83 citations · 99 across the 6 of their papers we have counts for
6 papers
The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods
Adrien Busnot Laurent, Hans Munthe-Kaas, Venkatesh G. S
Aromatic Butcher series were successfully introduced for the study and design of numerical integrators that preserve volume while solving differential equations in Euclidean spaces…
A short proof of Isserlis' theorem
Hans Z. Munthe-Kaas, Olivier Verdier, Gilles Vilmart
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
Geometric integration on symmetric spaces
Hans Munthe-Kaas
We consider geometric numerical integration algorithms for differential equations evolving on symmetric spaces. The integrators are constructed from canonical operations on the sym…
Algebraic aspects of connections: from torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials
M. J. H. Al-Kaabi, K. Ebrahimi-Fard, D. Manchon +1
Understanding the algebraic structure underlying a manifold with a general affine connection is a natural problem. In this context, A. V. Gavrilov introduced the notion of framed L…
What is a post-Lie algebra and why is it useful in geometric integration
Charles Curry, Kurusch Ebrahimi-Fard, Hans Munthe-Kaas
We explain the notion of a post-Lie algebra and outline its role in the theory of Lie group integrators.
On the Hopf Algebraic Structure of Lie Group Integrators
H. Z. Munthe-Kaas, W. M. Wright
A commutative but not cocommutative graded Hopf algebra $\Hn$, based on ordered rooted trees, is studied. This Hopf algebra generalizes the Hopf algebraic structure of unordered ro…