Nochetto, Ricardo H.; Walker, Shawn W. A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes. (English) Zbl 1197.65133 J. Comput. Phys. 229, No. 18, 6243-6269 (2010). Summary: We present a method for generating 2-D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level set method to guide the change of topology of the domain mesh. This is followed by an optimization procedure, using a variational formulation of active contours, that seeks to improve boundary mesh conformity to the zero level contour of the level set function. Our method is advantageous for arbitrary-Lagrangian-Eulerian type methods and directly allows for using a variational formulation of the physics being modeled and simulated, including the ability to account for important geometric information in the model (such as for surface tension driven flow). Furthermore, the meshing procedure is not required at every time-step and the level set update is only needed during a topological change. Hence, our method does not significantly affect computational cost. Cited in 7 Documents MSC: 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 49Q10 Optimization of shapes other than minimal surfaces 65K10 Numerical optimization and variational techniques Keywords:front tracking; arbitrary-Lagrangian-Eulerian mesh method; topological change; shape optimization; mesh generation; pinching; level-set method; numerical examples; graphical examples Software:El-Topo; DistMesh; McLite; Triangle; Netgen; PLTMG; ALBERTA PDFBibTeX XMLCite \textit{R. H. Nochetto} and \textit{S. W. Walker}, J. Comput. Phys. 229, No. 18, 6243--6269 (2010; Zbl 1197.65133) Full Text: DOI References: [1] Silas Alben, Michael J. Shelley, Coherent locomotion as an attracting state for a free flapping body, in: Proceedings of the National Academy of Sciences USA, vol. 102, 2005, pp. 11163-11166.; Silas Alben, Michael J. 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