Eikonal equation

[dokken]

Your variatonal form is not correct, as you are missing a sqrt.

Solving the unsmoothed version of the eikonal equations are notoriously difficult. Usually, one smooths the equation by adding a Laplace operator.
See:

Euclidean distance map of mesh (distance to surface)

Hi, one option (which works in parallel out of the box) is to get the distance by solving the Eikonal equation, see Johan Hake’s answer here. However, if the boundary is complex there are some difficulties in getting the Newton solver to converge on the nonlinear problem that is the Eikonal equation. You can try to make it more robust following the discussion in the linked post. An alternative presented below is to decompose the boundary, solve simpler problems and then get the final distance as…

and
https://fenicsproject.org/qa/1446/distance-to-boundary/

Me and collaborators are working on a new mixed method/variational form for solving the Eikonal equation. I will post it here once we have a preprint out.