Asymptotic preservation of an exponential Euler method under Hamiltonian fast advection with multiple critical points

This paper establishes the asymptotic-preserving property of the exponential Euler method for stochastic reaction-diffusion-advection equations in two dimensions under fast Hamiltonian advection with multiple critical points. The analysis shows that as the advection speed increases, the dynamics effectively reduce to a stochastic partial differential equation defined on a noncompact metric graph. The key contribution is a rigorous strong convergence proof for the exponential Euler scheme in this limiting regime, addressing the challenges posed by multiple critical points in the Hamiltonian flow.