Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

This paper gives a review of integration algorithms for finite dimensional mechanical
systems that are based on discrete variational principles. The variational technique gives a …

The purpose of this paper is to survey some recent advances in variational integrators for
both finite dimensional mechanical systems as well as continuum mechanics. These …

It has been 16 years since Kang Feng passed away. It is our honor to publish the English
version of Symplectic Algorithm for Hamiltonian Systems, so that more readers can see the …

We describe a new class of asynchronous variational integrators (AVI) for nonlinear
elastodynamics. The AVIs are distinguished by the following attributes:(i) The algorithms …

This paper is concerned with modeling the dynamics of N articulated solid bodies
submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals …

The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …

This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian
structure of classical field theories with constraints. Our goal is to explore some of the …

Learning workable representations of dynamical systems is becoming an increasingly
important problem in a number of application areas. By leveraging recent work connecting …

We develop a method for reliable simulation of elastica in complex contact scenarios. Our
focus is on firmly establishing three parameter-independent guarantees: that simulations of …