BoundaryElementVerfahren

Boundary Element Method (BEM) is a numerical computational method used to solve linear partial differential equations. It is particularly effective for problems involving infinite or semi-infinite domains, where traditional domain-based methods like the Finite Element Method (FEM) would require extensive discretization of the unbounded region. The core idea of BEM is to transform the governing differential equation into an integral equation defined only over the boundaries of the domain. This significantly reduces the dimensionality of the problem. For a 3D problem, BEM reduces it to a 2D boundary problem, and for a 2D problem, it reduces it to a 1D boundary problem.

The process typically involves discretizing the boundary into a series of elements, similar to how FEM discretizes the domain. However, instead of solving for unknown values within the domain, BEM solves for unknown values on the boundary, such as potentials or fluxes. This leads to a system of linear equations that is generally smaller than that produced by domain-based methods, especially for problems with large or unbounded domains. The efficiency of BEM is further enhanced by the fact that the fundamental solution (or Green's function) of the governing differential equation is often known analytically, which simplifies the integral calculations.

BEM finds applications in various fields, including acoustics, elasticity, fluid dynamics, and electromagnetics. It is well-suited for problems such as scattering, radiation, and crack propagation. While BEM offers advantages in terms of computational efficiency and ease of modeling infinite domains, it can be more complex to implement than FEM, especially for nonlinear problems or those with complex internal structures.