Research Group:

## Topics in Scientific Computing for the Solution of PDEs

## Numerical Methods for PDEs

- Finite Elements
- Elliptic Problems
- Parabolic Problems
- Hyperbolic Problems

HPC Techniques for the solutions of PDEs

- Domain Decomposition
- Reduced Basis Approximations
- Multipole Expansion

## Topics in Computational Fluid Dynamics

- Introduction to CFD, examples.
- Incompressible flows.
- Numerical methods for potential and thermal flows
- Numerical methods for viscous flows: steady Stokes equations
- Discretization techniques for steady and unsteady Navier-Stokes equations.
- Advanced optional topic (1): compressible flows.
- Advanced optional topic (2): fluid and structure interaction.

Material will be provided during classes.

## Topics in the mechanics of soft and bio-materials

Topics in the mechanics of soft and bio-materials

This course aims to provide an introduction to the mechanics of soft materials, of which biological materials are prominent examples. Soft materials are those that can be easily deformed by external stress, electromagnetic fields or even thermal fluctuations: in other words everything that is wet, squishy, sticky, flabby or spongy.

## Topics in the Mechanics of Solids

The course comprises topics in the field of Solid Mechanics and is aimed at the presentation of both theoretical and experimental results.The topics covered include:

## Introduction to Mechanics of Solids, Fluids, and Biological Systems

- Kinematics of deformable continua
- Eulerian and Lagrangian descriptions of motion
- The balance laws of continuum mechanics
- Conservation of mass
- Balance of linear and angular momentum
- Constitutive Equations
- Fluid dynamics: the Navier Stokes equations
- Solid mechanics: nonlinear and linear elasticity
- Selected topics from the mechanics of biological systems

## Introduction to numerical analysis

The foundations of Numerical analysis

- Resolution of linear systems with direct methods
- Resolution of linear systems with iterative methods
- Polynomial interpolation and projection
- Numerical Integration
- Numerical solutions of ODEs

Numerical Methods for PDEs

- Finite Elements
- Elliptic Problems
- Parabolic Problems
- Hyperbolic Problems

## Numerical Analysis and Scientific Computing

The research deals with the analysis, development, application of mathematical models for the integration of complex systems. The analysis is conducted using mathematical methods in several fields such as linear algebra, approximation theory, partial differential equations, optimization and control. Solution methods are developed and applied to domains as diverse as (potential and viscous) flow dynamics, (linear and nonlinear) structural analysis, mass transport, heat transfer and in general to multiscale and multiphysics applications.