This course introduces the principles underlying common methods of numerical simulations used in the nanosciences, going from the
atomistic scale to the continuum. It discusses the appropriateness of atomic scale and continuum modeling.
One of the goals is to understand the principles of the models and algorithms used in standard finite element codes, and finally possible extensions/bridges between atomistic and continuum modelling.
Outline of the course:
Part 1:
• Choice of models and methods
• Overview of problems and scales (from molecular dynamics to the continuum)
• Fundamental concepts of the continuum theory (linear elasticity and heat conduction)
• Fundamental concepts of the finite element method (strong, weak, variational and matrix formulation)
Part 2:
• Solution techniques for parabolic (static) and hyperbolic (dynamic) problems
• Discretization and numerical errors of the finite element method
Part 3:
• Solution techniques for atomistic / continuum coupling
• Application to fracture mechanics
A seminar on the application of nanoscale modelling in the aeronautic applications will be also organized.
