Commutator-free Lie group methods

摘要

We propose a new format of Lie group methods which does not involve commutators and which uses a much lower number of exponentials than those proposed by Crouch and Grossman. By reusing flow calculations in different stages, the complexity is even further reduced. We argue that the new methods may be particularly useful when applied to problems on homogeneous manifolds with large isotropy groups, or when used for stiff problems. Numerical experiments verify these claims when applied to a problem on the orthogonal Stiefel manifold, and to an example arising from the semidiscretization of a linear inhomogeneous heat conduction problem.