The partitioned finite element method for port-Hamiltonian systems: a structure-preserving discretization for boundary controlled wave and heat PDEs
Denis Matignon (ISAE-SUPAERO, Toulouse)
Abstract: Boundary controlled and observed wave and heat PDEs can be recast as port-Hamiltonian systems on an n-D domain, starting from physical principles and allowing for a power balance which proves most useful when interconnecting such subsystems.
A mixed finite element method ensures the preservation of these properties at the discrete level: this will be introduced with a primer on the finite element method (FEM); then, some optimal convergence results will be provided and illustrated on the 2D inhomogeneous and anisotropic wave equation.
Finally, the effectiveness of PFEM will finally be illustrated when capturing refined asymptotic behaviours of the coupled heat-wave PDE system in different geometric configurations.
Joint work partly with Ghislain Haine.
mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory
Audience: researchers in the discipline
( slides )
Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY
| Organizers: | Hannes Gernandt*, Birgit Jacob |
| *contact for this listing |