Mathematical Analysis, Modelling, and Applications | Mathematics Area - SISSA

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.

Optimization problems governed by PDEs under the influence of random variables, by Dr. Maria Strazzullo.

Read more about Optimization problems governed by PDEs under the influence of random variables, by Dr. Maria Strazzullo.

integrating data with PDE-based models under uncertainty, by Dr. Noemi Petra.

Read more about integrating data with PDE-based models under uncertainty, by Dr. Noemi Petra.

Roles of sensitivity analysis and uncertainty quantification for science and engineering models, by Dr. Ralph Smith.

Read more about Roles of sensitivity analysis and uncertainty quantification for science and engineering models, by Dr. Ralph Smith.

Statistics in uncertainty quantification and uncertainty quantification in statistics, by Dr. Amy Braverman.

Read more about Statistics in uncertainty quantification and uncertainty quantification in statistics, by Dr. Amy Braverman.

Optimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics

Prusak I, Torlo D, Nonino M, Rozza G. Optimisation–Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics.; 2024.

A general splitting principle on RCD spaces and applications to spaces with positive spectrum

Gigli N, Marconi F. A general splitting principle on RCD spaces and applications to spaces with positive spectrum.; 2023.

Uniqueness and nondegeneracy results for Lane-Emden type Dirichlet problems

Read more about Uniqueness and nondegeneracy results for Lane-Emden type Dirichlet problems

Structure preserving high order Lagrangian schemes for the solution of hyperbolic equations: from fluid-dynamics to astrophysics

Read more about Structure preserving high order Lagrangian schemes for the solution of hyperbolic equations: from fluid-dynamics to astrophysics

An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations

Prusak I, Nonino M, Torlo D, Ballarin F, Rozza G. An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations. [Internet]. 2023 ;151:172 - 189. Available from: https://www.sciencedirect.com/science/article/pii/S0898122123004248

Geometry based approximation of waves propagating through complex domains

Read more about Geometry based approximation of waves propagating through complex domains

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