o Discretization methods for partial differential equations; continuous and discontinuous Galerkin finite element methods; finite volume methods; wavelets; compatible discretizations; mimetic finite differences and virtual elements methods; polyhedral meshes; NURBS.
o Isogeometric analysis.
o A posteriori error estimates and adaptive methods.
o Multiscale methods and stabilizing methods.
o Conformal and nonconformal domain decomposition methods and preconditioners analysis.
o Parametric and nonparametric methods for systems identification.
o Signal and images processing methods.
o Nonlinear evolution problems.
o Nonlinear systems of conservation laws.
o Free boundary problems, phase transitions and mean curvature problems.
o Elasticity and computational mechanics.
o Shape memory alloys problems.
o Computational fluid dynamics.
o Computational electromagnetic problems.
o Semiconductor nanostructures problems.
o Computational electrocardiology.
o Metabolic and gene-regulation system identification for biological systems.
o Code designing and structuring for scientific computation.
STOCHASTIC MODELLING AND DATA ANALYSIS
o Methodologies for statistical inference, classical and Bayesian, parametric and nonparametric
- Combination of expert opinions;
- Multivariate data analysis;
- Survival data analysis;
- Bayesian robustness analysis;
- Bayesian nonparametric Statistics;
- Statistical design of experiments;
o Probability and statistics of stochastic processes
- Mothods for state-space models;
- Bayesian methods for stochastic processes;
- Stochastic differential equations and diffusion processes;
- Functionals of random probability measures;
o Stochastic simulation and computational statistics
- Monte Carlo methods;
- MCMC algorithm for model estimation and model selection;
- Simulation from laws of functionals of random probability measures.
o Applications in ecology
- Analysis of stochastic models for population dynamics and parameter estimation in prey-predator systems;
- Evaluation of strategies for ecosystem management.
o Applications in finance and economy
- Industrial project management;
- Pricing of non standard options;
o Applications in geophysics
- Seismic phases identification;
- Estimation of seismic risk using time-dependent models;
- Study of the attenuation of macroseismic intensity;
- Study of the time evolution of sequences of secondary shocks;
- Assessment of the probability of occurrence through stress-release models.
- Pattern recognition in macroseismic fields
o Applications in engineering and technology
- Atuomatic classification of digital images;
- Analysis of the aggregated behaviour of distributed loads and generators;
- Reliability analysis for repairable systems and failure data analysis;
o Applications in the medical and health sectors
- Methods for the optimal management of home-care assistance