Párování metod hraničních a konečných prvků v prostředí Netgen/NgSolve

Abstract

Coupling finite and boundary element methods is one of the most efficient numerical methods for solving elliptic boundary value problems. In practice, we often encounter problems that need to be solved on unbounded domains. These problems cannot be directly solved using the finite element method (FEM), but can be efficiently solved using the boundary element method (BEM), which we will describe in detail in this thesis. However, the BEM is only effective as long as the problem on the region of interest is described by a Laplace equation. But if the problem on this region is of Poisson type, then the boundary element method alone loses its effectiveness and must be paired with the finite element method. In this thesis, we show the use of our BEM library in the Netgen/NGSolve environment and we also demonstrate the Johnson-Nedellec FEM-BEM coupling for the transmission problem. We verify the functionality and efficiency of our implementation on various problems through numerical experiments.