Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements
Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements
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DOI：
10.1137/15m1021167
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发表时间：
2014-11
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通讯作者：
Andrew T. T. McRae-Andrew-T.-T.-McRae-3013986;Gheorghe-Teodor Bercea;L. Mitchell;D. Ham;C. Cotter
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作者：
Andrew T. T. McRae-Andrew-T.-T.-McRae-3013986;Gheorghe-Teodor Bercea;L. Mitchell;D. Ham;C. Cotter
我们描述并实现了一个符号代数标量和矢量值有限元，使计算机生成的元素与张量积结构的四边形，六面体和三角形棱柱细胞。该代数是作为特定领域语言UFL（统一形式语言）的扩展来实现的。这允许用户构建超出现有软件包支持的有限元空间。我们对FIAT（FInite元素自动制表器）进行了相应的扩展，以实现此类空间的数值制表。因此，在自动生成执行本地汇编操作的低级代码期间，在解决此类函数空间上的有限元问题的更广泛背景下，使用此制表。我们在软件包Firedrake的代码生成管道中完成了这项工作;我们使用完整的Firedrake包来呈现数值示例。
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.