- 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:
First cycle degree programme (L) in
Building Construction Engineering (cod. 5897)
Also valid for Second cycle degree programme (LM) in Offshore Engineering for Energy Transition (cod. 6056)
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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
A successful learner from this course will be able to: a) deal with numerical analysis topics such as: accuracy, truncation and round-off errors, condition numbers, convergence, stability, curve-fitting, interpolation, numerical differentiation and integration, numerical linear algebra; b) deal with numerical methods for solving ordinary and partial differential equations, with finite difference and finite element methods for parabolic and elliptic partial differential equations, applications of computer programs to case studies derived from civil engineering practice.
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