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 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.

In ACM Transactions on Graphics (TOG)


    author = {Schneider, Teseo and Dumas, J{\'e}r{\'e}mie and Gao, Xifeng and Botsch, Mario and Panozzo, Daniele and Zorin, Denis},
    title = {Poly-Spline Finite-Element Method},
    journal = {ACM Transactions on Graphics},
    volume = {38},
    number = {3},
    month = {3},
    year = {2019},
    url = {http://doi.acm.org/10.1145/3313797},
    doi = {10.1145/3313797},
    publisher = {ACM}


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.