Numerical Analysis and Scientific Computing
The team’s activities are finalized to the numerical treatment of mathematical models described by partial differential equations, which are discretized either directly or after transforming them into boundary integral equations. To this end, we mostly use finite element methods in the h and hp versions, spectral methods, boundary element methods. The research topics focus on both methodological aspects and applications.
Among the former, we quote the development and analysis of adaptive methods, the construction of quadrature formulas for implementing collocation and Galerkin schemes, the solution of (linear or nonlinear) algebraic systems by either domain decomposition, or preconditioning, or minimization techniques, the design of methods for the solution of integral and integro-differential equations of the Volterra type. In addition, the team possesses a significant expertise on multiscale and wavelet methods, on uncertainty quantification via the solution of differential equations with stochastic coefficients, on coupling techniques between different methods, on numerical optimization, on the implementation of numerical schemes in high-performance computing environments.
Applications concern various problems in Fluid Dynamics (evolution of pollutants in urban areas, flows in porofractured media, kinetic theories), in Applied Mechanics (linear elasticity, propagation of cracks and of seismic waves), in Acoustics and Electromagnetics.
- 3D-1D coupled problems
- Adaptive methods
- BEM FEM methods for PDEs
- Deep learning
- Domain decomposition
- Integral and integro-differential equations
- Numerical optimization
- Numerical solution of PDEs with classical discretization techniques and polygonal/polyhedral elements
- Spectral and h-p type finite element methods
- Uncertainty quantification by PDE-based models