Enrollment year
2015/2016
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Curriculum
BIOINGEGNERIA DELLE CELLULE E DEI TESSUTI
Period
1st semester (28/09/2015 - 15/01/2016)
Lesson hours
24 lesson hours
Activity type
WRITTEN AND ORAL TEST
Prerequisites
Basic mathematical courses of the "laurea triennale" or " undergraduate degree" and or "bachelor degree"
Learning outcomes
The aim of the course is divided in two parts. DYNAMICAL SYSTEMS: theory and numerical methods (6CFU) and FINITE ELEMENT METHOD AND APPLICATIONS (3CFU).
The second part of the course will be devoted to the introduction of the variation formulation of the stationary problema and to their numerical approximation by the finite element method.
Course contents
FINITE ELEMENT METHOD AND APPLICATIONS
Basic notions of functional analysis. Sobolev spaces. Variational formulation of elliptic problems (Poisson).
Ritz-Galerkin method
Mesh in one and more dimemsions -- Some finite elements -- Approximation properties -- Error estimates for elliptic problems of second order.
MATLAB solver implementation
Solution of the Poisson problem in one dimension. Solution of the Poisson problem in two dimension: assembling the linear system, numerical quadrature, system solving. Mesh refinement.
Teaching methods
Lectures (hours/year in lecture theatre): 44
Practical class (hours/year in lecture theatre): 57
Practicals / Workshops (hours/year in lecture theatre): 0
Reccomended or required readings
F. Verhulst. Nonlinear differential equations and dynamical systems. Springer-Verlag,Heidelberg, 2006..
R. Mattheij, J. Molenaar.. Ordinary differential equations in theory and practice.. SIAM, Philadelphia, 2002..
A. Quarteroni, R. Sacco, F. Saleri.. Matematica Numerica. Springer 3ra ed., 2008..
M. Crouzeix, A.L. Mignot.. Analyse Numeriques des Equations Differentielles.. Masson, Paris 1984..
A.M. Stuart , A.R. Humphries. . Dynamical Systems and Numerical Analysis.. Cambridge University Press 1998..
Quarteroni A.. Modellistica numerica per problemi differenziali. Springer Verlag, 2009.
Braess D.. Finite Elements. Theory, Fast Solvers, and Applications in Solid Mechanics.. Cambridge University Press..
Assessment methods
Oral examination with discussion and interpretation of the models simulations developed in the laboratory.
Further information
Oral examination with discussion and interpretation of the models simulations developed in the laboratory.
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