Seminar

(with C. L. Ellison, J. W. Burby, M. Kraus, H. Qin and W. M. Tang)

Variational integrators, or discretized action principles, provide a systematic way to derive symplectic integrators.  For degenerate Lagrangians, however, an issue arises: if not carefully constructed, the discretized action can lead to multistep methods, discrete equations of higher order than the original ODEs. For symplectic maps, multistep methods can lead to parasitic instabilities. We have devised a method of testing for multistep methods, based on the rank of the discrete Hessian. We show two examples of problems with degenerate Lagrangians, namely magnetic field line flow and the guiding center equations of plasma physics.