%0 Generic %1 schneider2018polyspline %A Schneider, Teseo %A Dumas, Jeremie %A Gao, Xifeng %A Botsch, Mario %A Panozzo, Daniele %A Zorin, Denis %D 2018 %K 2018 arxiv fem graphics mesh paper spline %T Poly-Spline Finite Element Method %U http://arxiv.org/abs/1804.03245 %X We introduce an integrated meshing and finite element method pipeline enabling black-box 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 basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), 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.

@misc{schneider2018polyspline, abstract = {We introduce an integrated meshing and finite element method pipeline enabling black-box 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 basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), 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.}, added-at = {2018-07-23T13:20:07.000+0200}, author = {Schneider, Teseo and Dumas, Jeremie and Gao, Xifeng and Botsch, Mario and Panozzo, Daniele and Zorin, Denis}, biburl = {https://www.bibsonomy.org/bibtex/27379ef02aced54fe2ac9725c4ebd6fc3/analyst}, description = {[1804.03245] Poly-Spline Finite Element Method}, interhash = {0fcbc48271b2c25b4e3ab0f087ceae24}, intrahash = {7379ef02aced54fe2ac9725c4ebd6fc3}, keywords = {2018 arxiv fem graphics mesh paper spline}, note = {cite arxiv:1804.03245}, timestamp = {2018-07-23T13:20:07.000+0200}, title = {Poly-Spline Finite Element Method}, url = {http://arxiv.org/abs/1804.03245}, year = 2018 }