arXiv subjects

Gabriele Ciaramella

Publications and source records attributed to Gabriele Ciaramella.

25 records · Page 2Linked to original sources

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↗

arXiv2019

On the Scalability of the Parallel Schwarz Method in One-Dimension

In contrast with classical Schwarz theory, recent results in computational chemistry have shown that for special domain geometries, the one-level parallel Schwarz method can be scalable. This property is not true in general, and the issue of quantifying the lack of scalability remains an open problem. Even though heuristic explanations are given in the literature, a rigorous and systematic analysis is still missing. In this short manuscript, we provide a first rigorous result that precisely quantifies the lack of scalability of the classical one-level parallel Schwarz method for the solution to the one-dimensional Laplace equation. Our analysis technique provides a possible roadmap for a systematic extension to more realistic problems in higher dimensions.

math.NA↗

arXiv2019

On the Scalability of the Schwarz Method

In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global domain. Such problems arise, for instance, in solvation models in computational chemistry. Existing results on the scalability of the one-level PSM are limited to situations where each subdomain has access to the external boundary, and at most only two subdomains have a common overlap. We develop a systematic framework that allows us to bound the norm of the Schwarz iteration operator for domain decomposition problems in which subdomains may be completely embedded in the interior of the global domain and an arbitrary number of subdomains may have a common overlap.

math.NA↗

arXiv2019

Optimal design of experiments for a lithium-ion cell: parameters identification of an isothermal single particle model with electrolyte dynamics

Advanced battery management systems rely on mathematical models to guarantee optimal functioning of Lithium-ion batteries. The Pseudo-Two Dimensional (P2D) model is a very detailed electrochemical model suitable for simulations. On the other side, its complexity prevents its usage in control and state estimation. Therefore, it is more appropriate the use of simplified electrochemical models such as the Single Particle Model with electrolyte dynamics (SPMe), which exhibits good adherence to real data when suitably calibrated. This work focuses on a Fisher-based optimal experimental design for identifying the SPMe parameters. The proposed approach relies on a nonlinear optimization to minimize the covariance parameters matrix. At first, the parameters are estimated by considering the SPMe as the real plant. Subsequently, a more realistic scenario is considered where the P2D model is used to reproduce a real battery behavior. Results show the effectiveness of the optimal experimental design when compared to standard strategies.

eess.SY↗

arXiv2019

A theoretical investigation of time-dependent Kohn-Sham equations: new proofs

In this paper, a new analysis for existence, uniqueness, and regularity of solutions to a time-dependent Kohn-Sham equation is presented. The Kohn-Sham equation is a nonlinear integral Schroedinger equation that is of great importance in many applications in physics and computational chemistry. To deal with the time-dependent, nonlinear and non-local potentials of the Kohn-Sham equation, the analysis presented in this manuscript makes use of energy estimates, fixed-point arguments, regularization techniques, and direct estimates of the non-local potential terms. The assumptions considered for the time-dependent and nonlinear potentials make the obtained theoretical results suitable to be used also in an optimal control framework.

math.AP↗

arXiv2017

Investigation of optimal control problems governed by a time-dependent Kohn-Sham model

Many application models in quantum physics and chemistry require to control multi-electron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schrödinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.

math.OC↗

arXiv2017

A theoretical investigation of time-dependent Kohn-Sham equations

In this work, the existence, uniqueness and regularity of solutions to the time-dependent Kohn-Sham equations are investigated. The Kohn-Sham equations are a system of nonlinear coupled Schrödinger equations that describe multi-particle quantum systems in the framework of the time dependent density functional theory. In view of applications with control problems, the presence of a control function and of an inhomogeneity are also taken into account.

math.AP↗