Numerical computations and their validation

Our group follows a methodology that incorporates both analytical or theoretical methods to show mathematical results, and numerical methods to verify these analytical results and to extend them and / or explore other parameter values for which the analytical results do not work. Often, these numerical methods involve a large amount of data and calculations. Therefore, the group has a state-of-the-art cluster of High Performance Computing with 160 CPUs running programs with large computation needs. (See a description of the cluster here: https://recerca.upc.edu/sd/computacio/eixam-maya).

Besides the semi-analytical methodology (ie, combining analytical and numerical methods), the group intends to incorporate the methodology of computer-assisted proofs (CAP) to rigorously validate those numerical results which we have not been able to prove so far, but which are strongly supported by careful numerical calculations. The use of this triple methodology (theory, numerics, and CAP) will represent a new dimension in the results obtained by the group, and strengthen it worldwide as a reference group.