Good knowledge of Calculus (functions, derivatives,intergrals and their properties). Theory of differential equations. Good knowledge of Numerical Analysis (numerical methods for linear systems, interpolation and approximation, numerical methods for ODE). Basic knowledge of Matlab programming.
The goal of the course is to introduce the main ideas and tools of Geometric Modelling and Computer Aided Geometric Design. In the second part the main approximation methods to solve problems modeled by partial differental equations are presented.
Introduction to Geometric Modeling. Parametric polynomial curves. Bezier curves and their main properties. B-spline curves. Extension to rational curves: NURBS. Tensor product surfaces: Bezier and B-spline patches.
Outline of the main numerical methods for Ordinary differential equations.
Introduction to Partial Differential equations (PDE). Elliptic equations. Strong and weak formulation. Galerkin method. Finite element methods (FEM). Advection-diffusion problems. Stabilization techniques. Some basic notions on approximation methods for parabolic and hyperbolic problems.
Isoeometric Analysis and open problem in the ongoing research.
J. Hoschek, D. Lasser : "Fundamentals of Computer Aided Geometric Design", A.K. Peters 1996.
Quarteroni, A., Valli, A.
"Numerical Approximation of Partial Differential Equations", Springer 1994.
Lectures and some tutorials in the computer lab