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An algorithm for triangulating smooth three‐dimensional domains immersed in universal meshes
Author(s) -
Rangarajan Ramsharan,
Kabaria Hardik,
Lew Adrian
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5949
Subject(s) - morphing , boundary (topology) , polygon mesh , algorithm , bounded function , domain (mathematical analysis) , triangulation , mathematics , tetrahedron , mesh generation , finite element method , geometry , computer science , mathematical analysis , computer vision , physics , thermodynamics
Summary We describe an algorithm to recover a boundary‐fitting triangulation for a bounded C 2 ‐regular domain Ω ⊂ R 3 immersed in a nonconforming background mesh of tetrahedra. The algorithm consists in identifying a polyhedral domain ω h bounded by facets in the background mesh and morphing ω h into a boundary‐fitting polyhedral approximation Ω h of Ω. 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.