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A multiple level set method for modeling grain boundary evolution of polycrystalline materials
Zhang, Xinwei,Chen, Jiun-Shyan,Osher, Stanley Techno-Press 2008 Interaction and multiscale mechanics Vol.1 No.2
In this paper, we model grain boundary evolution based on a multiple level set method. Grain boundary migration under a curvature-induced driving force is considered and the level set method is employed to deal with the resulting topological changes of grain structures. The complexity of using a level set method for modeling grain structure evolution is due to its N-phase nature and the associated geometry compatibility constraint. We employ a multiple level set method with a predictor-multicorrectors approach to reduce the gaps in the triple junctions down to the grid resolution level. A ghost cell approach for imposing periodic boundary conditions is introduced without solving a constrained problem with a Lagrange multiplier method or a penalty method. Numerical results for both uniform and random grain structures evolution are presented and the results are compared with the solutions based on a front tracking approach (Chen and Kotta et al. 2004b).
Revisiting the redistancing problem using the Hopf–Lax formula
Lee, Byungjoon,Darbon, Jé,rô,me,Osher, Stanley,Kang, Myungjoo Elsevier 2017 Journal of computational physics Vol.330 No.-
<P><B>Abstract</B></P> <P>This article presents a fast new numerical method for redistancing objective functions based on the Hopf–Lax formula . The algorithm suggested here is a special case of the previous work in and an extension that applies the Hopf–Lax formula for computing the signed distance to the front. We propose the split Bregman approach to solve the minimization problem as a solution of the eikonal equation obtained from Hopf–Lax formula. Our redistancing procedure is expected to be generalized and widely applied to many fields such as computational fluid dynamics, the minimal surface problem, and elsewhere.</P>