Leapfrog time-stepping for Hermite methods
This work provides a novel high-order time-stepping scheme for wave equations, benefiting computational scientists needing accurate and efficient simulations.
The paper introduces Hermite-leapfrog methods for first-order wave systems, achieving high-order accuracy and conservation properties in one dimension, with stability and convergence proven both analytically and numerically. GPU implementations demonstrate efficiency.
We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors. The new schemes stagger field variables in both time and space and are high-order accurate. We provide a detailed description of the method and demonstrate that the method conserves variable quantities in one-space dimension. Higher dimensional versions of the method are constructed via a tensor product construction. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.