Institut für Angewandte Mathematik
Vorlesung im SS 2025
Elective Subject Mathematics: Boundary Integral Equations
Grundthemen Analysis: Boundary Integral Equations
The representation of solutions of partial differential equations by using volume and surface potentials leads to boundary integral equations to be solved. We will discuss both indirect and direct approachs, where the latter is based on the use of related Green's formulae. In this lecture we will consider the formulation of boundary integral equations, the mapping properties of related boundary integral operators, and the solvability of associated boundary integral equations. These results are also important for the numerical analysis of related discretization schemes, i.e. related boundary element methods.
Content
  1. Fundamental solutions and representation formulae
  2. Mapping properties of boundary integral operators
  3. Boundary integral equations
Lecture
  • Tu, 8.30-10.00, SR AE02
  • We, 8.30-10.00, SR AE02 (alternating with Exercises)
  • Start: 4.3.2025
References
  1. O. Steinbach: Numerische Näherungsverfahren für elliptische Randwertprobleme. Finite Elemente und Randelemente. B.G. Teubner, Stuttgart, Leipzig, Wiesbaden, 2003.