Poly-spline finite-element method

Teseo Schneider, Jérémie Dumas, Xifeng Gao, Mario Botsch, Daniele Panozzo, Denis Zorin

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number19
JournalACM Transactions on Graphics
Volume38
Issue number3
DOIs
StatePublished - Jan 1 2019

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Poisson equation
Splines
Partial differential equations
Stars
Pipelines
Boundary conditions
Finite element method

Keywords

  • Finite elements
  • Polyhedral meshes
  • Simulation
  • Splines

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

Poly-spline finite-element method. / Schneider, Teseo; Dumas, Jérémie; Gao, Xifeng; Botsch, Mario; Panozzo, Daniele; Zorin, Denis.

In: ACM Transactions on Graphics, Vol. 38, No. 3, 19, 01.01.2019.

Research output: Contribution to journalArticle

Schneider, Teseo ; Dumas, Jérémie ; Gao, Xifeng ; Botsch, Mario ; Panozzo, Daniele ; Zorin, Denis. / Poly-spline finite-element method. In: ACM Transactions on Graphics. 2019 ; Vol. 38, No. 3.
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