From Efficient Symplectic Exponentiation of Matrices to Symplectic Integration of High-dimensional Hamiltonian Systems with Slowly Varying Quadratic Stiff Potentials

We propose a symplectic multiscale integrator for (possibly high-dimensional) Hamiltonian systems with slowly varying quadratic stiff potentials. This integrator is based on a generalization of the impulse method via a specific splitting of the vector field that guarantees uniform convergence. The proposed method does not require the exponentiation or diagonalization of the (possibly high-dimensional) stiffness matrix, but only needs $n+1$ matrix multiplication operations at each coarse time step for a preset fixed small number $n$.