Mathematics – Numerical Analysis
Scientific paper
2005-08-18
Mathematics
Numerical Analysis
30 pages, 7 figures
Scientific paper
We introduce generalized Galerkin variational integrators, which are a natural generalization of discrete variational mechanics, whereby the discrete action, as opposed to the discrete Lagrangian, is the fundamental object. This is achieved by approximating the action integral with appropriate choices of a finite-dimensional function space that approximate sections of the configuration bundle and numerical quadrature to approximate the integral. We discuss how this general framework allows us to recover higher-order Galerkin variational integrators, asynchronous variational integrators, and symplectic-energy-momentum integrators. In addition, we will consider function spaces that are not parameterized by field values evaluated at nodal points, which allows the construction of Lie group, multiscale, and pseudospectral variational integrators. The construction of pseudospectral variational integrators is illustrated by applying it to the (linear) Schrodinger equation. G-invariant discrete Lagrangians are constructed in the context of Lie group methods through the use of natural charts and interpolation at the level of the Lie algebra. The reduction of these G-invariant Lagrangians yield a higher-order analogue of discrete Euler-Poincare reduction. By considering nonlinear approximation spaces, spatio-temporally adaptive variational integrators can be introduced as well.
No associations
LandOfFree
Generalized Galerkin Variational Integrators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized Galerkin Variational Integrators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Galerkin Variational Integrators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-365718