Geometric Exponential Integrators
Provides more efficient geometric integrators for Hamiltonian PDEs, benefiting computational scientists needing long-time stable simulations.
The paper constructs exponential integrators for semilinear Poisson systems that preserve either the Poisson structure or energy, demonstrating better long-time stability than non-geometric integrators and higher computational efficiency than traditional symplectic or energy-preserving methods.
In this paper, we consider exponential integrators for semilinear Poisson systems. Two types of exponential integrators are constructed, one preserves the Poisson structure, and the other preserves energy. Numerical experiments for semilinear Possion systems obtained by semi-discretizing Hamiltonian PDEs are presented. These geometric exponential integrators exhibit better long time stability properties as compared to non-geometric integrators, and are computationally more efficient than traditional symplectic integrators and energy-preserving methods based on the discrete gradient method.