AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the module is to provide the students with basic numerical techniques in order to solve parabolic, hyperbolic and elliptic partial differential equations, so that the students are able to solve problems relevant to their field of interest.

AIMS AND LEARNING OUTCOMES

The aim of the module is to provide the students with basic numerical techniques in order to solve parabolic, hyperbolic and elliptic partial differential equations, so that the students are able to solve problems relevant to their field of interest.

By the end of the course, the students will be able to:

• Derive a finite-difference approximation of arbitrary accuracy
• Identify if a non-uniform discretisation is necessary or not
• Predict the local and global truncation error for a given finite-difference approximation
• Formulate the discrete form of an ordinary or partial differential equation
• Plan a Design-of-Experiment (DoE) campaign for an experimental analysis
• Formulate a Response Surface Model (RSM) for a given set of DoE
• Solve numerically a linear ODE or PDE by integration in time 
• Evaluate the numerical stability characteristics of a certain discretisation

TEACHING METHODS

The lectures are divided into theory and practice. All theory presented in the course is used in the exercises in order for the students to apply what they learn and understand the difficulties in the applications.

SYLLABUS/CONTENT

This is the course content

• Introduction and motivation
• Introduction to matlab programming by video lectures and exercises in class
• NUMERICAL APPROXIMATIONS OF SYSTEM OF LINEAR EQUATIONS: Approximation with finite differences. Convergence, consistency, zero-stability and absolute stability. Forward Euler-centered scheme. Upwind, Lax-Friedrichs and Lax- Wendroff schemes. 
• INITIAL VALUE PROBLEMS: Analysis of the schemes, CFL condition and its meaning. Backward Euler-centered scheme. A quick description of systems and of non-linear problems.
• EXERCISES: basic derivations and analysis, solution of equations related to chemical engineering problems.
• HOME WORK: programming and derivations
• Design of Experiments (DoE)
• Response Surface Modeling (RSM) 
• Finite Volume Methods, Introduction to Ansys Fluent including tutorials 

RECOMMENDED READING/BIBLIOGRAPHY

• Quarteroni, Alfio; Saleri, Fausto; Gervasio, Paola , Scientific Computing with MATLAB and Octave, Editore: Springer, Anno edizione: 2010 
• Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto , Numerical Mathematics, Editore: Springer, Anno edizione: 2007
• Optimization Methods: From Theory to Design by Marco Cavazzuti, Springer

TEACHERS AND EXAM BOARD

Exam Board

JAN OSCAR PRALITS (President)

ELISABETTA ARATO

CRISTINA ELIA MOLINER ESTOPINAN (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/10376/p/studenti-orario

EXAMS

EXAM DESCRIPTION

The examination consists of two written exams; one mid-term exam at roughly 50% of the course, and one final exam at the end of the course. The final grade is the average value of the two exams. Each written exam is passed with a grade larger or equal to 18/30. Exams that are passed have no due date. 

ASSESSMENT METHODS

During the course practical programming exercises are given for the students to apply the theory they have learned.

The examination consists of written exams.

Exam schedule

FURTHER INFORMATION

Students with SLD, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods that, in compliance with the teaching objectives, take into account the modalities learning opportunities and provide suitable compensatory tools.