I want to solve the Poisson equation for a 2D polar system:
$$\Delta_r f(r) = u(r)$$ with the Laplace operator: $ \Delta_r f(r) = \frac{1}{r}\frac{\partial}{\partial r} \left[r \frac{\partial}{\partial r} f(r) \right] $
I have $u(r)$ given as a vector for a non-uniform (quasi-logarithmic) grid. Any ideas how to solve this?