Lecture SS 21 Advanced Topics in Numerical Analysis
Boundary Integral Equations and Boundary Element Methods
More information, exercices, etc. can be found on eCampus.
One of the disadvantages of the finite element method is that the entire computational domain must be meshed using a volume mesh. In some cases, for example when dealing with unbounded domains, it is much more convenient to reformulate the problem in terms of boundary integral equations, which reduces the whole problem to the domain’s boundary. This process reduces the problem’s dimensionality by one, with the disadvantage of leading to dense system matrices when being discretized.
The lecture starts with the basic derivation and analysis of boundary integral equations and discusses their discretization and convergence analysis. Time permitting, we will have the opportunity to discuss state-of-the-art compression techniques that have led to the boundary element method becoming the preferred simulation method in several industrial application areas.
Knowledge from numerical analysis (finite element method) and functional analysis (basics on Sobolev spaces) as they are taught in Scientific Computing I are a prerequisite to follow the course.