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Introduction to numerical modelling
MSE-369
Lecturer(s) :
Drezet Jean-MarieLanguage:
English
Summary
This course aims to give a broad introduction to the basic numerical methods used to model physical phenomenon such as diffusion, heat transport, elasticity and the wave equation, and incompressible fluid dynamics. Computational examples will be given within the python framework.Content
Recap on the ordinary differential equations (ODE) initial value problem
- the initial value (Cauchy) boundary condition
- numerical integration methods (Euler and Runge'Kutta, implicit trapezoidal)
- reduction of higher order ODEs to a system of 1st order ODEs
- truncation error, stability, stiffness, and propagation of error
The ODE boundary value problem
- General formulation of the ODE boundary value problem (Dirchlet/Neumann boundary conditions)
- numerical solution methods (shooting and finite difference)
- 1D solution examples
Partial differential equations (PDE)
- general definition of PDEs and their boundary conditions
- differential operators ' their physical origin, continuity, flux conservation, material derivative
- development of well known examples (diffusion, heat and wave equation, the Navier-Stokes equation, and solid mechanics (elasticity
- numerical solution methods (finite difference and finite element)
Keywords
Numerical methods, Ordinary Differential Equations, Partial Differential Equations, Finite difference methods, Finite element methods
Learning Prerequisites
Important concepts to start the course
- finite difference representation of derivatives
- numerical integration ' quadrature (Newton-Coates)
- basic linear algebra ' solution of linear systems
- numerical solution of non-linear equations
Learning Outcomes
By the end of the course, the student must be able to:- Model some common physical phenomenon
- Propose the appropriate numerical solution strategy for a variety of different physical models
Transversal skills
- Use a work methodology appropriate to the task.
- Communicate effectively with professionals from other disciplines.
- Demonstrate the capacity for critical thinking
- Take feedback (critique) and respond in an appropriate manner.
Teaching methods
A weekly lecture will be given covering all theoretical concepts. Included in these lectures will be numerical solution examples using python
Expected student activities
Attendance to lectures
Assessment methods
Assessment is via an oral exam
In the programs
- SemesterFall
- Exam formDuring the semester
- Credits
1 - Subject examined
Introduction to numerical modelling - Lecture
1 Hour(s) per week x 14 weeks
- Semester
Reference week
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15-16 | INF213 MXF014 | ||||
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21-22 |
Lecture
Exercise, TP
Project, other
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- Autumn semester
- Winter sessions
- Spring semester
- Summer sessions
- Lecture in French
- Lecture in English
- Lecture in German