This course introduces the principles underlying common methods of numerical simulations used in nano sciences, going from the continuum to the atomic scale. 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. A focus will be done on the finite element method (linear elasticity, heat conduction), and solutions techniques for atomistic / continuum coupling.
• Application of FEM + DM to dynamics fracture mechanics • Fundamental concepts of the finite element method (strong form, weak form, matrix form, linear elasticity, heat conduction) • Solutions techniques for parabolic and hyperbolic problems, discretization and numerical errors • Solutions techniques for atomistic / continuum coupling, application to dynamic fracture mechanics