Solution of the Laplace equation by means of BEM
The Laplace equation
∂²u/∂x² + ∂²u/∂y² = 0
can be solved numerically by means of the boundary element method (BEM).
Unlike in FEM, only the border of the investigated area must be discretized here.
The solutions u(x,y) and ∂u/∂n(x,y) are initially determined only for points on the border.
In addition, you can also calculate solutions u(x,y) for points 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 on the edge ∂u/∂n, pointing to the outside of the area.
If both input fields are used here, they are used for a Robin boundary condition of type ∂u/∂n + a u = b.
- If desired, internal points of the area for which the solution will be determined.