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MACS 2 Projects in applied mathematics and scientific computing Professor : Caroline Japhet |
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Manyphysical phenomena can be formulated as differential equations, for example the airflow around an aircraft, the evolution of a glacier (see also here) or the temperature in your room. Most of these equations however can not be solved exactly by analytical tools. Their solution has to be approximated using numerical methods. The goal of this course is to implement finite element methods in 2D learned in numerical analysis course of MACS 2. That is, starting with a physical model problem, to perform and implement finite element methods to solve it, and interpret the simulations results (are the results accurate and close to the physics ?). We use the Matlab langages first, to implement the methods in 1D. Then, you will be able to develop prototype codes with Matlab and Freefem++ . Once the initial problem is validate, you will be able to define relevant tests to recover the theoretical results (consistency, stability,...) studied in class. You will be able to understand problems in your calculations and deal with them.
Handouts
- Algorithmic langage common to MACS 1 and MACS 2
- Secure SHell (J. Ryan)
- Freefem++
- Numerical Analysis and Optimization (G. Allaire)
FEM Project
Introduction to Latex
- Short Math Guide for Latex
- Introduction to Latex (ENSTA)
- Latex
symbols
- Introduction
to Latex (D. Mateo, MACS engineer)
Introduction to Matlab
- Introduction ŕ Matlab (M. Postel)
- Introduction ŕ Matlab (E. Luneville & P. Ciarlet)
- An introductionto Matlab (D.F. Griffiths)