@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 paper graphics spline fem arxiv mesh},
  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
}

{"_id":"76tiXxkrAiJ76mFrJ","bibbaseid":"schneider-dumas-gao-botsch-panozzo-zorin-polysplinefiniteelementmethod-2018","author_short":["Schneider, T.","Dumas, J.","Gao, X.","Botsch, M.","Panozzo, D.","Zorin, D."],"bibdata":{"bibtype":"misc","type":"misc","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":[{"propositions":[],"lastnames":["Schneider"],"firstnames":["Teseo"],"suffixes":[]},{"propositions":[],"lastnames":["Dumas"],"firstnames":["Jeremie"],"suffixes":[]},{"propositions":[],"lastnames":["Gao"],"firstnames":["Xifeng"],"suffixes":[]},{"propositions":[],"lastnames":["Botsch"],"firstnames":["Mario"],"suffixes":[]},{"propositions":[],"lastnames":["Panozzo"],"firstnames":["Daniele"],"suffixes":[]},{"propositions":[],"lastnames":["Zorin"],"firstnames":["Denis"],"suffixes":[]}],"biburl":"https://www.bibsonomy.org/bibtex/27379ef02aced54fe2ac9725c4ebd6fc3/analyst","description":"[1804.03245] Poly-Spline Finite Element Method","interhash":"0fcbc48271b2c25b4e3ab0f087ceae24","intrahash":"7379ef02aced54fe2ac9725c4ebd6fc3","keywords":"2018 paper graphics spline fem arxiv mesh","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","bibtex":"@misc{schneider2018polyspline,\n abstract = {We introduce an integrated meshing and finite element method pipeline\r\nenabling black-box solution of partial differential equations in the volume\r\nenclosed by a boundary representation. We construct a hybrid\r\nhexahedral-dominant mesh, which contains a small number of star-shaped\r\npolyhedra, and build a set of high-order basis on its elements, combining\r\ntriquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), and\r\nharmonic elements. We demonstrate that our approach converges cubically under\r\nrefinement, while requiring around 50% of the degrees of freedom than a\r\nsimilarly dense hexahedral mesh composed of triquadratic hexahedra. We validate\r\nour approach solving Poisson's equation on a large collection of models, which\r\nare automatically processed by our algorithm, only requiring the user to\r\nprovide boundary conditions on their surface.},\n added-at = {2018-07-23T13:20:07.000+0200},\n author = {Schneider, Teseo and Dumas, Jeremie and Gao, Xifeng and Botsch, Mario and Panozzo, Daniele and Zorin, Denis},\n biburl = {https://www.bibsonomy.org/bibtex/27379ef02aced54fe2ac9725c4ebd6fc3/analyst},\n description = {[1804.03245] Poly-Spline Finite Element Method},\n interhash = {0fcbc48271b2c25b4e3ab0f087ceae24},\n intrahash = {7379ef02aced54fe2ac9725c4ebd6fc3},\n keywords = {2018 paper graphics spline fem arxiv mesh},\n note = {cite arxiv:1804.03245},\n timestamp = {2018-07-23T13:20:07.000+0200},\n title = {Poly-Spline Finite Element Method},\n url = {http://arxiv.org/abs/1804.03245},\n year = 2018\n}\n\n","author_short":["Schneider, T.","Dumas, J.","Gao, X.","Botsch, M.","Panozzo, D.","Zorin, D."],"key":"schneider2018polyspline","id":"schneider2018polyspline","bibbaseid":"schneider-dumas-gao-botsch-panozzo-zorin-polysplinefiniteelementmethod-2018","role":"author","urls":{"Paper":"http://arxiv.org/abs/1804.03245"},"keyword":["2018 paper graphics spline fem arxiv mesh"],"metadata":{"authorlinks":{}}},"bibtype":"misc","biburl":"http://www.bibsonomy.org/bib/author/Dumas?items=1000","dataSources":["gzytHe9CAy6apLxQh"],"keywords":["2018 paper graphics spline fem arxiv mesh"],"search_terms":["poly","spline","finite","element","method","schneider","dumas","gao","botsch","panozzo","zorin"],"title":"Poly-Spline Finite Element Method","year":2018}