Qualitative models and fuzzy logic in Medicine
Numerical approximation of linear elasticity problems
Theoretical and numerical study of electromagnetic problems
Macroscopic "bidomain" models of reaction-diffusion equations
Numerical approximation of fluid-mechanic problems
Basic properties of discrete schemes (numerical linear algebra, eigenvalue problems, domain decomposition, stabilization techniques)
and fuzzy logic in Medicine. The central issue of the research activity deals with the application of
qualitative modelling and simulation techniques, with the final goal to build a robust input-output model
of the nonlinear dynamics of complex systems which can not be described by means of ordinary or partial differential equations.
Qualitative models (QSIM) are integrated with fuzzy logic systems: in such a way we can exploit the available
structural knowledge, even if incomplete, and embed it in a fuzzy approximator. This approach allows us to automatically determine the optimal
structure of the fuzzy model.
From the methodological point of view, the main problems addressed are:
The main application field is Medicine because in this context the incompleteness of the available structural knowledge prevents from formulating a classical quantitative model of complex systems. In particular glucose-insulin system and thiamine kinetics have been studied.
Numerical approximation of linear elasticity problems.
Particular attention is devoted to plate bending problems, using the
Reissner-Mindlin's model, and thin shell problems,
according to the Koiter and Naghdi models.
The principal research lines are:
Theoretical and numerical study of Maxwell equations for electromagnetic problems. We have been working on the following topics:
Macroscopic "bidomain" models of reaction-diffusion equations. Theoretical and numerical study of macroscopic "bidomain" models of reaction-diffusion type equations for the simulation of the electric propagation in cardiac ventricular. Developing and testing of numerical methods for eikonal equations for describing the motion of electric excitation wavefronts in the myocardial tissue.
Numerical approximation of fluid mechanics problems. Theoretical study and implementation of numerical methods for Stokes, Oseen and Navier-Stokes equations. We are mainly interested in
Basic properties of discrete schemes. We have been working on