Contenu
Course description : theoretical courses
M1 : Continuum Mechanics and Finite Element Computations
- Reviews of Basic Continuum Mechanics.
- Thermomechanical conservation laws for continuous media
- Finite element method.
- Boundary conditions implementation : Neumann or Dirichlet condition, free surface, unilateral contact, interface.
- Volume and surface mapping problems (CAD).
- 2-D and 3-D meshing techniques - remeshing.
M2 : Solid Mechanics
- Elasticity, Plasticity, Viscoplasticity
- Large deformation of elastic solids
- Vibrations
- Dynamics.
- Finite elements for solids
- Space discretization : 2-D, axisymmetric, 3-D, membrane, thin shell
M3: Fluid Mechanics, Heat Transfer and Multiphysics
- Inviscid fluids
- Newtonian fluids
- Non-newtonian fluids
- Turbulence.
- Acoustics
- Electromagnetism
- Finite elements for fluids
- Introduction to other numerical methods : finite differences, finite volumes, integral equations, spectral methods.
- Introduction to multigrid methods.
M4: Numerical analysis and software tools for computational mechanics
- Basic Methods: linear and non-linear systems (direct or iterative solving – preconditioning techniques), optimization, numerical integration, numerical solutions of differential equations, eigenvalues and eigenvectors computation.
- Mechanical formulation and time integration – numerical scheme stability.
- Inverse analysis : direct method, adjoint method
- Programming languages for scientific applications: review of Fortran 90 and C
- Introduction to parallel scientific computing and programming tools (PVM, MPI, HPF)
- Object-oriented programming introduction to C++.
- Symbolic Computation
Tous les étudiants bénéficient d’un partenariat industriel assurant le support technique (stage) et financier (financement de la formation et rémunération sur l'année). Outre le label attribué par la Conférence des Grandes Ecoles, ces cycles sont sanctionnés par un diplôme de Formation Spécialisée de l'Ecole des Mines de Paris.