I am solving the signed distance equation

\frac{\partial \phi}{\partial t} + sign (\phi_{0})(|\nabla \phi| - 1) = 0

using a Local Discontinuous Galerkin (LDG) method as described in https://www.sciencedirect.com/science/article/pii/S0021999110005255

I am interested in solving it close to steady state. I was hoping I could measure how close to steady state the solution is by using the TSSetEventHandler infrastructure, but the handler does not have information on the time derivative. I looked at TSPSEUDO, but it forces me to use an implicit method, which I cannot provide because how the LDG method works (it calculates the fluxes solving additional equations). This makes me wonder if the LDG method is the best choice, so I am open to suggestions.

Given my current progress with the LDG approach, I am wondering if there is a way to solve to steady state using explicit algorithms such as Runge-Kutta.

Thanks

Miguel

Miguel A. Salazar de Troya

Postdoctoral Researcher, Lawrence Livermore National Laboratory

B141

Rm: 1085-5

Ph: 1(925) 422-6411