Mercoledì 15 marzo un nuovo seminario della serie "Seminari generali dell'IAC 2023".
Ospite è Ludmil Zikatanov, Full Professor al Dipartimento di matematica della Penn State University, USA.
Titolo del seminario: Multilevel methods for nearly-singular problems in mixed dimensions
We consider nearly singular problems, that is, problems with operators that are small, but nonsingular perturbations of singular operators. Discretizations of such problems lead to matrices with condition numbers of the system growing rapidly with mesh size and model parameters. This results in slow convergence even when using preconditioners which are optimal when the nonsingular perturbation dominates.
To design efficient preconditioners we follow the theory of the method of subspace corrections and construct block Schwarz smoothers for the underlying multilevel solution method. The blocks are chosen specifically to cover the supports of the vectors/functions spanning the kernel of the singular part of the operator. We demonstrate key features of such solvers on a mixed-dimensional model of electrodiffusion in brain tissue. This is a joint work with Ana Budisa, Miroslav Kuchta, Kent-Andre Mardal (from University of Oslo and Simula) and James Adler and Xiaozhe Hu (Tufts University).