Phase fitted variational integrators using interpolation techniques on non regular grids

Abstract

Multiscale reactive molecular dynamics J. Chem. Phys. 137, 22A525 (2012) Quantification of the specific membrane capacitance of single cells using a microfluidic device and impedance spectroscopy measurement Biomicrofluidics 6, 034112 (2012) Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme Phys. Plasmas 19, 084501 (2012) Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality J. Math. Phys. 52, 093706 (2011) Additional information on AIP Conf. Proc. Chair of Applied Dynamics, University of Erlangen-Nuremberg, GermanyAbstract. The possibility of deriving a high order variational integrator that utilizes intermediate nodes within one time interval time to approximate the action integral is investigated. To this purpose, we consider time nodes chosen through linear or exponential expressions and through the roots of Chebyshev polynomial of the first kind in order to approximate the configurations and velocities at those nodes. Then, by defining the Lagrange function as a weighted sum over the discrete Lagrangians corresponding to the curve segments, we apply the phase fitted technique to obtain an exponentially fitted numerical scheme. The resulting integrators are tested for the numerical simulation of the planar two body problem with high eccentricity and of the three-body orbital motion within a solar system.