Research

This group has being doing research for many years on (thermo) mechanical mathematical models for various systems (particle, rigid, and deformable continua). Some among these are of interest for the research activities of the centre.

The research activity of the group has explored various aspects of the analysis of mechanical properties of deformable continua by means of ultrasonic nondestructive techniques, and is turning his attention to the characterization of mechanical properties of biological tissues. Another area of future research is the construction of continuum models for bodies capable of growing, this being an important property of biological tissues. In fact, growth cannot be easily included in the classical teories of continua, as assessed for instance by C. Truesdell, W. Noll and associates in the seventies.

Moreover, from several years there is an high interest on Tikhonov regularization, a well-known technique for solving ill conditioned linear systems. Also, new approaches based on the computation of matrix functions by means of Krylov type methods, and suitable extrapolation techniques are object of study. Due to the large number of applications in physics, medicine, engineering,… the problem is considered of great interest by the scientific community. Ill-posed linear systems often arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about some interior properties using exterior measurements, as for instance in image restoration and tomography.