Solution of the Laplace equation by means of BEM
The Laplace equation
∂²u/∂x² + ∂²u/∂y² = 0
can be solved numerically with the boundary element method (BEM).
Unlike the FEM, only the border of the investigated area must be discretized here.
The solutions u(x,y) are initially determined only for the border.
In addition, you can also calculate solutions within the area.
A model to be examined is determined by:
- A polygon of edge points (counterclockwise, the area numbered around)
- Boundary conditions for each polygon segment, either for the unknown function (u) or its normal directional derivative in the edge ∂u/∂n, looking outward.
If both input fields are used here, a condition of the type ∂u/∂n + a u = b is meant.
- If desired, internal points of the area for which the solution will be determined.