Teseo Schneider
Jérémie Dumas
Mario Botsch
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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.
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This repository contains the scripts to regenerate the figures in the paper "Poly-Spline Finite-Element Method", published in ACM Trans. on Graphics, Vol 38(3), 2019.This code is also available on GitHub: https://github.com/polyfem/Poly-Spline-Finite-Element-Method
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Poly-Spline Finite-Element Method
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