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B018805 - TOPICS IN NUMERICAL ANALYSIS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2017-18
Coorte 2017 - Second Cycle Degree in MATHEMATICS
Course year
First year - First Semester
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
9
Teaching Hours
72
Teaching Term
18/09/2017 ⇒ 22/12/2017
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Finite difference methods for 1D boundary value problems. Variational formulation of a boundary value problem (1D e 2D). The finite element method for stationary and parabolic problems. Splines and the B-spline basis. Elements of isogeometric analysis.
Suggested readings (Search our library's catalogue)
- W. Gautcshi (2012), Numerical Analysis, Second Edition, Birk ̈auser, New York.
-A. Quarteroni (2012), Modellistica Numerica per Problemi Differenziali, quinta edizione, Springer–Verlag, Milano.
-L. Formaggia, F. Saleri, A. Veneziani, Solving numerical PDE's: problems, applications, exercises, 2012, Springer-Verlag, Milano, Italia.
-C de Boor (2001), A Practical Guide to Splines, Revised edition, Applied Mathematical Sciences 27, Springer–Verlag, New York.
-A. Quarteroni (2012), Modellistica Numerica per Problemi Differenziali, quinta edizione, Springer–Verlag, Milano.
-L. Formaggia, F. Saleri, A. Veneziani, Solving numerical PDE's: problems, applications, exercises, 2012, Springer-Verlag, Milano, Italia.
-C de Boor (2001), A Practical Guide to Splines, Revised edition, Applied Mathematical Sciences 27, Springer–Verlag, New York.
Learning Objectives
Knowledge: finite difference schemes for 1D boundary value problems; variational formulaton of a boundary value problem; the finite element method; splines and their application in isogeometric analysis.
Expertise: being able to implement and evaluate a numerical scheme for boundary value problems; familiarity with splines an their applications.
Expertise: being able to implement and evaluate a numerical scheme for boundary value problems; familiarity with splines an their applications.
Prerequisites
Basics of Numerical Calculus (finite arithmetic, zeros of functions, numerical methods for linear systems) and knowledge of the Matlab environment and programming language.
Teaching Methods
6 hours a week, 4 in classroom (frontal teaching) and 2 in computer lab (implementation of the introduced schemes and numerical experiments)
Type of Assessment
The exam consists in an oral interrogation and in discussing a student's work developed in Matlab.
Course program
The centered and upwind finite difference methods for 1D boundary value problems: a model problem, the diffusion-transport problem, the general second order nonlinear problem. Basics on Sobolev spaces. Variational formulation of a boundary value problem (1D and 2D). Galerkin discretization. Finite elment method for stationary and parabolic problems. Mesh adaptivity. Splines and the B-spline basis. Curry-Schoenberg theorem. Witney-Schoenberg theorem. Elements of isogeometric analysis.