Modul

The examination is carried out by an oral examination (approx. 30 minutes).

Students are able to apply the analytic foundations of defining potentials and boundary operators, such as distributions, Sobolev spaces on boundaries of Lipschitz domains and trace operators to specific problems. They understand the definition of potentials, boundary operators and important mathematical statements about them. They are able to formulate boundary integral equations for concrete elliptic boundary value problems and to comprehend the proofs for their solvability.

Students are able to name and describe classes of boundary elements. They are familiar with the use of various boundary elements for numerically solving boundary integral equations by Galerkin methods. They can explain results  on convergence of such methods. The students can describe techniques for improving practical handling of boundary element methods such as matrix compression schemes and preconditioning.

None

• Sobolev spaces
• function spaces on Lipschitz boundaries
• boundary value problems for elliptic partial differential equations
• potentials and boundary operators
• boundary integral equations
• boundary elements
• Galerkin boundary element methods
• preconditioning
• matrix compression

We recommend attendance of the module "Numerical Methods for Integral Equations".

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 h

• increased understanding of module content by wrapping up lectures at home
• work on exercises
• increased understanding of module content by self study of literature and internet research
• preparing for the examination