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Numerical Analysis

Advanced Topics in Numerical Solutions of PDEs

  • Isogeometric Analysis Techniques (LH)
  • Boundary Element Methods (LH)
  • Numerical Optimal Control of PDEs (GR)
  • Reduced Basis Methods in Computational Mechanics (GR)
  • Shape Optimization (optional)

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

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