Teaching notes:
Finite Element Analysis: Fundamental concepts and techniques of primal finite element methods. Method of weighted residuals, Galerkin's method and variational equations. Linear eliptic boundary value problems in one, two and three space dimensions; applications in structural, solid and fluid mechanics and heat transfer. Properties of standard element families and numerically integrated elements. Implementation of the finite element method using Matlab, assembly of equations, and element routines. Lagrange multiplier and penalty methods for treatment of constraints. The mathematical theory of finite elements.
- [Problem Session 1]: Formulation of variational problems for PDEs.
- [Problem Session 2]: Vector space of functions and clarification of concepts.
- [Problem Session 3]: Solving (discretized) variational problems with shape functions.
- [Problem Session 4]: Local-to-global map and assembly with shape functions.
- [Problem Session 5]: Solving variational problems with LG matrix.
- [Problem Session 6]: Global assembly in 2D with P1 elements.
- [Firedrake Tutorial]: Solving a 2D Poisson equation.
- [FEniCS Tutorial]: Solving a 2D Poisson equation.
- [Problem Session 8]: Norms and convergence (numerical analysis).
- [Problem Session 9]: (final review) Heat transfer in 2D using P1 elements.
- [Course Summary] | [Teaching Evaluation]
Foundations of Solid Mechanics. [PDF]
Elasticity & Inelasticity. [PDF]
Finite Element Analysis. [PDF]
Nonlinear Finite Element Analysis. [PDF]
Partial Differential Equations. [PDF]
Defects & Disorders in Materials. [PDF]
Linear Algebra. [PDF]
Atomistic Modeling. [PDF]
Inverse Problems. [PDF]
Engineering Thermodynamics. [PDF]
Computational Fluid Dynamics. [PDF]
Density Functional Theory. [Notebooks 1; Notebooks 2]
Design Optimization. [PDF]
Mathematical Modeling. [PDF]
Smoothed-Particles Hydrodynamics. [PDF]
Finite Volume Method. [PDF]
Neural Networks. [PDF]
Dynamics of Janus Particles. [PDF]
Machine Learning for Multiscale Modeling. [PDF]
Course and learning notes: