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Center for Nonlinear Studies |
The behavior exhibited by dynamical systems is strongly influenced by the presence or absence of conserved quantities. When numerically modeling these systems, obtaining the correct long-term qualitative behavior requires retaining conservation laws in the numerical update rule. One method for constructing conservative numerical models is to derive the algorithm from a variational principle discretely analogous to the one used when deriving the dynamical equations. This technique, called "variational integration," has wide-reaching implications for the central models used to describe astrophysical and laboratory plasmas. This presentation will highlight algorithmic advances in plasma physics stemming from the application of variational integrators. In the ODE context, the Lorentz, force system illustrates a conventional application of variational integrators, while the non-cannonical Hamiltonian description of guiding center test particles requires extending the variational integrator theory to degenerate Lagrangian systems. in the PDE context, variational integrators may be deployed to achieve numerically reconnectionless idea MHD and multisymplectic current-conserving particle-in-cell simulations of Maxwell-Vlasov dynamics. Overall, variational integration guides the development of new, well-behaved algorithms that are unlikely to emerge from consideration of the new differential equations alone.
Host: Jerome Daligault, T-5