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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 analysismechanics of materialsmicromagneticsmodelling 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.

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Research fields

  • geometry, in particular algebraic, differential, and noncommutative geometry, also with applications to quantum field and string theory
  • mathematical analysis, in particular calculus of variations, control theory, partial and ordinary differential equations
  • mathematical modelling, in particular mechanics of solids and fluids, modelling of complex and biological systems, multiscale analysis
  • mathematical physics, in particular integrable systems and their applications, nonlinear partial differential equations, mathematical aspects of quantum physics
  • numerical analysis and scientific computing, applied to partial differential equations and to control problems

PhD and MSC courses:

Laboratories:

  • SISSA MathLab: a laboratory for mathematical modeling and scientific computing
  • SAMBA a laboratory in collaboration with the Cognitive Neuroscience Group

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Numerical Solution of PDEs Using the Finite Element Method

The course "Numerical Solution of PDEs using the Finite Element Method" offers a focused exploration of solving Partial Differential Equations (PDEs) using the Finite Element Method (FEM), employing the deal.II software library. Key components of the course include an introduction to PDEs, basics of numerical methods and FEM analysis, practical training using deal.II, and hands-on projects. The course will also cover High-Performance Computing (HPC) techniques for parallelizing, optimizing, and load balancing FEM simulations for real-world applications.

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