In contrast to finite elements or finite volumes, shape functions do not have local support but they are non-zero throughout the simulation domain. Normally, basis functions are defined in a manner that they are defined by functions having boundary facets as local support. These facets are incident with a common vertex. In the two-dimensional case, the facets are (boundary) edges incident with a boundary vertex.

The typical formulation of a boundary element scheme can be written in the following manner (Galerkin formulation)

(3.46) |

where and are indices of vertices. For each vertex an equation is assembled. The fundamental solution [81] function denotes a fundamental solution of the respective differential operator :

(3.47) |

The parameters and denote the position at the boundary surface or curve. The linear boundary operator can be written as linear combination in the following manner.

Michael 2008-01-16