@article{McRae:2016:10.1137/15M1021167, author = {McRae, ATT and Mitchell, L and Bercea and Ham, DA and Cotter and McRae and Bercea and Mitchell and Ham and Cotter}, doi = {10.1137/15M1021167}, journal = {SIAM Journal on Scientific Computing}, pages = {S25--S47}, title = {Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements}, url = {http://dx.doi.org/10.1137/15M1021167}, volume = {38}, year = {2016} }
TY - JOUR AB - We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral, and triangular prismatic cells. The algebra is implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to construct many finite element spaces beyond those supported by existing software packages. We have made corresponding extensions to FIAT, the FInite element Automatic Tabulator, to enable numerical tabulation of such spaces. This tabulation is consequently used during the automatic generation of low-level code that carries out local assembly operations, within the wider context of solving finite element problems posed over such function spaces. We have done this work within the code-generation pipeline of the software package Firedrake; we make use of the full Firedrake package to present numerical examples. AU - McRae,ATT AU - Mitchell,L AU - Bercea AU - Ham,DA AU - Cotter AU - McRae AU - Bercea AU - Mitchell AU - Ham AU - Cotter DO - 10.1137/15M1021167 EP - 47 PY - 2016/// SN - 1064-8275 SP - 25 TI - Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements T2 - SIAM Journal on Scientific Computing UR - http://dx.doi.org/10.1137/15M1021167 UR - http://arxiv.org/abs/1411.2940 UR - http://hdl.handle.net/10044/1/21268 VL - 38 ER -
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