Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
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DOI：
10.1145/1039813.1039820
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发表时间：
2004-12-01
影响因子：
2.7
通讯作者：
Kirby, RC
中科院分区：
文献类型：
--
作者：
Kirby, RC
许多有限元计算受到高阶节点基函数难以求值的限制。虽然大多数代码依赖于这些基函数的显式公式，但我们提出了一种新的方法，允许我们从标准正交多项式构造一类一般的有限元基函数，并在任何点对它们进行评估和微分。这种方法依赖于线性代数的基本思想，并使用几种面向对象和函数式编程技术在Python中实现。
Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques.