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University of Parma
Course catalogue
Università degli Studi di Parma
course catalogue

APPROXIMATION METHODS
cod. 07610

Academic year 2008/09
1° year of course - First semester
Professor
Academic discipline
Analisi numerica (MAT/08)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
60 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Introduction to modern techniques for the approximate solution of real problems modelled by partial differential equations.

Prerequisites

Knowledge of the fundamental notions of Numerical Analysis.

Course unit content

Variational formulation of elliptic<br />
boundary value problems. Approximation techniques: collocation and<br />
Galerkin methods. Finite elements and spectral methods.<br />
Stabilization methods for advection-diffusion problems.<br />
Approximation of time-dependent problems<br />
for parabolic equations. Semi-discretization in space and time.<br />
Teta-method. Crank-Nicolson method.<br />
Iterative algorithms for the numerical<br />
solution of linear systems of high dimensions associated to<br />
partial differential equations: relaxation methods (S.O.R. and<br />
S.S.O.R.); stationary and dynamical Richardson method; gradient and<br />
conjugate gradient methods. Preconditioning. Gradient and Lanczos<br />
methods for non symmetric problems. GCR and CGNR algorithms.<br />
Arnoldi algorithm, GMRES, Bi-CGSTAB.<br />

Full programme

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Bibliography

Quarteroni A., Modellistica Numerica per Problemi Differenziali, Springer, (2000)<br />
Quarteroni A., Valli A., Numerical Approximation of Partial Differential Equations, Springer, (1994)

Teaching methods

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Assessment methods and criteria

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Other information

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