5 papers
A Geometric Approach to Structure-Preserving Integrators for Mechanical Systems
Viyom Vivek, David Martin de Diego, Ravi N. Banavar
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting the…
Jacobi equation for field theories and a geometric variational description of dissipation
David Martin de Diego, Najma Mosadegh
In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian on a -cosymp…
Momentum-based gradient descent methods for Lie groups
Cédric M. Campos, David MartÃn de Diego, José Torrente
Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well-established momentum-descent methods for opti…
Numerical Integrators for Mechanical Systems on Lie Groups
Viyom Vivek, David Martin de Diego, Ravi N Banavar
Retraction maps are known to be the seed for all numerical integrators. These retraction maps-based integrators can be further lifted to tangent and cotangent bundles, giving rise…
Retraction maps: A seed of geometric integrators. Part II: Symmetry and reduction
MarÃa Barbero Liñán, Juan Carlos Marrero, David MartÃn de Diego
In this paper we use retraction and discretization maps (see [Barbero Liñán and MartÃn de Diego, 2022]) as a tool for deriving in a systematic way numerical integrators preservi…