Combining finite element space-discretizations with symplectic time-marching schemes for linear Hamiltonian systems

We provide a short introduction to the devising of special type methods for numerically approximating solution Hamiltonian partial differential equations. These use Galerkin space-discretizations which result in system ODEs displaying discrete version structure original system. The resulting is then discretized by symplectic time-marching method. This combination results high-order accurate, fully can preserve invariants defining ODE restrict our attention linear systems, as main be obtained easily and directly, are applicable many systems practical interest including acoustics, elastodynamics, electromagnetism. After brief description interest, we does not require any background on subject. describe case finite-difference used focus popular Yee scheme (1966) Finally, consider finite-element space discretizations. emphasis placed conservation properties schemes. end describing ongoing work.