Journal ArticleA Primal-Dual Level Set Method for Computing Geodesic DistancesLiu, Hailiang (ORCID:0000000339482150); Zinnel, LauraThe numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.SIAM2026-02-2810678661SIAM Journal on Numerical Analysis641224 to 2500036-1429https://doi.org/10.1137/24M17210862152117National Science Foundation