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An algorithm for triangulating smooth three-dimensional domains immersed in universal meshes

Rangarajan, Ramsharan and Kabaria, Hardik and Lew, Adrian (2019) An algorithm for triangulating smooth three-dimensional domains immersed in universal meshes. In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 117 (1). pp. 84-117.

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Official URL: https://doi.org/10.1002/nme.5949


We describe an algorithm to recover a boundary-fitting triangulation for a bounded C-2-regular domain omega subset of R3 immersed in a nonconforming background mesh of tetrahedra. The algorithm consists in identifying a polyhedral domain omega(h) bounded by facets in the background mesh and morphing omega(h) into a boundary-fitting polyhedral approximation omega(h) of omega. We discuss assumptions on the regularity of the domain, on element sizes and on specific angles in the background mesh that appear to render the algorithm robust. With the distinctive feature of involving just small perturbations of a few elements of the background mesh that are in the vicinity of the immersed boundary, the algorithm is designed to benefit numerical schemes for simulating free and moving boundary problems. In such problems, it is now possible to immerse an evolving geometry in the same background mesh, called a universal mesh, and recover conforming discretizations for it. In particular, the algorithm entirely avoids remeshing-type operations and its complexity scales approximately linearly with the number of elements in the vicinity of the immersed boundary. We include detailed examples examining its performance.

Item Type: Journal Article
Keywords: background meshes; evolving boundary; immersed boundary; mesh relaxation; moving mesh; 3D meshing
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Francis Jayakanth
Date Deposited: 10 Feb 2019 08:39
Last Modified: 11 Feb 2019 05:00
URI: http://eprints.iisc.ac.in/id/eprint/61335

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