Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System

摘要

Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM)equations is currently an active research topic. We show thatspatially-discretized Hamiltonian systems for the VM equations admit a localenergy conservation law in space-time. This is accomplished by proving that fora general spatially-discretized system, a global conservation law alwaysimplies a discrete local conservation law in space-time when the algorithm islocal. This general result demonstrates that Hamiltonian discretizations canpreserve local conservation laws, in addition to the symplectic structure, bothof which are the intrinsic physical properties of infinite dimensionalHamiltonian systems in physics.