Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations

CCMA PDEs and Numerical Methods Seminar Series

Meeting Details

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Speaker: Yang He, University of Science and Technology Beijing

Abstract: Since 2012, structure-preserving geometric algorithms for Vlasov-Maxwell (VM) system have been an active research area. Variational, noncanonical and canonical symplectic particle-in-cell methods for the VM system have been successfully developed and applied. In this talk, I will give a Hamiltonian particle-in-cell method for the VM system by employing mixed finite element methods in space and splitting methods in time. Specifically, the discretization preserves the non-cannonical symplectic structure of the VM equations given by the Morrison-Marsden-Weinstein Poisson bracket. In order to derive the semi-discretized system which possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. When the Hamiltonian splitting method is used to discretize the semi-discrete system in time, we can prove that the resulting algorithm is explicit and preserves the Poisson structure. Due to the conservative properties of the new derived algorithms, superior numerical simulations over long-time can be guaranteed.

Room Reservation Information

Room Number: 315 McAllister

Date: 10/11/2017

Time: 10:00am - 12:00pm