- Docente: Fabiana Zama
- Credits: 6
- SSD: MAT/08
- Language: English
- Moduli: Fabiana Zama (Modulo 1) Nicholas Fantuzzi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Ravenna
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Corso:
Second cycle degree programme (LM) in
Offshore Engineering for Energy Transition (cod. 6056)
Also valid for First cycle degree programme (L) in Building Construction Engineering (cod. 5897)
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from Sep 25, 2024 to Nov 08, 2024
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from Nov 06, 2024 to Dec 18, 2024
Learning outcomes
At the end of the course, the students know the basic notions of scientific numerical calculus. They possess the knowledge of some of the most important computational tools useful for offshore systems, processes, and structures, with particular reference to numerical methods for the solution of systems of linear equations and differential equations. They are able to use the MATLAB environment for testing methods and critically evaluate the results obtained.
Course contents
The course is divided into two modules:
- Module 1: Numerical Computation with MATLAB (Prof. F. Zama)
- Module 2: Numerical Modelling (Prof. N. Fantuzzi)
Module 1:
- Matlab programming.
- Numerical derivation and integration:
- Finite difference formulas
- Basic Quadrature Formulas
- Numerical Interpolation:
- Lagrange and Chebyshev Interpolation
- Piecewise Polynomial Interpolation.
- Ordinary Differential Equations:
- Numerical solution of Initial Value Problems.
Module 2:
Some classes of differential equations:
- Elliptic equations
- Parabolic equations
- Hyperbolic equations
Interpolation and collocation:
- Cardinal functions
- Gauss integral
- Transformation and derivation
- Solution of a boundary value problem
- Solution with basis recombination
Time-step approximations:
- Parabolic equations
- Finite differences in time
- Finite differences in space
- Hyperbolic
Change of coordinates
- Chebyshev polynomials
Virtual work and energy principles in mechanics:
- Principle of virtual displacements
- Principle of minimum of total potential energy
- Hamilton’s principle for discrete systems (Lagrange method)
- Hamilton’s principle for continuum mechanics
Direct variational methods:
- Strong, weak, and variational formulations
- Ritz method
- Weighted-residual methods
Finite element method:
- 1D isoparametric elements
- 2D isoparametric elements
Readings/Bibliography
- U. Ascher, C. Greif, A first course in Numerical Methods, SIAM, 2011.
- J. P. Boyd: Chebyshev and Fourier spectral methods. Dover, 2000.
- A. J. M. Ferreira, N. Fantuzzi: MATLAB codes for finite element Analysis. Springer, 2020.
Throughout the course, Course Notes and Matlab scripts will be provided.
Teaching methods
Lectures, guided exercises in the laboratory, and group work.
Given the type of activity and teaching methods adopted, the attendance of this course requires the prior participation of all students in the training modules 1 and 2 on safety in the study places ( https://elearning-sicurezza.unibo. it/ ) in e-learning mode.
Assessment methods
Exam:
- Part 1: Written test, with theory and Matlab programming
- Part 2: Homework and multiple choice quiz.
The final grade is obtained as the average of the two parts; part 1 is a prerequisite for part 2.
Teaching tools
The teaching material will be available on the University of Bologna e-learning platform (https://virtuale.unibo.it).
Office hours
See the website of Fabiana Zama
See the website of Nicholas Fantuzzi