Geometric Discretization of the EPDiff Equations
This work provides a geometric discretization framework for a class of infinite-dimensional systems, but it is an incremental extension of existing methods applied to a specific equation.
The paper develops a general geometric discretization method for infinite-dimensional systems and applies it to the EPDiff equation, extending prior work on incompressible Euler fluids. Numerical results for the one-dimensional EPDiff equation are presented.
The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for incompressible Euler fluids. Here this method is presented in a general case applicable to all, not only divergence-free, vector fields. Also, a different (pseudospectral) representation of the velocity field is used. We will apply this method to the one-dimensional EPDiff equation and present numerical results.