PDEs & Manifolds: Implementation Aspects

In this class, numerical methods for partial differential equations with the domain a manifold or the range a manifold, will be studied and discussed. We want to look at the implementation of these methods and get an understanding of applications for PDEs on and in manifolds. Examples of the considered methods include the surface finite element method, trace FEM, diffuse interface and levelset methods. Needed requirements are a basic knowledge of numerical methods for PDEs, like the finite element method, and some programming skills. The course will be in English on request.

Room and Time

Lecture: Mo. 4.DS, Room:  WIL/C204
Lecture: Wed. 5.DS, Room:  WIL/B216 or Exercise: Wed. 6.DS, Room WIL/B221

Projects

• Discretization with Surface-FEM and Surface-FV on triangulated surface. Download
  Presentation and Discussion: Mo. Jun. 4th 4.DS
• Discretization with Trace-FEM, Unfitted Narrow-Band FEM, or Diffuse-Interface Method. Download
  Presentation and Discussion: Wed. July 11th, 6. DS (or after the semester if not finished)
  See also:
  • TPMC implementation: github/tpmc dune-tpmc
  • Dune-Subgrid module: dune-subgrid