PhD Seminars II
November 18, 2019 –
Foivos Fioravantes (COATI)
Distinguishing labelings of Graphs
Many real life scenarios can be modeled as graph colouring problems. Among these, the problem of minimizing number of colours needed for a proper colouring (in which adjacent vertices have different colours) is of particular significance (Four-Colour Theorem). Solving this problem is, in general, hard. Furthermore, there are graphs that require a large number of colours to be properly coloured; this can pose serious issues for practical applications. In recent years, an alternative way to deal with these problems has been studied: finding labelings of a graph that allows us to distinguish some of its elements (for example its vertices). In this presentation we explain these notions, the state of the art and some of our preliminary results.
The role of geometry in numerical simulation
Abstract: In industrial numerical simulation, it is estimated that 80% of the analysis time is dedicated to the generation of the computational grid, mainly due to the different mathematical representations used in the geometric design and in the numerical solvers (structure, fluid, acoustics, etc.). In this talk, two opposite approaches to reduce the cost of mesh generation will be presented, the immersed boundary method, that aims to completely separate the computational grid from the geometry, and the isogeometric analysis, whose goal is to unify design and simulation tools. Some numerical examples will be given.