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.