The Helmholtz Class

The Helmholtz class defines the Helmholtz problem

$$\omega \; u - (k\; u\hackscore{,j})\hackscore{,j} = f$$ (94)

with natural boundary conditions

$$k\; u\hackscore{,j} n\hackscore{,j} = g- \alpha \; u$$ (95)

and constraints:

$$u=r q>0$$ (96)

$\omega$ , $k$ , $f$ 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.