Description

Numerical analysis is a branch of mathematics that addresses problems in the applied sciences, specifically real-world phenomena that cannot be analyzed with analytical techniques. Its approach involves proposing methodologies to approximate solutions using computers. Thanks to technological advancements, numerical analysis is constantly evolving and introducing new computational techniques and algorithms that optimize accuracy and computational times through automated processes. Theoretical studies are also conducted to analyze error estimates, applicability, and process convergence.

Numerical analysis has its origins in the work of great mathematicians such as Newton, Lagrange, von Seidel, Jacobi, Gauss, Euler, and others, long before the invention of electronic calculators. However, the advent of electronic calculators greatly influenced the development of numerical analysis, enabling increasingly complex computations and the ability to handle non-trivial models that require large amounts of data.

High-quality mathematical software and high-performance calculation techniques are essential tools for simulating observed phenomena. Numerical analysis has become a crucial part of the skill set for anyone working or training in the fields of engineering, information technology, physics, chemistry, and other technical-scientific sectors.

Research Topics

At the Engineering Department, we focus on four main research topics:

• Approximation theory: This topic involves the theoretical and computational study of meshless methods, wavelet transforms, and subdivision schemes to solve realistic problems in science and engineering. Our work in this area includes computational electromagnetics problems, dynamical systems for epidemiological problems, electromagnetic simulation of metallic carbon nanotubes, computer vision, and machine learning.
• Advanced numerical modeling in bioelectromagnetism: This topic involves the development of neuroimaging techniques for studying human brain activity, such as electroencephalography, magnetoencephalography, transcranial direct current stimulation, and particle imaging magnetic.
• High Performance Computing (HPC): Our research in this area focuses on parallel paradigms, distributed computing, and graphics processing units (GPUs) for software development in numerical linear algebra and engineering topics.
• Numerical treatment of integro-differential equations and inverse problems: This topic involves the numerical treatment of integro-differential equations and inverse problems for various applications such as endodontic procedures, electromagnetic transient analysis, lightning, electromagnetic compatibility, and electrical analogies in the viscoelastic behavior of materials.

Funded Project

• PRIN 2020 ISoREC PRJ-0845 Innovative Solutions for Renewables in Energy Communities
• Progetto PON 4FRAILTY – Sensoristica intelligente, infrastrutture e modelli gestionali per la sicurezza di soggetti fragili (ARS01_00345)
• PRIN 2022-Towards ADDitive manufacturing of MAGnetic components for electrical machines and power converters.
• PNRR Cognitive evolution in Ai: Explainable and Self-Aware Robots through multimodal data processing – CAESAR.

Keywords

Approximation theory; High Performance Computing; integro-differential equations; inverse problems; bio-electromagnetism; neuroimaging.