# GDMSeminar: Abstracts of the Talks (2021/15)

**David Martin de Diego** (ICMAT, Madrid)

*Geometric integration and discrete variational calculus: some new developments*

Tuesday, August 31, 2021, 15:00 GMT

**Abstract**: This talk will have two different parts. The first one will give a motivation to the importance of geometric integration and, in particular, to the discrete variational calculus for the numerical integration of continuous systems of differential equations with some preservation properties. In the second part, two recent results of the author and his collaborators will be reviewed. One on the use of retraction maps for the geometric derivation of symplectic integrators and how classical techniques of symplectic geometry are useful in their derivation. The last result to be discussed will be a recent derivation of an iterative method for discrete variational methods appropriate for boundary value problems. More concretely, we explore a parallelization strategy that leverages the power of multicore CPUs and GPUs (graphics cards). We study this parallel method for first-order and second-order Lagrangians and we illustrate its excellent behavior in some interesting applications, namely Zermelo’s navigation problem, a fuel-optimal navigation problem, and an interpolation problem... all this if time allows (of course :) )