I have been scouting the internet for ways to numerically solve the eikonal equation:
$$|\nabla\phi(x)| = 1$$ $$\partial \phi = g(x)$$
Where $g(x)$ is known.
I know about both Fast Marching and Fast sweeping. However both of those seem to have been developed to solve 0 boundary conditions, at least when you read Hongkai's Zhao paper.
Is there a way to solve the problem when the boundary conditions are a known function (approximated as discrete point samples with known values on the grid upon which one runs the algorithm).