The Helmholtz Class

The Helmholtz class defines the Helmholtz problem

$\displaystyle \omega \; u - (k\; u\hackscore{,j})\hackscore{,j} = f$ (84)

with natural boundary conditions

$\displaystyle k\; u\hackscore{,j} n\hackscore{,j} = g- \alpha \; u$ (85)

and constraints:

$\displaystyle u=r$    where $\displaystyle q>0$ (86)

$ \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.


\begin{classdesc}{Helmholtz}{domain}
opens a Helmholtz equation on the \class{Do...
...ass{Helmholtz}\xspace is derived from \class{LinearPDE}\xspace .
\end{classdesc}

\begin{methoddesc}[Helmholtz]{setValue}{ \optional{omega} \optional{, k} \option...
...g}, \var{r}, \var{q}. By default all values are set to be zero.
\end{methoddesc}

esys@esscc.uq.edu.au