Corners and cross-points in DDM for Helmholtz equation

Anouk Nicolopoulos

UZH - anouk.nicolopoulos@math.uzh.ch

With B. Després and B. Thierry from LJLL (Sorbonne Université), we have developped a new mathematical framework to take into account corners (in a first paper), and then cross-points (in a second paper) in optimized Schwarz methods with second order transmission conditions. All of the methods developed are endowed with an energy defined on the skeleton of the decomposition which enables us to prove the convergence. An originality of these methods is that the transmission operators are non-hermitians.