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math.NA2025
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…
math.NA2025
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…
math.DG2025
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…