Volume 14, Issue 6
Sparse Automatic Differentiation for Complex Networks of Differential-Algebraic Equations Using Abstract Elementary Algebra

Slaven Peleš & Stefan Klus

DOI:

Int. J. Numer. Anal. Mod., 14 (2017), pp. 916-934.

Published online: 2017-10

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  • Abstract

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, the built-in elementary algebra typically has limited functionality and often restricts the flexibility of mathematical models and the analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages such as gPROMS or Modelica with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than the language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in a distributed memory setting. Furthermore, we show that the computational cost scales linearly with the size of the system.

  • Keywords

Sparse automatic differentiation differential-algebraic equations abstract elementary algebra

  • AMS Subject Headings

68W30 68U20 68N19.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-916, author = {}, title = {Sparse Automatic Differentiation for Complex Networks of Differential-Algebraic Equations Using Abstract Elementary Algebra}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {6}, pages = {916--934}, abstract = {Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, the built-in elementary algebra typically has limited functionality and often restricts the flexibility of mathematical models and the analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages such as gPROMS or Modelica with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than the language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in a distributed memory setting. Furthermore, we show that the computational cost scales linearly with the size of the system.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10487.html} }
TY - JOUR T1 - Sparse Automatic Differentiation for Complex Networks of Differential-Algebraic Equations Using Abstract Elementary Algebra JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 916 EP - 934 PY - 2017 DA - 2017/10 SN - 14 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10487.html KW - Sparse automatic differentiation KW - differential-algebraic equations KW - abstract elementary algebra AB - Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, the built-in elementary algebra typically has limited functionality and often restricts the flexibility of mathematical models and the analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages such as gPROMS or Modelica with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than the language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in a distributed memory setting. Furthermore, we show that the computational cost scales linearly with the size of the system.
Slaven Peleš & Stefan Klus. (2020). Sparse Automatic Differentiation for Complex Networks of Differential-Algebraic Equations Using Abstract Elementary Algebra. International Journal of Numerical Analysis and Modeling. 14 (6). 916-934. doi:
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