Poly-Spline Finite-Element Method

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 hi...

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Bibliographic Details
Published inACM transactions on graphics Vol. 38; no. 3; pp. 1 - 16
Main Authors Schneider, Teseo, Dumas, Jérémie, Gao, Xifeng, Botsch, Mario, Panozzo, Daniele, Zorin, Denis
Format Journal Article
LanguageEnglish
Published 30.06.2019
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ISSN0730-0301
1557-7368
1557-7368
DOI10.1145/3313797

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Summary: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.
ISSN:0730-0301
1557-7368
1557-7368
DOI:10.1145/3313797