Dr. Hongling Su, School of Mathematics, Chinese Minmin University

Yifa Tang, Professor

Energy/dissipation-preserving split Birkhoffian multi-symplectic methods for Maxwell’s equations

14:00-15:00 November 8(Tuesday), N702

We propose a novel kind of energy/dissipation-preserving split Birkhoffian multi-symplectic (S-BMS) methods for Maxwell's equations with dissipation terms.  After investigating the non-autonomous and autonomous Birkhoffian formalism of Maxwell's equations which are split into local one-dimensional (LOD) systems of equations with  Birkhoffian structures, a pair of Birkhoffian-structure-preserving  schemes are implemented to each resulted LOD equations, hence leading to S-BMS integrators. A theoretical discussion of how the S-BMS methods preserve the discrete versions of the global energy-dissipation laws is presented, and the behavior is verified in numerical experiments on 2D and 3D Maxwell's equations. Furthermore, theoretical analysis shows that the methods are not only unconditionally stable, but also dissipation-preserving for Maxwell's equations in a perfectly matched layer  medium. We also extend the discussion on dispersion for the new schemes applied to the LOD equations.