Numerical Analysis and Scientific Computing

The group carries out research activities in computational mathematics and its applications in the physical and social sciences with a focus in the following areas:

• Solution techniques for large-scale matrix problems including sparse linear systems, eigenvalue problems and functions of matrices (Krylov subspace methods, preconditioners).
• Numerical methods for coupled PDE problems leading to systems in saddle point form; these include the Stokes and Navier-Stokes equations, the coupled Stokes-Darcy problem, optimal control problems with partial differential equations as constraints, etc.
• Algorithms for the analysis of large complex networks including centrality and communicability computations, network robustness, Markov processes on graphs, quantum graphs.
• Numerical Optimal Transport.
• Basic research in Matrix Analysis and Spectral Graph Theory.
• Applications to Computational Fluid Mechanics, Data Science, Quantum Chemistry.