Understanding the mathematical bases of the finite element method:
| On completion of the unit, the student will be capable of: | Classification level | Priority |
|---|---|---|
| Differentiating between weak and strong problems | 1. Knowledge | Important |
| Differentiating between weak and strong problems | 2. Understand | Important |
| Analysing a strong problem, showing its singularity then writing the variational formulation and finally discretizing it to achieve a linear system KU=F | 3. Apply | Essential |
| Analysing a strong problem, showing its singularity then writing the variational formulation and finally discretizing it to achieve a linear system KU=F | 4. Analyse | Essential |
| Percentage ratio of individual assessment | Percentage ratio of group assessment | ||||
|---|---|---|---|---|---|
| Written exam: | 100 | % | Project submission: | % | |
| Individual oral exam: | % | Group presentation: | % | ||
| Individual presentation: | % | Group practical exercise: | % | ||
| Individual practical exercise: | % | Group report: | % | ||
| Individual report: | % | ||||
| Other(s): % | |||||
| Type of teaching activity | Content, sequencing and organisation |
|---|---|
| Course/Supervised study | 1. Introduction : examples of problems solved by the finite elements method 2. Mathematic reminders of divergence, gradient and Laplacian operators 3. Properties of partial differential equations of the elliptic type: existence and singularity depending on the type of limit conditions (Dirichlet, Neumann, Robin) 4. Exercices |
| Course/Supervised study | 1. Variational formulation, minimisation of the energy function and strong problems 2. Galerkin method principle and error calculation (Cea’s Lemma) 3. Discrete formulations : KU=F for determining unknown nodals; expression of form functions and elementary integrals 4. Detailed dimension study : problem of the p-n junction (theoretical and digital study with P1 approximation) 5.Exercices |
| Course/Supervised study | 1. Detailed dimension study 2: Thermal and load problem of a condenser (theoretical and digital study with P1 approximation on triangular mesh) |