Oscar Cosserat
We exhibit a new pre-Lie algebra in the framework of symplectic groupoids and, in turn, use Butcher trees to compute the Taylor series of a solution of a Hamilton-Jacobi equation o…
Control theory and splitting methods
Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…