### 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.

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