I am trying to solve the following equation for $P(x,y)$:$$I = P \nabla \cdot \frac{1}{P^2} \nabla{P}$$where $P$ and $I$ are functions of x and y.  $I(x,y)$ and $P(x,y)$I want to understand the algorithm for solving this equation; andan optimized Python/Fortran/C code that solve it.
how to solve a 2D non-linear Poisson equation?
optimization;finite element;finite difference;numpy