TY - JOUR
T1 - Sparse Automatic Differentiation for Complex Networks of Differential-Algebraic Equations Using Abstract Elementary Algebra
AU - Slaven Peleš & Stefan Klus
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 916
EP - 934
PY - 2017
DA - 2017/10
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10487.html
KW - Sparse automatic differentiation, differential-algebraic equations, abstract elementary algebra.
AB - <p style="text-align: justify;">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.</p>