Learning outcomes of the course unit
Introduction to modern techniques for the approximate solution of real problems modelled by partial differential equations.
Knowledge of the fundamental notions of Numerical Analysis.
Course contents summary
Variational formulation of elliptic
boundary value problems. Approximation techniques: collocation and
Galerkin methods. Finite elements and spectral methods.
Stabilization methods for advection-diffusion problems.
Approximation of time-dependent problems
for parabolic equations. Semi-discretization in space and time.
Teta-method. Crank-Nicolson method.
Iterative algorithms for the numerical
solution of linear systems of high dimensions associated to
partial differential equations: relaxation methods (S.O.R. and
S.S.O.R.); stationary and dynamical Richardson method; gradient and
conjugate gradient methods. Preconditioning. Gradient and Lanczos
methods for non symmetric problems. GCR and CGNR algorithms.
Arnoldi algorithm, GMRES, Bi-CGSTAB.
Quarteroni A., Modellistica Numerica per Problemi Differenziali, Springer, (2000)
Quarteroni A., Valli A., Numerical Approximation of Partial Differential Equations, Springer, (1994)