Topics in Scientific Computing
A.Y. 2019/2020
Learning objectives
The course aims to offer an enlarged vision on the various aspects - both from the theoretical and implementation viewpoints - that characterize the modern use of Scientific Computing, along with its application to problems arising in physics, biology and engineering.
Expected learning outcomes
Upon completing the course, the students will be able to apply adequate discretization techniques to handle partial differential equation problems of elliptic, parabolic and hyperbolic type. They will also be able to quantify the accuracy of the chosen method and to produce an adequate implementation in Matlab.
Lesson period: Second semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
Second semester
Course syllabus
Introduction to partial differential equation problems and their importance in the applications.
Non-dimensionalization and scaling procedures. Discretization of ordinary derivative equations :
multistep and Runge Kutta methods. Analysis and Matlab implementation. Partial derivative
equations: theoretical properties and finite difference discretization in 1D and nD for elliptic,
parabolic, hyperbolic equations. Convection-diffusion-reaction problems with transport /
dominant reaction. Matlab implementation. Introduction to inverse problems. Each topic is
studied theoretically and a numerical solution is proposed via a Matlab implementation.
Non-dimensionalization and scaling procedures. Discretization of ordinary derivative equations :
multistep and Runge Kutta methods. Analysis and Matlab implementation. Partial derivative
equations: theoretical properties and finite difference discretization in 1D and nD for elliptic,
parabolic, hyperbolic equations. Convection-diffusion-reaction problems with transport /
dominant reaction. Matlab implementation. Introduction to inverse problems. Each topic is
studied theoretically and a numerical solution is proposed via a Matlab implementation.
Prerequisites for admission
Fundamentals of Numerical Analysis, Matlab Programming, Calculus
Teaching methods
lectures and lab sessions
Teaching Resources
notes of the course, study material provided during the course
Assessment methods and Criteria
Projects to be done during the term, including theoretical and coding points.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professor:
Causin Paola
Shifts:
-
Professor:
Causin PaolaProfessor(s)