An algorithm for triangulating smooth three-dimensional domains immersed in universal meshes |
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Authors: | Ramsharan Rangarajan Hardik Kabaria Adrian Lew |
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Affiliation: | 1. Department of Mechanical Engineering, Indian Institute of Science Bangalore, Bengaluru, India;2. Carbon, Inc, Redwood City, California;3. Department of Mechanical Engineering, Stanford University, Stanford, California |
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Abstract: | We describe an algorithm to recover a boundary-fitting triangulation for a bounded C2-regular domain immersed in a nonconforming background mesh of tetrahedra. The algorithm consists in identifying a polyhedral domain ωh bounded by facets in the background mesh and morphing ωh into a boundary-fitting polyhedral approximation Ωh 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. |
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Keywords: | background meshes evolving boundary immersed boundary mesh relaxation moving mesh 3D meshing |
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