Rapid development and adjoining of transient finite element models
Rapid development and adjoining of transient finite element models
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DOI：
10.1016/j.cma.2014.03.010
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发表时间：
2014-07
影响因子：
7.2
通讯作者：
J. Maddison;P. Farrell
中科院分区：
文献类型：
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作者：
J. Maddison;P. Farrell
高级有限元系统的最新进展已经允许离散的符号表示及其作为模型源代码的有效自动化实现。这允许在少数几行高级代码中极其紧凑地实现复杂的非线性模型。在这项工作中，我们扩展了高级有限元FEniCS系统，以引入时间离散化的抽象表示：这使得瞬态有限元模型的类似快速发展成为可能。效率是通过积极的优化来实现的，这些优化利用了时间结构，例如表单的自动预组装和缓存，以及矩阵分解和预处理数据的强大重用。生成的模型与手工优化的有限元代码一样快，甚至更快。系统的高级表示仍然非常紧凑，易于操作。利用该结构可自动导出相关联的离散伴随模型，伴随模型继承了正演模型的性能优势。结合起来，这为快速开发有效的瞬态模型及其离散伴随提供了一个系统。
Recent advances in high level finite element systems have allowed for the symbolic representation of discretisations and their efficient automated implementation as model source code. This allows for the extremely compact implementation of complex non-linear models in a handful of lines of high level code. In this work we extend the high level finite element FEniCS system to introduce an abstract representation of the temporal discretisation: this enables the similarly rapid development of transient finite element models. Efficiency is achieved via aggressive optimisations that exploit the temporal structure, such as automated pre-assembly and caching of forms, and the robust re-use of matrix factorisations and preconditioner data. The resulting models are as fast or faster than hand-optimised finite element codes. The high level representation of the system remains extremely compact and easily manipulated. This structure is exploited to derive the associated discrete adjoint model automatically, with the adjoint model inheriting the performance advantages of the forward model. Combined, this provides a system for the rapid development of efficient transient models, together with their discrete adjoints.