Speaker: Milo Viviani
Affiliation: Scuola Normale Superiore
Venue: Aula Magna, Dipartimento di Matematica
Time: Thursday, 10/02/2022, 11:00
Title:Solving cubic matrix equations arising in conservative dynamics
Spatial semi-discretization of conservative PDEs can be described as
flows in suitable matrix spaces, which in turn leads to the need to
solve polynomial matrix equations, a classical and important topic both
in theoretical and in applied mathematics.
Solving these equations
numerically is challenging due to the presence of several conservation
laws which our finite models incorporate and which must be retained
while integrating the equations of motion. In the last thirty years, the
theory of geometric integration has provided a variety of techniques to
tackle this problem. These numerical methods require to solve both
direct and inverse problems in matrix spaces.
We present two algorithms to solve a cubic matrix equation arising
in the geometric integration of isospectral flows. This type of ODEs
includes finite models of ideal hydrodynamics, plasma dynamics,
and spin particles, which we use as test problems for our algorithms.
Meeting link:https://hausdorff.dm.unipi.it/b/leo-xik-xu4
