Research project

Analisi Numerica e Matematica Computazionale (DIT.AD021.117)

Thematic area

Engineering, ICT and technologies for energy and transportation

Project area

Matematica Applicata (DIT.AD021)

Structure responsible for the research project

Institute for applied mathematics and information technologies (IMATI)

Project manager

MICOL PENNACCHIO
Phone number: 0382 548217
Email: micol.pennacchio@imati.cnr.it

Abstract

In continuity with the long standing tradition that IMATI has in the field, we pursue the study of numerical tools for the solution of PDE's, with emphasis on: a) the methods for spatial discretization, for which several approaches are considered, from the more classical ones (finite elements, finite differences, finite volumes) to the more recently proposed, such as the different approaches to discretization based on polygonal/polyhedral tessellation (virtual elements, mimetic finite differences), isogeometric analysis; b) the efficient implementation of the resulting algorithms with the related linear algebra questions; c) the reliability assessment of the resulting predictions in the presence of uncertainty (uncertainty quantification UQ); d) the application of the different methods to problems arising from fields as diverse as medicine, smart materials, fluid dynamics.

Goals

The goal of this project is the state of the art in the field of the numerical treatment of Partial Differential Equations. More precisely we aim at
a) develop new numerical methods for the numerical solution of Partial Differential Equations of different kind
b) provide new theoretical results on existing as well as newly devised numerical methods, addressing properties such as stability, convergence
c) study the different questions relative to the implementation of the different methods in a modern computing architecture, and to the efficiency of the whole solution procedures, by addressing questions such as preconditioning and parallel implementation
d) adapt different methods to the specific requirements arising from application fields, and use the knowledge acquired to provide numerical solvers for relevant real-life problems.

Start date of activity

07/07/2020

Keywords

Analisi Numerica, Matematica Computazionale, Algoritmi

Last update: 29/03/2024