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 codes.

Part 1:

• Choice of models and methods

• Overview of problems and scales

• Atomistic models (with and without electrons)

• Classical molecular dynamics: from statistical mechanics to the algorithms

Part 2:

• Finite element methods

• Interpolation functions for the estimating displacements

• Construction of the elementary operators after discretization

• Governing principles and variational formulation

• Couples models (molecular dynamics and continuum mechanics by finite elements)

- Final written exam

- Daan Frenkel, Berend Smit, “Understanding Molecular Simulation: From Algorithms to Applications”, Academic Press, San Diego, second edition, 2002

- lecture: 14h
- tutorial: 7h
- practicals:7h
- seminar:2h
- ECTS: 3