Many important physical problems have a Hamiltonian structure and contain important symmetries and invariants. Preserving these structures in the numerical discretization and developing efficient numerical algorithms or this class of problems is a great challenge, but if successful, it generally results in superior (long time) numerical accuracy and stability.
A focal point is the analysis and development of numerical discretizations for various classes of wave problems, e.g. seismic and electromagnetic waves. For example, in his PhD project, Nishant Kumar combines expertise from Numerical Mathematics with Systems Theory to link Port-Hamiltonian Systems to Discontinuous Galerkin Finite Element Methods.
People working on this subject within SACS are:
Post Doc / PhD