@article{c15a2fe075f64abfa4b6d2024648b89a,
title = "Poly-spline finite-element method",
abstract = "We introduce an integrated meshing and finite-element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson's equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.",
keywords = "Finite elements, Polyhedral meshes, Simulation, Splines",
author = "Teseo Schneider and J{\'e}r{\'e}mie Dumas and Xifeng Gao and Mario Botsch and Daniele Panozzo and Denis Zorin",
note = "Funding Information: We are grateful to the NYU HPC staff for providing computing cluster service. This work was partially supported by the NSF CAREER award 1652515, the NSF grant IIS-1320635, the NSF grant DMS-1436591, the NSF grant 1835712, the SNSF grant P2TIP2_175859, a gift from Adobe Research, and a gift from nTopology. Funding Information: We are grateful to the NYU HPC staff for providing computing cluster service. This work was partially supported by the NSF CAREER award 1652515, the NSF grant IIS-1320635, the NSF grant DMS-1436591, the NSF grant 1835712, the SNSF grant P2TIP2_175859, a gift from Adobe Research, and a gift from nTopology. Authors{\textquoteright} addresses: T. Schneide, D. Panozzo, and D. Zorin, NYU Courant Institute of Mathematical Sciences, 60 5th Ave, New York, NY 10011; emails: {teseo.schneider, panozzo}@nyu.edu, dzorin@cs.nyu.edu; J. Dumas, nTopology, 153 Lafayette St, New York, NY 10013; email: jeremie.dumas@ens-lyon.org; X. Gao, Computer Science Department, Florida State University, 171 James Love Building, 1017 Academic Way, Tallahassee, FL 32306; email: gxf.xisha@gmail.com; M. Botsch, Bielefeld University, Inspiration 1, 33615 Bielefeld, Germany; email: botsch@techfak.uni-bielefeld.de. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2019 Association for Computing Machinery. 0730-0301/2019/03-ART19 $15.00 https://doi.org/10.1145/3313797 Publisher Copyright: {\textcopyright} 2019 Association for Computing Machinery.",
year = "2019",
doi = "10.1145/3313797",
language = "English (US)",
volume = "38",
journal = "ACM Transactions on Graphics",
issn = "0730-0301",
publisher = "Association for Computing Machinery (ACM)",
number = "3",
}