www.Autodiff.org - Publication: Lazy K-Way Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++

Lazy K-Way Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++

- incollection -

Author(s)
Rami M. Younis , Hamdi A. Tchelepi

Published in
Recent Advances in Algorithmic Differentiation

Editor(s)
Shaun Forth, Paul Hovland, Eric Phipps, Jean Utke, Andrea Walther

Year
2012

Publisher
Springer

Abstract
The most notoriously expensive component to develop, extend, and maintain within implicit PDAE-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.

Cross-References
Forth2012RAi

AD Theory and Techniques
Sparsity

BibTeX
@INCOLLECTION{
         Younis2012LKW,
       title = "Lazy K-Way Linear Combination Kernels for Efficient Runtime Sparse {J}acobian Matrix
         Evaluations in {C}++",
       doi = "10.1007/978-3-642-30023-3_30",
       author = "Rami M. Younis and Hamdi A. Tchelepi",
       abstract = "The most notoriously expensive component to develop, extend, and maintain within
         implicit PDAE-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.",
       pages = "333--342",
       crossref = "Forth2012RAi",
       booktitle = "Recent Advances in Algorithmic Differentiation",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       address = "Berlin",
       volume = "87",
       editor = "Shaun Forth and Paul Hovland and Eric Phipps and Jean Utke and Andrea Walther",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2012",
       ad_theotech = "Sparsity"
}

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