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Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Computational Mechanics by Reduced order methods

Learning outcomes and 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.

Topics in Computational Fluid Dynamics

Topics/Syllabus

  • Introduction to CFD, examples.
  • Constitutive laws
  • Incompressible flows.
  • Numerical methods for potential and thermal flows
  • Boundary layer theory
  • Thermodynamics effects, energy equation, enthalpy and entropy
  • Vorticity equations
  • Introduction to turbulence
  • Numerical methods for viscous flows: steady Stokes equations
  • Stabilisation (SUPG) and inf-sup condition

Topics in continuum mechanics

This is a 60-hours introductory course on continuum mechanics and its applications. The aim is to provide first year students with a solid understanding of the fundamental principles of the subject.

Advanced FEM Techniques

This course provides a high level introduction to the numerical analysis of PDES and related high-performance computing techniques, focusing on problems in mechanics such as fluid dynamics. Students will acquire advanced understanding on Computational modelling techniques, both theoretical and practical. The course will utilise a combination of frontal lectures and live programming demonstrations using the C++ deal.ii (dealii.org) Finite Element Library. All lectures are in A-133, except for the last one which is in A-004.

Numerical Methods for PDEs

This is a Joint course, between SISSA PhD in Mathematical Analysis, Modeling, and Applications, Laurea Magistrale in Matematica, and the Laurea Magistrale in Data Science and Scientific Computing.

Course materials are available on the course github repository.

Syllabus

Metric mathematical relativity and optimal transport

Abstract. Lorentzian geometry is the mathematical foundation of Einstein's theory of general relativity, which explains gravity as a manifestation of spacetime curvature (unlike Newton’s theory, which treats gravity as a force). This course has two objectives. First, we give an overview of classical concepts from Lorentzian geometry, encompassing e.g.

Optimal Transport

Location and selected dates:

Lectures will take place in Room 133-Ambrosetti.

  • October: 2, 3, 9, 10, 23, 24, 30, 31
  • November: 6, 13, 20, 21, 27, 28
  • December: 4, 5, 12, 18, 19
  • January: 8, 9, 15, 16, 22, 23, 29, 30
  • February: 5, 6, 25, 26, 27
  • March:   5, 6, 12, 13, 19, 20, 26, 27

 

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