Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the
purpose of explaining structure preserving numerical algorithms. Geometric structures …

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass
transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of …

Recent development of structure-preserving geometric particle-in-cell (PIC) algorithms for
Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop …

In this work, we consider the error estimates of some splitting schemes for the charged-
particle dynamics under a strong magnetic field. We first propose a novel energy-preserving …

This paper provides a first contribution to port-Hamiltonian modeling of district heating
networks. By introducing a model hierarchy of flow equations on the network, this work aims …

This paper discusses energy-conserving time-discretizations for finite element particle-in-
cell discretizations of the Vlasov–Maxwell system. A geometric spatially discrete system can …

In this article we apply a discrete action principle for the Vlasov–Maxwell equations in a
structure-preserving particle-field discretization framework. In this framework the finite …

We propose a low-rank tensor approach to approximate linear transport and nonlinear
Vlasov solutions and their associated flow maps. The approach takes advantage of the fact …

A method for machine learning and serving of discrete field theories in physics is developed.
The learning algorithm trains a discrete field theory from a set of observational data on a …

We develop structure-preserving reduced basis methods for a large class of nondissipative
problems by resorting to their formulation as Hamiltonian dynamical systems. With this …