arXiv subjects

Tommaso Vanzan

Publications and source records attributed to Tommaso Vanzan.

21 records · Page 2Linked to original sources

arXiv2021

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Substructured domain decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. We introduce here a substructured version of Restricted Additive Schwarz (RAS) which we call SRAS, and we discuss its advantages compared to the standard volume formulation of the Schwarz method when they are used both as iterative solvers and preconditioners for a Krylov method. To extend SRAS to nonlinear problems, we introduce SRASPEN (Substructured Restricted Additive Schwarz Preconditioned Exact Newton), where SRAS is used as a preconditioner for Newton's method. We study carefully the impact of substructuring on the convergence and performance of these methods as well as their implementations. We finally introduce two-level versions of nonlinear SRAS and SRASPEN. Numerical experiments confirm the advantages of formulating a Schwarz method at the substructured level.

math.NA↗

arXiv2021

On the asymptotic optimality of spectral coarse spaces

This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very efficient and, in some cases, optimal. However, the results of this paper show that spectral coarse spaces do not necessarily minimize the asymptotic contraction factor of a two-level iterative method. Moreover, numerical experiments show that there exist coarse spaces that are asymptotically more efficient and lead to preconditioned systems with improved conditioning properties.

math.NA↗

arXiv2017

Quantum thermostatted disordered systems and sensitivity under compression

A one-dimensional quantum system with off diagonal disorder, consisting of a sample of conducting regions randomly interspersed within potential barriers is considered. Results mainly concerning the large $N$ limit are presented. In particular, the effect of compression on the transmission coefficient is investigated. A numerical method to simulate such a system, for a physically relevant number of barriers, is proposed. It is shown that the disordered model converges to the periodic case as $N$ increases, with a rate of convergence which depends on the disorder degree. Compression always leads to a decrease of the transmission coefficient which may be exploited to design nano-technological sensors. Effective choices for the physical parameters to improve the sensitivity are provided. Eventually large fluctuations and rate functions are analysed.

cond-mat.dis-nn↗