
Université
Paris
13
MACS 1
Projects in applied mathematics
and
scientific computing
Professor : Caroline Japhet


Many physical
phenomena
can
be
formulated as differential equations, for example the airflow
around
an
aircraft, the evolution
of a
glacier 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, in a first step, to implement the numerical
methods learned in numerical analysis courses of MACS 1. Then, in a
second step, starting with a physical model problem, to perform and
implement algorithms to solve it, and interpret the simulations results
(are the results accurate and close to the physics ?). In this second
step, on project is given by student. We use the Matlab langage
to develop prototype codes. After the course you will be able, from a
complex problem, to decompose it in a sequence of simple subproblems
(modules) that will be implemented and validated independently as soon
as possible. Modules will then be brought together to solve the
original problem. Once the initial problem is validate, you will be
able to define relevant tests to recover the theoretical results
(consistency, stability,...) studied in class, compare different
numerical methods and choose the "best one" to get an accurate
solution, close to the physics with a minimum computational time and
storage. You will be able to understand problems in your calculations
and deal with them.
