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Numerical Analysis

Topics in computational fluid dynamics

On April 12 and 19, 2016 classes will be given in room A-134. 

Advanced Topics in Numerical Modelling of PDEs: Part I

Part I: "Reduced Basis Methods and a Posteriori Error Bounds for Parametrized Partial Differential Equations", March 15-17, 2016, Lecturer Prof. Gianluigi Rozza, Tutorials Dr. Francesco Ballarin

Learning outcomes/Objectives:

The course aims to provide the basic aspects of numerical approximation and efficient solution of parametrized; PDEs for computational mechanics problem (heat and mass transfer, linear elasticity, viscous and potential flows) using reduced order methods.

Module Description:

Applied Mathematics: an Introduction to Scientific Computing

  • Frontal Lectures (about 30h), Interleaved with Laboratories (about 30h): total 60h
  •  This course is shared between the PhD in Mathematical Analysis, Modeling, and Applications, the Master in High Performance Computing (www.mhpc.it) and the Laurea Magistrale in Matematica

 

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.

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)

 

Material will be provided during classes, a calendar with topics and organization will be given during the first lecture.

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