The Augmented Fast Marching Method for Level Set Reinitialization
This work provides an improved numerical method for level set reinitialization, which is important for simulations of moving interfaces in computational physics and engineering.
The paper presents a new level set reinitialization technique that computes the signed distance function and its first and second derivatives using an augmented fast marching method. The method ensures smooth level set and curvature fields even on coarse grids, achieving second-order accuracy for the level set and gradient, and first-order accuracy for curvature.
Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition $|\nablaϕ|^2=1$, where $ϕ$ is the level set function, the method ensures that $\nabla(|\nablaϕ|)^2=0$ and $\nabla\nabla(|\nablaϕ|)^2=0$ are also satisfied. Results indicate that for both two- and three-dimensional interfaces the resulting level set and curvature field are smooth even for coarse grids. Convergence results show that using first-order upwind derivatives and the augmented fast marching method result in a second-order accurate level set and gradient field and a first-order accurate curvature field.