Lecture SS 24 Advanced Topics in Numerical Analysis
Boundary Integral Equations and Boundary Element Methods
Topics
In this course, we will reformulate partial differential equations (PDEs) on bounded or unbounded domains as integral equations on the compact boundary of these domains. We will study the mapping properties of the resulting boundary integral operators in terms of Sobolev spaces on the boundary. Finally, we will discuss how to numerically discretize the considered integral equations via the boundary element method (BEM). In contrast to the finite element method (FEM), which directly discretizes the PDE at hand, BEM only requires a mesh of the (d-1)-dimensional boundary rather than a mesh of the d-dimensional domain.