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Lazy K-way linear combination kernels for efficient runtime sparse Jacobian matrix evaluations in C++. (English) Zbl 1251.65038

Forth, Shaun (ed.) et al., Recent advances in algorithmic differentiation. Selected papers based on the presentations at the 6th international conference on automatic differentiation (AD2012), Fort Collins, CO, USA, July 23–27, 2012. Berlin: Springer (ISBN 978-3-642-30022-6/hbk; 978-3-642-30023-3/ebook). Lecture Notes in Computational Science and Engineering 87, 333-342 (2012).
Summary: The most notoriously expensive component to develop, extend, and maintain within implicit partial differential-algebraic equation-based predictive simulation software is the Jacobian evaluation component. While the Jacobian is invariably sparse, its structure and dimensionality are functions of the point of evaluation. The application of automatic differentiation to develop these tools is highly desirable. The challenge presented is in providing implementations that treat dynamic sparsity efficiently without requiring the developer to have any a priori knowledge of sparsity structure. Under the context of dynamic sparse operator overloading implementations, we develop a direct sparse lazy evaluation approach. In this approach, an efficient runtime variant of the classic expression templates technique is proposed to support sparsity. The second aspect is the development of two alternate multi-way sparse vector linear combination kernels that yield efficient runtime sparsity detection and evaluation.
For the entire collection see [Zbl 1247.65002].

MSC:

65D25 Numerical differentiation

Software:

ColPack; ADIFOR; ADIC
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