The Helmholtz Class

The Helmholtz class defines the Helmholtz problem

$$\omega \; u - (k\; u\hackscore{,j})\hackscore{,j} = f$$ (82)

with natural boundary conditions

$$k\; u\hackscore{,j} n\hackscore{,j} = g- \alpha \; u$$ (83)

and constraints:

$$u=r q>0$$ (84)

$\omega$, $k$, $f$ have to be a scalar Data object in the general FunctionSpace, $g$ and $\alpha$ must be a scalar Data object in the boundary FunctionSpace, and $q$ and $r$ must be a scalar Data object in the solution FunctionSpace or must be mapped or interpolated into the particular FunctionSpace.