Poisson's equation on on a sphere
This application solves Poisson's equation on a sphere domain with Dirichlet boundary condition in the form \[ \begin{align} -\Delta u(\mathbf{x}) &= f(\mathbf{x}),\quad \mathbf{x}\in\Omega \\ u(\mathbf{x}) &= 0,\quad \mathbf{x}\in \partial\Omega \end{align} \] where $\mathbf{x}$ is $(x,y,z)$ in the domain $\Omega=\{(x,y,z)|x^2+y^2+z^2 < r^2\}$ and $\partial\Omega=\{(x,y)|x^2+y^2+z^2 = r^2\}$ is the domain boundary. See Poisson's equation on rectangular domains I for more detail of the problem.
Data Input
The calculator requires two parts of input. The first part is function $f(x,y,z)$ in the equation above and it must be entered as f(x1,x2,x3). The second part is the sphere radius $r$, where $3\leqslant r\leqslant 8$.