Geometric numerical integration on Lie groups
[…] we develop a higher order symmetric partitioned Runge–Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge–Kutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize the method to a symmetric partitioned Runge–Kutta (SPRK) scheme. Furthermore, we derive a set of coefficients for convergence order 4. The SPRK integration method can be used, for example, in simulations of quantum field theories. Finally, we compare the new SPRK scheme numerically with the Störmer–Verlet scheme, one of the state-of-the-art schemes used in this subject.y allow for larger step-sizes than the Leapfrog method
M. Wandelt, M. Günther, F. Knechtli, M. Striebel, Symmetric partitioned Runge–Kutta methods for differential equations on Lie groups, Appl. Numer. Math. 62 (12), 2012, 1740–1748.
2009 -2012
| Wuppertal | University of Wuppertal, Applied and Computational Mathematics Postdoctoral Fellow Prof. Dr. M. Günther |
| DFG SFB/TR-Project 55 „Hadron Physics from Lattice QCD„ |
