Laurence Halpern, Professor, Université Sorbonne Paris-Nord, France

龚伟 研究员

The amazing spectral properties of the Robin-Schwarz operator

6月11日（周四）9:00-10:00，南楼202

The Robin-Schwarz operator describes one iteration of the non overlapping domain decomposition Schwarz algorithm with Robin transmission  conditions. It hase none of the usual properties one could expect, such as self-adjointness, compact resolvent, ..

We analyze the special case of 2 x 2 subdomains, hence with a crossing point. We first compute eigenmodes by separation of variables. These modes are of paramount importance for the design of multi-level domain decomposition methods.

Then, we completely describe the spectrum of this operator, using a vast range of analysis tools. In particular, we show that the eigenvalues obtained by separation of variables cover...almost...the spectrum, depending on the value of the Robin parameter $p$.  

This analysis, by its fundamental aspects, and the form of the results, opens the door to more general geometries.

This work is a part of a joint project with Daniel Bennequin, François Cuvelier et Martin Gander.